orange chaddi Flashcards by Sameer Desai

A constant force of 12 N in the positive x direction acts on a 4.0 kg object as it moves from the origin point (6i-8j) m. How much work is done by the given force during this displacement?

a. +60 J
b. +84 J
c. +72 J
d. +48 J
e. +57 J

c. +72 J

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A 5.0 kg object is pulled along a horizontal surface at a constant speed by a 15 N force acting 20 degrees above the horizontal. How much work is done by this force as the object moves 6.0 m?

a. 78 J
b. 82 J
c. 85 J
d. 74 J
e. 43 J

c. 85 J

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A 2.0 kg projectile moves from its initial position to a point that is displaced 20 m horizontally and 15 m above its initial position. How much work is done by the gravitational force on the projectile?

a. +0.29 kJ
b. -0.29 kJ
c. +30 J
d. -30 J
e. -50 J

b. -0.29 kJ

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How much work is done by a person lifting a 2.0 kg object from the bottom of a well at a constant speed of 2.0 m/s for 5.0 s?

a. 0.22 kJ
b. 0.20 kJ
c. 0.24 kJ
d. 0.27 kJ
e. 0.31 kJ

b. 0.20 kJ

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A 2.5 kg object falls vertically downward in a viscous medium at a constant speed of 2.5 m/s. How much is work by the force the viscous medium exerts on the object as it falls 80 cm?

a. +2.0 J
b. +20 J
c. -2.0 J
d. -20 J
e. +40 J

d. -20 J

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A 2.0 kg particle has an initial velocity of (5i-4j) m/s. Some time later, its velocity is 7i+3j m/s. How much work was done by the resultant force during this time interval, assuming no energy is lost in the process?

a. 17 J
b. 49 J
c. 19 J
d. 53 J
e. 27 J

a. 17 J

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A block is pushed across a rough horizontal surface from point A to point B by a force (magnitude P = 5.4 N) as shown in the figure. The magnitude of the force of friction acting on the block between A and B is 1.2 N and points A and B are 0.5 m apart. If the kinetic energies of the block at A and B are 4.0 J and 5.6 J, respectively, how much work is done on the block by the force P between A and B?

a. 2.7 J
b. 1.0 J
c. 2.2 J
d. 1.6 J
e. 3.2 J

c. 2.2 J

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A constant force of 15 N in the negative y direction acts on a particle as it moves from the origin to the point (3i-3j-1k) m. How much work is done by the given force during this displacement?

a. +45 J
b. -45 J
c. +30 J
d. -30 J
e. +75 J

b. -45 J

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An object moving along the x axis is acted upon by a force Fx that varies with position as shown. How much work is done by this force as the object moves from x = 2 to x = 8 m?

a. -10 J
b. +10 J
c. +30 J
d. -30 J
e. +40 J

c. +30 J

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A body moving along the x axis is acted upon by a force Fx that varies with x as shown. How much work is done by this force as the object moves from x =1 to x = 8 m?

a. -2 J
b. -18 J
c. -10 J
d. -26 J
e. +18 J

d. -26 J

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A force acting on an object moving along the x axis is given by Fx = (14x-3x^2) N where x is in m. How much work is done by this force as the object moves from x=-1 to x=+2 m?

a. +12 J
b. +28 J
c. +40 J
d. +42 J
e. -28 J

a. +12 J

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The force an ideal spring exerts on an object is given by Fx = -kx, where x measures the displacement of the object from its equilibrium (x=0) position. If k = 60 N/m, how much work is done by this force as the object moves from x = -0.20 to x = 0?

a. -1.2 J
b. +1.2 J
c. +2.4 J
d. -2.4 J
e. +3.6 J

b. +1.2 J

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A 4.0 kg block is lowered down a 37 degree incline a distance of 5.0 m from point A to point B. A horizontal force (F = 10 N) is applied to the block between A and B as shown in the figure. The kinetic energy of the block at A is 10 J and at B is 20 J. How much work is done on the block by the force of friction between A and B?

a. -58 J
b. -53 J
c. -68 J
d. -63 J
e. -47 J

c. -68 J

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If the resultant force acting on a 2.0 kg object is equal to (3i+4j) N, what is the change in kinetic energy as the object moves from (7i-8j) m to (11i-5j) m?

a. +36 J
b. +28 J
c. +32 J
d. +24 J
e. +60 J

d. +24 J

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As a 2.0 kg object moves from (2i+5j) m to (6i-2j) m the constant resultant force acting on it is equal to (4i-3j) N. If the speed of the object at the initial position is 4.0 m/s, what is the kinetic energy at its final position?

a. 62 J
b. 53 J
c. 73 J
d. 86 J
e. 24 J

b. 53 J

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A block slides on a rough horizontal surface from point A to point B. A force (magnitude P = 2.0 N) acts on the block between A and B as shown. Points A and B are 1.5 m apart. If the kinetic energies of the block at A and B are 5.0 J and 4.0 J respectively, how much work is done on the block by the force of friction as the block moves from A to B?

a. -3.3 J
b. +1.3 J
c. +3.3 J
d. -1.3 J
e. +4.6 J

a. -3.3 J

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A 2.0 kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?

a. 27 J
b. 20 J
c. 24 J
d. 17 J
e. 37 J

c. 24 J

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A 3.0 kg block is dragged over a rough horizontal surface by a constant force of 16 N acting at an angle of 37 degrees above the horizontal as shown. The speed of the block increases from 4.0 m/s to 6.0 m/s in a displacement of 5.0 m. What work was done by the friction force during this displacement?

a. -34 J
b. -64 J
c. -30 J
d. -94 J
e. +64 J

a. -34 J

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A 10 kg block on a horizontal frictionless surface is attached to a light string (force constant = 0.80 kN/m) The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N) acting parallel to the surface is applied to the block, as shown. What is the speed of the block when it is 13 cm from its equilibrium position?

a. 0.85 m/s
b. 0.89 m/s
c. 0.77 m/s
d. 0.64 m/s
e. 0.52 m/s

a. 0.85 m/s

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A 10 kg block on a horizontal frictionless surface is attached to a light spring (force constant = 1.2 kN/m) The block is initially at rest at its equilibrium position when a force (magnitude P) acting parallel to the surface is applied to the block, as shown. When the block is 8.0 cm from the equilibrium position, it has a speed of 0.80 m/s. How much work is done on the block by the force P as the block moves the 8.0 cm?

a. 8.3 J
b. 6.4 J
c. 7.0 J
d. 7.7 J
e. 3.9 J

c. 7.0 J

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A 20 kg block on a horizontal surface is attached to a light spring (force constant = 8.0 kN/m). The block is pulled 10 cm to the right from its equilibrium position and released from rest. When the block has moved 2.0 cm toward its equilibrium position, its kinetic energy is 13 J. How much work is done by the frictional force on the block as it moves the 2.0 cm?

a. -2.5 J
b. -1.4 J
c. -3.0 J
d. -1.9 J
e. -14 J

b. -1.4 J

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The horizontal surface on which the block slides is frictionless. The speed of the block before it touches the spring is 6.0 m/s. How fast is the block moving at the instant the spring has been compressed 15 cm? k = 2.0 kN/m

a. 3.7 m/s
b. 4.4 m/s
c. 4.9 m/s
d. 5.4 m/s
e. 14 m/s

a. 3.7 m/s

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A 2.0 kg block situated on a frictionless incline is connected to a light spring (k = 100 N/m) as shown. The block is released from rest when the spring is unstretched. The pulley is frictionless and has negligible mass. What is the speed of the block when it has moved 0.20 m down the plane?

a. 76 cm/s
b. 68 cm/s
c. 60 cm/s
d. 82 cm/s
e. 57 cm/s

c. 60 cm/s

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A 2.0 kg block sliding on a frictionless horizontal surface is attached to one end of a horizontal spring (k = 600 N/m) which has its other end fixed. The speed of the block when the spring is extended 20 cm is equal to 3.0 m/s. What is the maximum speed of this block as it oscillates?

a. 4.6 m/s
b. 5.3 m/s
c. 5.7 m/s
d. 4.9 m/s
e. 3.5 m/s

a. 4.6 m/s

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A 10 kg block on a rough horizontal surface is attached to a light spring (force constant = 1.4 kN/m). The block is pulled 8.0 cm to the right from its equilibrium position and released from rest. The frictional force between the block and surface has a magnitude of 30 N. What is the kinetic energy of the block as it passes through its equilibrium position. a. 4.5 J b. 2.1 J c. 6.9 J d. 6.6 J e. 4.9 J

b. 2.1 J

A 2.0 kg body moving along the x axis has a velocity vx = 5.0 m/s at x=0. The only force acting on the object is given by Fx = (-4.0x) N, where x is in mm. For what value of x will this object first come (momentarily) to rest? a. 4.2 m b. 3.5 m c. 5.3 m d. 6.4 m e. 5.0 m

b. 3.5 m

A 1.5 kg object moving along the x axis has a velocity of +4.0 m/s at x = 0. If the only force acting on this object is shown in the figure, what is the kinetic energy of the object at x = 3.0 m? a. 18 J b. 21 J c. 23 J d. 26 J e. 8 J

a. 18 J

The only force acting on a 1.6 kg body as it moves along the x axis is given in the figure. If the velocity of the body at x = 2.0 m is 5.0 m/s, what is its kinetic energy at x= 5.0 m? a. 52 J b. 44 J c. 36 J d. 60 J e. 25 J

c. 36 J

The only force acting on a 2.0 kg body moving along the x axis is given by Fx = (2.0x) N, where x is in m. If the velocity of the object at x = 0 is +3.0 m/s, how fast is it moving at x = 2.0 m? a. 4.2 m/s b. 3.6 m/s c. 5.0 m/s d. 5.8 m/s e. 2.8 m/s

b. 3.6 m/s

The only force acting on a 2.0 kg body as it moves along the x axis is given by Fx = (12-2.0x) N where x is in m. The velocity of the body at x = 2.0 m is 5.5i m/s. What is the maximum kinetic energy attained by the body while moving in the +x direction? a. 36 J b. 39 J c. 43 J d. 46 J e. 30 J

d. 46 J

The only force acting on a 1.8 kg body as it moves along the x axis is given by Fx = (-3.0x) N where x is in m. If the velocity of the body at x = 0 is vx = +8.0 m/s, at what value of x will the body have a velocity of +4.0 m/s? a. 5.7 m b. 5.4 m c. 4.8 m d. 4.1 m e. 6.6 m

b. 5.4 m

Two vectors A and B are given by A = 5i+6j+7k and B = 3i-8j+2k. If these two vectors are drawn starting at the same point, what is the angle between them? a. 106 degrees b. 102 degrees c. 110 degrees d. 113 degrees e. 97 degrees

b. 102 degrees

If A = 7i-6j+5k, |B|=7, and the angle between A and B (when the two are drawn starting from the same point) is 60 degrees, what is the scalar product of these two vectors? a. -13 b. +13 c. +37 d. -37 e. 73

c. +37

If vectors A and B have magnitudes 12 and 15, respectively, and the angle between the two where they are drawn starting from the same point is 110 degrees, what is the scalar product of these two vectors? a. -76 b. -62 c. -90 d. -47 e. -170

b. -62

If the vectors A and B have magnitudes of 10 and 11, respectively, and the scalar product of these two vectors is -100, what is the magnitude of the sum of these two vectors? a. 6.6 b. 4.6 c. 8.3 d. 9.8 e. 7.6

b. 4.6

If the scalar product of two vectors, A and C is equal to -3.5, if |A| = 2.0, and the angle between the two vectors when they are drawn starting from the same point is equal to 130 degrees, what is the magnitude of C? a. 2.1 b. 2.5 c. 2.3 d. 2.7 e. 3.1

d. 2.7

If A * C = -7.5, A = 3i-4j and |C| = 6.5, what is the angle between the two vectors when they are drawn starting from the same point? a. 118 degrees b. 107 degrees c. 112 degrees d. 103 degrees e. 77 degrees

d. 103 degrees

Two vectors A and B are given by A = 4i+8j, and B = 6i-2j. The scalar product of A and a third vector C is -16. The scalar product of B and C is +18. The z component of C is 0. What is the magnitude of C? a. 7.8 b. 6.4 c. 3.6 d. 5.0 e. 4.8

c. 3.6

If A = 10,, B = 15, and a = 130 degrees, determine the scalar product of the two vectors shown. a. +96 b. -96 c. +51 d. -51 e. -35

a. +96

If A = 5.0, B = 8.0, and a = 30 degrees, determine the scalar product of the two vectors shown. a. -35 b. +35 c. -20 d. +20 e. +40

a. -35

If |A| = 6.0, |B| = 5.0 and a = 40 degrees, determine the scalar product of the two vectors shown. a. +19 b. +23 c. -19 d. -23 e. +30

d. -23

The same constant force is used to accelerate two carts of the same mass, initially at rest, on horizontal frictionless tracks. The force is applied to cart A for twice as long a time as it is applied to cart B. The work the force does on A is WA; that on B is WB. What statement is correct? a. WA = WB b. WA = sqrt2 WB c. WA = 2 WB d. WA = 4 WB e. WB = 2 WA

d. WA = 4 WB

Carts A and B have equal masses and travel equal distances on straight frictionless tracks while a constant force F is applied to A, and a constant force 2F is applied to B. The relative amounts of work done yb the two forces are related by: a. WA = 4 WB b. WA = 2 WB c. WA = WB d. WB = 2 WA e. WB = 4 WA

d. WB = 2 WA

Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B. Both carts start from rest. The velocities VA and VB of the bodies at the end of distance D are related by a. VB = WA b. VB = sqrt2VA c. VB = 2 VA d. VB = 4 VA e. VA = 2 VB

b. VB = sqrt2 VA

When a ball rises vertically to a height h and returns to its original point of projection, the work done by the gravitational force is a. 0 b. -mgh c. +mgh d. -2mgh e. +2mgh

a. 0

When a crate of mass m is dragged a distance d along a surface with coefficient of kinetic friction (mew k) then dragged back along the same path to its original position, the work done by friction is a. 0 b. -(mewk)mgd c. (mewk)mgd d. -2(mewk)mgd e. 2(mewk)mgd

d. -2(mewk)mgd

Two balls, A and B, of mass m and 2m respectively, are carried to height h at constant velocity, but B rises twice as fast as A. The work the gravitational force does on B is a. one quarter the work done on A b. one half the work done on A c. the same as the work done on A d. twice the work done on A e. four times the work done on A

d. twice the work done on A

Equal amounts of work are performed on two bodies, A and B, initially at rest, and of masses M and 2M respectively. The relation between their speeds immediately after the work has been done on them is a. VA = sqrt2 VB b. VA = 2 VB c. VA = VB d. VB = sqrt2 VA e. VB = 2 VA

a. VA = sqrt2 VB

Two cannonballs are dropped from a second floor physics lab at height h above the ground. Ball B has four times the mass of ball A. When the balls pass the bottom of a first floor window at height h/4 above the ground, the relation between their kinetic energies, KA and KB is a. KA = 4 KB b. KA = 2 KB c. KA = KB d. KB = 2KA e. KB = 4KA

e. KB = 4KA

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time. Clown A has a 40-kg mass; clown B has a 60-kg mass. The relation between their kinetic energies at the instant of launch is a. KA = 3/2KB b. KA = sqrt3/2 KB c. KA = KB d. KB = sqrt3/2 KA e. KB = 3/2KA

c. KA = KB

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time. Clown A has a 40-kg mass, clown B a 60-kg mass. The relation between their speeds at the instant of launch is a. VA = 3/2 VB b. VA = sqrt3/2 VB c. VA = VB d. VB = sqrt3/2 VA e. VB = 3/2 VA

b. VA = sqrt3/2 VB

In a contest, two tractors pull two identical blocks of stone the same distance over identical surfaces. However, block A is moving twice as fast as block B when it crosses the finish line. Which statement is correct? a. Block A has twice as much kinetic energy as block B b. Block B has lost twice as much kinetic energy to friction as block A c. Block B has lost twice as much kinetic energy as block A d. Both blocks have had equal losses of energy to friction e. No energy is lost to friction because the ground has no displacement

d. Both blocks have had equal losses of energy to friction.

If the scalar (dot) product of two vectors is negative, it means that a. there was a calculator error b. the angle between the vectors is less than 90 degrees c. the angle between the vectors is 90 degrees d. the angle between the vectors is greater than 270 degrees e. the angle between the vectors is between 90 and 180 degrees

e. the angle between the vectors is between 90 and 180 degrees

Two eggs of equal mass are thrown at a blanket with equal velocity. Egg B hits the blanket but egg A hits the wall instead. Compare the work done on the eggs in reducing their velocities to zero. a. More work was done on A than on B b. More work was done on B than on A c. The amount of work is the same for both d. It is meaningless to compare the amount of work because the forces were so different e. Work was done on B, but no work was done on A because the wall did not move

c. The amount of work is the same for both.

Planets go around the sun in elliptical orbits. The highly exaggerate ddiagram below shows a portion of such an orbit and the force on the planet at one position along that orbit. The planet is moving to the right F||, and F (perpendicular), are the components of the force parallel (tangential) and perpendicular (normal) to the orbit. The work they do is W|| and W (perpendicular). At the position shown a. W|| slows the planet down; W(perpendicular) speeds it up b. W || slows the planet down; W(perpendicular) does no work on it c. W|| speeds the planet up; W(perpendicular) does no work on it d. W|| speeds the planet up; W(perpendicular) slows it down e. W|| does no work on it; W(perpendicular speeds it up)

b. W|| slows the planet down; W(perpendicular) does no work on it

A mass is attached to the end of a spring is pulled out and released on a surface with friction. The work Fsp * dx done on the mass by the force exerted by the spring a. never has the same sign as the change in energy owing to friction b. always has the same sign as the change in energy owing to friction c. has the same sign as the change in energy owing to friction during one half of each cycle d. never has the same sign as the change in the energy owing to friction if the force of friction is greater than the spring force e. always has the same sign as the change in energy owing to friction if the force of friction is greater than the spring force

c. has the same sign as the change in energy owing to friction during one half of each cycle

The work Fsp * dx done by the force exerted by the spring on a mass attached to the end of the spring when the mass has displacement dx is a. always negative b. always positive c. negative half the time, positive the other half of the time d. positive more than it is negative e. negative more than it is positive

c. negative half the time, positive the other half of the time

A 30-kg child sitting 5.0 from the center of a merry-g-round has a constant speed of 5.0 m/s. While she remains seated in the same spot and travels in a circle, the work the seat performs on her in one complete rotation is a. 0 J b. 150 J c. 1500 J d. 4700 J e. 46000 J

a. 0 J

Sally, who weights 450 N, stands on a skate board while Roger pushes it forward 13.0 m at constant velocity on a level straight street. He applies a constant 100N force. a. The work Roger does on the skateboard is 0 J b. The work Roger does on the skateboard is 1300 J c. The work Sally does on the skateboard is 1300 J d. The work Sally does on the skateboard is 5850 J e. The work Roger does on the skateboard is 5850 J

b. The work Roger does on the skateboard is 1300 J.

negative work can be done a. by friction on the tires while a car is accelerating without skidding b. by a spring at the bottom of an elevator shaft when it stops a falling elevator c. by a hand catching a ball d. by all of the above e. only by (b) and (c) above

(only by B and C above) - by a spring at the bottom of an elevator shaft when it stops a falling elevator - by a hand catching a ball

Positive work can be done a. by friction on the tires when a car is accelerating without skidding b. by a spring when it launches a clown in the air c. by a hand throwing a ball d. by all of the above e. only by (b) and (c) above

(only by B and C above) - by a spring when it launches a clown in the air - by a hand throwing a ball

The force of static friction exerted on an automobile's tires by the ground a. provides the accelerating force that makes the car move forward b. does positive work on the car while it is accelerating c. does negative work on the car while it is decelerating d. does everything listed in (a), (b), and (c) e. only does positive or negative work as in (b) or (c)

a. provides the accelerating force that makes the car move forward

The graph below shows how the force on a 0.500 kg particle varies with position. If the particle has speed v = 2.23 m/s at x = 0.00 m, what is its speed in m/s when x = 8.00 m? a. 2.00 b. 10.7 c. 14.8 d. 15.0 e. 21.1

d. 15.0

The equation below is the solution to a physics problem: 1/2(2.30 kg)(3.9m/s)^2 = 1/2(2.30 kg)(2.33m/s)^2 + (2.30kg)(9.8 m/s^2)(1.00 m)(cos 60) The most likely physical situation it describes is a. a 2.30 kg cart rolling up a 30 degree incline b. a 2.30 kg cart rolling down a 30 degree incline c. a 2.30 kg cart rolling up a 60 degree incline d. a 2.30 kg cart rolling down a 60 degree incline e. a 2.30 kg cart rolling down a 90 degree incline

b. a 2.30 kg cart rolling down a 30 degree incline

After a skydiver reaches terminal velocity a. the force of gravity no longer performs work on the skydiver b. work performed by the force of gravity is converted into gravitational potential energy c. gravitational potential energy is no longer available to the system of the skydiver plus the Earth d. gravitational potential energy is converted into thermal energy e. thermal energy is converted into gravitational potential energy

d. gravitational potential energy is converted into thermal energy

Each of two vectors, D1 and D2, lies along a coordinate axis in the xy plane. Each vector has its tail at the origin and the dot product of the two vectors is D1*D2 = 0. Which possibility is correct? a. D1 and D2 both lie along the positive x axis b. D1 lies along the positive x axis. D2 lies along the negative x axis c. D1 and D2 both lie along the positive y axis d. D1 lies along the negative x axis. D2 lies along the negative y axis. e. D1 lies along the positive y axis. D2 lies along the negative y axis.

d. D1 lies along the negative x axis. D2 lies along the negative y axis.

Each of two vectors, D1 and D2, lies along a coordinate axis in the xy plane. Each vector has its tail at the origin and the dot product of the two vectors is D1*D2 = -|D1||D2|. Which possibility is correct? a. D1 and D2 both lie along the positive x axis. b. D1 lies along the positive x axis. D2 lies along the negative x axis. c. D1 and D2 both lie along the positive y axis d. D1 lies along the negative x axis. D2 lies along the negative y axis. e. D1 lies along the positive y axis. D2 lies along the negative x axis.

b. D1 lies along the positive x axis. D2 lies along the negative x axis.

Two identical springs with spring constant 50 N/m support a 5.0 N weight as in the picture below. What is the change in length of each spring when the weight is hung on the springs? a. 2.9 cm b. 5.0 cm c. 5.8 cm d. 7.5 cm e. 10.0 cm

c. 5.8 cm

A baseball is thrown and lands 120 m away. While the ball is in flight, assuming the effect of air friction is negligible, which of the following is true? a. At maximum height the ball has its greatest kinetic energy. b. The horizontal component of the baseballs' kinetic energy is constant. c. The vertical component of the baseball's kinetic energy is constant d. The mechanical energy of the baseball is greater when nearer to the ground e. No answer above is correct

e. No answer above is correct

A moving particle is subject to conservative forces only. When its kinetic energy decreases by 10 J, what happens to its mechanical energy? a. It increases by 10 J. b. It decreases by 10 J c. It increases, but not necessarily by 10 J d. It decreases, but not necessarily by 10 J e. It remains the same

e. It remains the same

A conservative force on a particle moving along the x axis is given by F = (3x^2-2x)i. Which of the following is a potential that is associated with this force? a. (6x-2)i b. (-6x+2)i c. x^3-x^2+3 d. -x^3+x^2+3 e. No answer given above is correct

d. -x^3+x^2+3

A particle is subject to the potential U = 2x^2y+6y. What is the value of the y component of the force on the particle at the point (x,y) = (2.0,3.0)? a. 24 b. -24 c. 14 d. -14 e. 28

d. -14

A baseball outfielder throws a baseball of mass 0.15 kg at a speed of 40 m/s and initial angle of 30 degrees. What is the kinetic energy of the baseball at the highest point of the trajectory? 90 J

90 J

For the potential U = 2x^2-8x, find the stable equilibrium point, if any x=2

x=2

Chapter 8

natak

A single conservative force Fx = (6.0x-12) N (x is in m) acts on a particle moving along the x axis. The potential energy associated with this force is assigned a value of +20 J at x=0.What is the potential energy at x = 3.0 m? a. +11 J b. + 29 J c. + 9.0 J d. - 9.0 J e. +20 J

b. 29 J

As a particle moves along the x axis it is acted upon by a single conservative force given by Fx = (20-4.0x) N where x is in m. The potential energy associated with this force has the value +30 J ta the origin (x=0). What is the value of the potential energy at x = 4.0 m? a. -48 J b. +78 J c. -18 J d. +48 J e. +80 J

c. -18 J

A 0.40-kg particle moves under the influence of a single conservative force. At point A where the particle has a speed of 10 m/s, the potential energy associated with the conservative force is +40 J. As the particle moves from A to B, the force does +25 J of work on the particle. What is the value of the potential energy at point B? a. +65 J b. +15 J c. +35 J d. +45 J e. -40 J

b. +15 J

As a 1.0 kg object moves from point A to point B, it is acted upon by a single conservative force which does -40 J of work during this motion. At point A the speed of the particle is 6.0 m/s and the potential energy associated with the force is +50 J. What is the potential energy at point B? a. +72 J b. +10 J c. +90 J d. +28 J e. +68 J

c. +90 J

A 12-kg block on a horizontal frictionless surface is attached to a light spring (force constant = 0.90 kN/m). The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N) acting parallel to the surface is applied to the block, as shown. What is the speed of the block when it is 13 cm from its equilibrium position? a. 0.78 m/s b. 0.81 m/s c. 0.71 m/s d. 0.58 m/s e. 0.64 m/s

a. 0.78 m/s

A 7.0 kg block on a horizontal frictionless surface is attached to a light spring (force constant = 1.2 kN/m) The block is initially at rest at its equilibrium position when a force of magnitude P acting parallel to the surface is applied to the block, as shown. When the block is 8.0 cm from the equilibrium position, it has a speed of 0.80 m/s. How much work is done on the block by the force P as the block moves the 8.0 cm? a. 7.4 J b. 5.4 J c. 6.1 J d. 6.7 J e. 4.9 J

c. 6.1 J

A 0.60-kg is suspended from the ceiling at the end of a 2.0-m string. When pulled to the side and released, it has a speed of 4.0 m/s at the lowest point of its path. What maximum angle does the string make with the vertical as the object swings up? a. 61 degrees b. 54 degrees c. 69 degrees d. 77 degrees e. 47 degrees

b. 54 degrees

A pendulum is made by letting a 2.0-kg object swing at the end of a string that has a length of 1.5m. The maximum angle the string makes with the vertical as the pendulum swings is 30 degrees. What is the speed of the object at the lowest point in its trajectory? a. 2.0 m/s b. 2.2 m/s c. 2.5 m/s d. 2.7 m/s e. 3.1 m/s

a. 2.0 m/s

A 2.0-kg mass swings at the end of a light string (length = 3.0 m) Its speed at the lowest point on its circular path is 6.0 m/s. What is its kinetic energy at an instant when the string makes an angle of 50 degrees with the vertical? a. 21 J b. 15 J c. 28 J d. 36 J e. 23 J

b. 15 J

A 2.5-kg object suspended from the ceiling by a string that has a length of 2.5 m is released from rest with the string 40 degrees below the horizontal position. What is the tension in the string at the end instant when the object passes through its lowest position? a. 11 N b. 25 N c. 42 N d. 18 N e. 32 N

c. 42 N

A certain pendulum consists of a 1.5-kg mass swinging at the end of a string (length = 2.0 m) At the lowest point in the swing the tension in the string is equal to 20 N. To what maximum height about the lowest point will the mass rise during its oscillation? a. 77 cm b. 50 cm c. 63 cm d. 36 cm e. 95 cm

d. 36 cm

A 0.80-kg object tied to the end of a 2.0-m string swings as a pendulum. At the lowest point of its swing, the object has a kinetic energy of 10 J. Determine the speed of the object at the instant when the string makes an angle of 50° with the vertical. a. 5.6 m/s b. 4.4 m/s c. 3.3 m/s d. 5.0 m/s e. 6.1 m/s

c. 3.3 m/s

A 0.04-kg ball is thrown from the top of a 30-m tall building (point A) at an unknown angle above the horizontal. As shown in the figure, the ball attains a maximum height of 10 m above the top of the building before striking the ground at point B. If air resistance is negligible, what is the value of the kinetic energy of the ball at B minus the kinetic energy of the ball at A (KB − KA)? a. 12 J b. −12 J c. 20 J d. −20 J e. 32 J

a. 12 J

A 1.2-kg mass is projected from ground level with a velocity of 30 m/s at some unknown angle above the horizontal. A short time after being projected, the mass barely clears a 16-m tall fence. Disregard air resistance and assume the ground is level. What is the kinetic energy of the mass as it clears the fence? a. 0.35 kJ b. 0.73 kJ c. 0.40 kJ d. 0.68 kJ e. 0.19 kJ

a. 0.35 kJ

. A 2.0-kg mass is projected from the edge of the top of a 20-m tall building with a velocity of 24 m/s at some unknown angle above the horizontal. Disregard air resistance and assume the ground is level. What is the kinetic energy of the mass just before it strikes the ground? a. 0.18 kJ b. 0.97 kJ c. 0.89 kJ d. 0.26 kJ e. 0.40 kJ

b. 0.97 kJ

A skier weighing 0.70 kN goes over a frictionless circular hill as shown. If the skier's speed at point A is 9.2 m/s, what is his speed at the top of the hill (point B)? a. 3.1 m/s b. 6.2 m/s c. 5.2 m/s d. 4.1 m/s e. 6.5 m/s

c. 5.2 m/s

A skier weighing 0.80 kN comes down a frictionless ski run that is circular (R = 30 m) at the bottom, as shown. If her speed is 12 m/s at point A, what is her speed at the bottom of the hill (point B)? a. 17 m/s b. 19 m/s c. 18 m/s d. 20 m/s e. 12 m/s

a. 17 m/s

A spring (k = 600 N/m) is placed in a vertical position with its lower end supported by a horizontal surface. The upper end is depressed 20 cm, and a 4.0-kg block is placed on top of the depressed spring. The system is then released from rest. How far above the point of release will the block rise? a. 46 cm b. 36 cm c. 41 cm d. 31 cm e. 20 cm

d. 31 cm

A spring (k = 200 N/m) is suspended with its upper end supported from a ceiling. With the spring hanging in its equilibrium configuration, an object (mass = 2.0 kg) is attached to the lower end and released from rest. What is the speed of the object after it has fallen 4.0 cm? a. 90 cm/s b. 79 cm/s c. 96 cm/s d. 83 cm/s e. 57 cm/s

b. 79 cm/s

A 2.0-kg block sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 200 N/m) which has its other end fixed. If the block has a speed of 4.0 m/s as it passes through the equilibrium position, what is its speed when it is 20 cm from the equilibrium position? a. 2.6 m/s b. 3.1 m/s c. 3.5 m/s d. 1.9 m/s e. 2.3 m/s

c. 3.5 m/s

A block (mass = 4.0 kg) sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 100 N/m) which has its other end fixed. If the maximum distance the block slides from the equilibrium position is equal to 20 cm, what is the speed of the block at an instant when it is a distance of 16 cm from the equilibrium position? a. 71 cm/s b. 60 cm/s c. 80 cm/s d. 87 cm/s e. 57 cm/s

b. 60 cm/s

A 1.0-kg block is released from rest at the top of a frictionless incline that makes an angle of 37° with the horizontal. An unknown distance down the incline from the point of release, there is a spring with k = 200 N/m. It is observed that the mass is brought momentarily to rest after compressing the spring 0.20 m. How far does the mass slide from the point of release until it is brought momentarily to rest? a. 0.98 m b. 0.68 m c. 0.82 m d. 0.55 m e. 0.20 m

b. 0.68 m

A 20-kg mass is fastened to a light spring (k = 380 N/m) that passes over a pulley as shown. The pulley is frictionless, and the mass is released from rest when the spring is unstretched. After the mass has dropped 0.40 m, what is its speed? a. 2.2 m/s b. 2.5 m/s c. 1.9 m/s d. 1.5 m/s e. 3.6 m/s

a. 2.2 m/s

A spring (k = 600 N/m) is at the bottom of a frictionless plane that makes an angle of 30° with the horizontal. The upper end of the spring is depressed 0.10 m, and a 2.0-kg block is placed against the depressed spring. The system is then released from rest. What is the kinetic energy of the block at the instant it has traveled 0.10 m and the spring has returned to its uncompressed length? a. 2.0 J b. 1.8 J c. 2.2 J d. 1.6 J e. 1.0 J

a. 2.0 J

A spring (k = 600 N/m) is placed in a vertical position with its lower end supported by a horizontal surface. A 2.0-kg block that is initially 0.40 m above the upper end of the spring is dropped from rest onto the spring. What is the kinetic energy of the block at the instant it has fallen 0.50 m (compressing the spring 0.10 m)? a. 5.3 J b. 6.8 J c. 6.3 J d. 5.8 J e. 6.5 J

b. 6.8 J

A 2.0-kg block slides down a fixed, rough curved track. The block has a speed of 5.0 m/s after its height above a horizontal surface has decreased by 1.8 m. Assume the block starts from rest. What is the change in mechanical energy of the block caused by the force of friction during this descent? a. −14 J b. −12 J c. −10 J d. −16 J e. −25 J

c. −10 J

A 1.5-kg block sliding on a rough horizontal surface is attached to one end of a horizontal spring (k = 200 N/m) which has its other end fixed. If this system is displaced 20 cm horizontally from the equilibrium position and released from rest, the block first reaches the equilibrium position with a speed of 2.0 m/s. What is the coefficient of kinetic friction between the block and the horizontal surface on which it slides? a. 0.34 b. 0.24 c. 0.13 d. 0.44 e. 0.17

a. 0.34

A 0.75-kg sphere is released from rest and is moving 5.0 m/s after falling 2.0 m in a viscous medium. What is the change in mechanical energy caused by the force the viscous medium exerts on the sphere during this descent? a. −6.1 J b. −4.6 J c. −5.3 J d. −6.8 J e. −2.7 J

c. −5.3 J

A 12-kg projectile is launched with an initial vertical speed of 20 m/s. It rises to a maximum height of 18 m above the launch point. What is the change in mechanical energy caused by the dissipative (air) resistive force on the projectile during this ascent? a. −0.64 kJ b. −0.40 kJ c. −0.52 kJ d. −0.28 kJ e. −0.76 kJ

d. −0.28 kJ

A 10-kg object is dropped from rest. After falling a distance of 50 m, it has a speed of 26 m/s. What is the change in mechanical energy caused by the dissipative (air) resistive force on the object during this descent? a. −1.3 kJ b. −1.5 kJ c. −1.8 kJ d. −2.0 kJ e. −2.3 kJ

b. −1.5 kJ

The block shown is released from rest when the spring is stretched a distance d. If k = 50 N/m, m = 0.50 kg, d = 10 cm, and the coefficient of kinetic friction between the block and the horizontal surface is equal to 0.25, determine the speed of the block when it first passes through the position for which the spring is unstretched. a. 92 cm/s b. 61 cm/s c. 71 cm/s d. 82 cm/s e. 53 cm/s

c. 71 cm/s

A 2.0-kg block sliding on a rough horizontal surface is attached to one end of a horizontal spring (k = 250 N/m) which has its other end fixed. The block passes through the equilibrium position with a speed of 2.6 m/s and first comes to rest at a displacement of 0.20 m from equilibrium. What is the coefficient of kinetic friction between the block and the horizontal surface? a. 0.32 b. 0.45 c. 0.58 d. 0.19 e. 0.26

b. 0.45

In a given frictionless displacement of a particle, its kinetic energy increases by 25 J while its potential energy decreases by 10 J. Determine the work of the nonconservative forces acting on the particle during this displacement. a. −15 J b. +35 J c. +15 J d. −35 J e. +55 J

c. +15 J

. A particle is acted upon by only two forces, one conservative and one nonconservative and neither being a force of friction, as it moves from point A to point B. The kinetic energies of the particle at points A and B are equal if a. the sum of the works of the two forces is zero. b. the work of the conservative force is equal to the work of the nonconservative force. c. the work of the conservative force is zero. d. the work of the nonconservative force is zero. e. None of the above.

a. the sum of the works of the two forces is zero.

A 1.2-kg mass is projected down a rough circular track (radius = 2.0 m) as shown. The speed of the mass at point A is 3.2 m/s, and at point B, it is 6.0 m/s. What is the change in mechanical energy done on the system between A and B by the force of friction? a. −8.9 J b. −7.3 J c. −8.1 J d. −6.6 J e. −24 J

c. −8.1 J

A 1.2-kg mass is projected up a rough circular track (radius = 0.80 m) as shown. The speed of the mass at point A is 8.4 m/s, and at point B, it is 5.6 m/s. What is the change in mechanical energy between A and B caused by the force of friction? a. −2.7 J b. −8.8 J c. −4.7 J d. −6.7 J e. −19 J

c. −4.7 J

A 3.0-kg mass is dropped from the edge of a 50-m tall building with an initial speed of zero. The mass strikes the ground with a downward velocity of 25 m/s. Find the change in mechanical energy of the mass caused by air resistance between the point where it is dropped and the point where it strikes the ground? a. −0.46 kJ b. −0.53 kJ c. −0.61 kJ d. −0.38 kJ e. −0.81 kJ

b. −0.53 kJ

A 2.0-kg mass is projected vertically upward from ground level with an initial speed of 30 m/s. The mass rises to a maximum height of 35 m above ground level. What is the change in mechanical energy of the mass caused by air resistance between the point of projection and the point of maximum height? a. −0.21 kJ b. −0.47 kJ c. −0.40 kJ d. −0.34 kJ e. −0.69 kJ

a. −0.21 kJ

A 25-kg block on a horizontal surface is attached to a light spring (force constant = 8.0 kN/m). The block is pulled 10 cm to the right from its equilibrium position and released from rest. When the block has moved 2.0 cm toward its equilibrium position, its kinetic energy is 12 J. What is the change in mechanical energy caused by the frictional force on the block as it moves the 2.0 cm? a. −4.0 J b. −3.5 J c. −2.4 J d. −2.9 J e. −15 J

c. −2.4 J

. The two masses in the figure are released from rest. After the 3.0-kg mass has fallen 1.5 m, it is moving with a speed of 3.8 m/s. What is the change in mechanical energy done on the system during this time interval by the frictional force on the 2.0 kg mass? a. −12 J b. −17 J c. −20 J d. −8.0 J e. −28 J

d. −8.0 J

A 2.0-kg block is projected down a plane that makes an angle of 20° with the horizontal with an initial kinetic energy of 2.0 J. If the coefficient of kinetic friction between the block and plane is 0.40, how far will the block slide down the plane before coming to rest? a. 3.0 m b. 1.8 m c. 0.30 m d. 1.0 m e. 1.3 m

a. 3.0 m

A large spring is used to stop the cars after they come down the last hill of a roller coaster. The cars start at rest at the top of the hill and are caught by a mechanism at the instant their velocities at the bottom are zero. Compare the compression of the spring, xA, for a fully loaded car with that, xB, for a lightly loaded car when mA = 2mB. a. xA = 1/2xB. b. xA = xB. c. xA = sqrt2xB. d. xA = 2 xB. e. xA = 4 xB.

c. xA = sqrt2xB.

A small lead sphere of mass m is hung from a spring of spring constant k. The gravitational potential energy of the system equals zero at the equilibrium position of the spring before the weight is attached. The total mechanical energy of the system when the mass is hanging at rest is: a. -kx^2 b. -1/2kx^2 c. 0 d. +1/2kx^2 e. +kx^2

b. -1/2kx^2

Cubical blocks of mass m and side l are piled up in a vertical column. The total gravitational potential energy of a column of three blocks is a. 5/2mgl b. 3mgl c. 9/2mgl d. 6mgl e. 9mgl

c. 9/2mgl

An all-terrain vehicle of 2000 kg mass moves up a 15.0° slope at a constant velocity of 6.00 m/s. The rate of change of gravitational potential energy with time is a. 5.25 kW. b. 24.8 kW. c. 30.4 kW. d. 118 kW. e. 439 kW.

c. 30.4 kW.

A pendulum bob has potential energy U0 when held taut in a horizontal position. The bob falls until it is 30° away from the horizontal position, when it has potential energy UA. It continues to fall until the string is vertical, when it has potential energy UB. Compare its potential energies at O, A, and B. a. U0 = UA = UB. b. UA − UB = 2U0. c. UA − UB = U0 − UA. d. U0 = UB = 2UA. e. U0 − UA = 2(UA − UB).

c. UA − UB = U0 − UA.

A spring with spring constant k = 800 N/m is compressed 12 cm from its equilibrium position. A spring with spring constant k = 400 N/m has the same elastic potential energy as the first spring when its extension is a. 0.060 m. b. 0.085 m. c. 0.12 m. d. 0.17 m. e. 0.24 m.

d. 0.17 m.

A spring with spring constant k = 800 N/m is extended 12 cm from its equilibrium position. A spring with 6.0 cm extension from equilibrium will have the same potential energy as the first spring if its spring constant is a. 200 N/m. b. 400 N/m. c. 800 N/m. d. 1 600 N/m. e. 3 200 N/m.

e. 3 200 N/m.

A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would have used at least ____ J of energy. a. 746 b. 3.43 × 105 c. 3.73 × 105 d. 7.46 × 105 e. 2.61 × 107

b. 3.43 × 105

A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would reach the summit in ____ seconds. a. 1 b. 460 c. 500 d. 1 000 e. 35 000

b. 460

A champion athlete can produce one horsepower (746 W) for a short period of time. The number of 16 cm high steps a 70 kg athlete could ascend in one minute while expending one horsepower is a. 4. b. 7. c. 65. d. 408. e. 4 567.

d. 408.

Objects A and B, of mass M and 2M respectively, are each pushed a distance d straight up an inclined plane by a force F parallel to the plane. The coefficient of kinetic friction between each mass and the plane has the same value μk. At the highest point, a. KA = Fd = KB. b. KA = (F − μkMg cosθ)d; KB = (F − 2μkMg cosθ)d. c. KA = (F − Mg sinθ)d; KB = (F − 2Mg sinθ)d. d. KA = (F − Mg sinθ − μkMg cosθ)d; KB = (F − Mg sinθ − μkMg cosθ)d. e. KA = (F − Mg sinθ − μkMg cosθ)d; KB = (F − 2Mg sinθ − 2μkMg cosθ)d.

e. KA = (F − Mg sinθ − μkMg cosθ)d; KB = (F − 2Mg sinθ − 2μkMg cosθ)d.

. As an object moves from point A to point B only two forces act on it: one force is nonconservative and does −30 J of work, the other force is conservative and does +50 J of work. Between A and B, a. the kinetic energy of object increases, mechanical energy decreases. b. the kinetic energy of object decreases, mechanical energy decreases. c. the kinetic energy of object decreases, mechanical energy increases. d. the kinetic energy of object increases, mechanical energy increases. e. None of the above.

a. the kinetic energy of object increases, mechanical energy decreases.

As an object moves from point A to point B only two forces act on it: one force is conservative and does −70 J of work, the other force is nonconservative and does +50 J of work. Between A and B, a. the kinetic energy of object increases, mechanical energy increases. b. the kinetic energy of object decreases, mechanical energy increases. c. the kinetic energy of object decreases, mechanical energy decreases. d. the kinetic energy of object increases, mechanical energy decreases. e. None of the above.

b. the kinetic energy of object decreases, mechanical energy increases.

An astronaut tosses a ball out in space where gravitational forces may be neglected. What will happen to the ball? a. It will stop as soon as the force the astronaut gave it is used up. b. It will stop when the energy the astronaut gave it runs out. c. It will stop after a short time because there is no gravity to keep it moving. d. It will move in a circle like a boomerang. e. It will be slowed down very gradually by collisions with molecules in space.

e. It will be slowed down very gradually by collisions with molecules in space.

Which of the following is a conservative force? (All refer to a car on a slope.) a. The force you exert on the car pushing it uphill. b. The force exerted by rain drops falling on the car. c. The frictional force of the road on the car. d. The gravitational force acting on the car. e. The force you exert on the car (pushing it uphill) after it starts to slide downhill.

d. The gravitational force acting on the car.

For a force to be a conservative force, when applied to a single test body a. it must have the same value at all points in space. b. it must have the same direction at all points in space. c. it must be parallel to a displacement in any direction. d. equal work must be done in equal displacements. e. no net work must be done for motion in closed paths.

e. no net work must be done for motion in closed paths.

The force a spring exerts on a body is a conservative force because a. a spring always exerts a force opposite to the displacement of the body. b. a spring always exerts a force parallel to the displacement of the body. c. the work a spring does on a body is equal for compressions and extensions of equal magnitude. d. the work a spring does on a body is equal and opposite for compressions and extensions of equal magnitude. e. the net work a spring does on a body is zero when the body returns to its initial position.

e. the net work a spring does on a body is zero when the body returns to its initial position.

Identical masses m are attached to identical springs of spring constant k suspended from the ceiling. With both masses hanging in their equilibrium positions, mass A is pulled down 10 cm and released while mass B is pushed up 10 cm and released. Which statement is correct? a. Mass A will travel a smaller distance to its highest point than mass B will travel to its lowest point. b. Mass A will travel a greater distance to its highest point than mass B will travel to its lowest point. c. Masses A and B will travel equal distances between their highest and lowest points. d. More work was done on mass A by the extending force than on mass B by the compressing force. e. The total work done on mass A by the extending force was equal to the total work done on mass B by the compressing force.

c. Masses A and B will travel equal distances between their highest and lowest points.

Objects A and B, of mass M and 2M respectively, are each pushed a distance d straight up an inclined plane by a force F parallel to the plane. The coefficient of kinetic friction between each mass and the plane has the same value μk. At the highest point, a. KA > KB. b. KA = KB. c. KA < KB. d. The work done by F on A is greater than the work done by F on B. e. The work done by F on A is less than the work done by F on B.

a. KA > KB.

The equation below describes a physical situation: 1/2(1.70 kg)(3.30 m/s)^2 + (1.70 kg)(9.8 m/s^2)(2.35 m)sin30 = 1/2(1.70 kg)(4.60 m/s)^2+0.320(1.70 kg)(9.8 m/s^2)(2.35 m)cos30 Which description best fits the equation? a. A 1.70 kg block slows down while sliding down a frictionless plane inclined at a 30° angle. b. A 1.70 kg block slows down while sliding down a plane with μk = 0.320, with the plane inclined at a 30° angle. c. A 1.70 kg block speeds up while sliding up a frictionless plane inclined at a 30° angle. d. A 1.70 kg block speeds up while sliding down a plane with μk = 0.320, with the plane inclined at a 30° angle. e. A 1.70 kg block slides over the top of an inclined plane and then descends on the other side. Both planes, inclined at a 30° angle, have μk = 0.320.

d. A 1.70 kg block speeds up while sliding down a plane with μk = 0.320, with the plane inclined at a 30° angle.

A spring with spring constant 800 N/m compressed 0.200 m is released and projects a 0.800 kg mass along a frictionless surface. The mass reaches a surface area where μk = 0.400 and comes to a stop. The following student solution contains at least one error. What is the error? 1/2(800 N/m)(0.200 m)^2 = 1/2(0.500 kg)(8 m/s)^2+0.4(0.500 kg)(9.8 m/s^2)(8.16 m) a. The elastic potential energy is equal only to the kinetic energy on the right, and is never equal to the internal thermal energy. b. The elastic potential energy is equal only to the internal thermal energy on the right, and is never equal to the kinetic energy. c. The elastic potential energy is equal to either the kinetic energy or the internal thermal energy on the right, but not to their sum, depending on the part of the problem being done. d. Elastic potential energy cannot end up as internal energy change caused by friction. e. Change in mechanical energy by friction cannot end up as elastic potential energy.

c. The elastic potential energy is equal to either the kinetic energy or the internal thermal energy on the right, but not to their sum, depending on the part of the problem being done.

The solution to a problem is the equation below. Which description best fits this solution? 1/2(500 N/m)(0.120 m)^2 - (2.00 kg)(9.80 m/s^2)(0.120 m) = 1/2(2.00 kg)(0.824 m/s)^2 + (2.00 kg)(9.8 m/s^2)(0.0290 m) a. A vertical spring compressed 0.120 m shoots a 2.00 kg mass 2.90 cm above the equilibrium position of the spring. b. A vertical spring stretched 0.120 m shoots a 2.00 kg mass 9.10 cm above the equilibrium position of the spring. c. A vertical spring compressed 0.120 m shoots a 2.00 kg mass 12.0 cm above the equilibrium position of the spring. d. A vertical spring compressed 0.120 m shoots a 2.00 kg mass 14.9 cm above the equilibrium position of the spring. e. A 2.00 kg mass has fallen 0.820 m and compressed the upper end of a vertical spring 12.0 cm below the equilibrium position.

a. A vertical spring compressed 0.120 m shoots a 2.00 kg mass 2.90 cm above the equilibrium position of the spring.

64. As a result of friction between internal parts of an isolated system a. the total mechanical energy of the system increases. b. the total mechanical energy of the system decreases. c. the total mechanical energy of the system remains the same. d. the potential energy of the system increases but the kinetic energy remains the same. e. the kinetic energy of the system increases but the potential energy of the system remains the same.

b. the total mechanical energy of the system decreases.

A 3.50 kg block is pulled along a moving conveyor belt at a constant speed of 0.500 m/s relative to a stationary observer while the belt moves at a constant speed of 0.200 m/s in the same direction. If the coefficient of kinetic friction is 0.400, the magnitude of the mechanical energy dissipated, in J, caused by the force of friction on the block in 8.00 s is a. 5.6. b. 22.0. c. 32.9. d. 54.8. e. 76.8.

c. 32.9.

A 3.50 kg block is pulled along a moving conveyor belt at a constant speed of 0.500 m/s relative to a stationary observer while the belt moves at a constant speed of 0.200 m/s in the opposite direction. If the coefficient of kinetic friction is 0.400, the magnitude of the mechanical energy dissipated, in J, caused by the force of friction on the block in 8.00 s is a. 5.6. b. 22.0. c. 32.9. d. 54.8. e. 76.8.

e. 76.8.

Jane and Jake are looking at what happens to body 1 of mass m and body 2 of mass 2m, initially at rest, when equal forces are applied separately to the two bodies. Jake says that equal forces applied for equal times do equal amounts of work on the two bodies. Jane says that the two forces do equal amounts of work only if the two bodies move equal distances in the direction of the forces. Which one, if either, is correct? a. Jake, because the speed of body 1 is half the speed of body 2, but m1v1 = m2v2. b. Jane, because work does not depend on mass, only on force times distance. c. Jake, because all bodies travel equal distances when equal forces are applied for equal times. d. Jane, because it takes the same time for all bodies to travel equal distances when equal forces are involved. e. Neither, because we can't compare the amounts of work done on bodies of different mass.

b. Jane, because work does not depend on mass, only on force times distance.

The same force F is applied horizontally to bodies 1, 2, 3 and 4, of masses m, 2m, 3m and 4m, initially at rest and on a frictionless surface, until each body has traveled distance d. The correct listing of the magnitudes of the velocities of the bodies, v1, v2, v3, and v4 is a. v4 = sqrt4/3 v3 = sqrt3/2 v2 = 2v1 b. v4 = v2 > v3 = v1 c. v1 = sqrt2 v2 = sqrt3 v3 = 2v4 d. v1 = 2v2 = 3v3 = 4v4 e. v4 = 3/4 v3 = 2/3v2 = 1/2v1

c. v1 = sqrt2 v2 = sqrt3 v3 = 2v4

69. Any change of the energy of a system occurs because of a. energy transfer across the boundaries of the system. b. combustion of fuels within the system. c. radioactive decay of elements within the system. d. all of the above. e. only (b) and (c) above.

a. energy transfer across the boundaries of the system.

Two masses, MA and MB, with MB = 2MA, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen equal distances, we find that a. KB = KA. b. KB = 2KA. c. KB = 4KA. d. KA = 2KB. e. KA = 4KB.

b. KB = 2KA.

Two masses, MA and MB, with MB = 2MA, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen for equal times, we find that a. KB = KA. b. KB = 2KA. c. KB = 4KA. d. KA = 2KB. e. KA = 4KB.

b. KB = 2KA.

A 6.0-kg block slides along a horizontal surface. If µk = 0.20 for the block and surface, at what rate is the friction force changing the mechanical energy of the block at an instant when its speed is 4.0 m/s? a. −59 W b. −47 W c. −71 W d. −82 W e. +71 W

b. −47 W

At what rate is the gravitational force on a 2.0-kg projectile doing work at an instant when the velocity of the projectile is 4.0 m/s directed 30° above the horizontal? a. +39 W b. −78 W c. −39 W d. +78 W e. +25 W

c. −39 W

A 2.0-kg block slides down a plane (inclined at 40° with the horizontal) at a constant speed of 5.0 m/s. At what rate is the gravitational force on the block doing work? a. +98 W b. +63 W c. zero d. +75 W e. −75 W

b. +63 W

. The speed of a 4.0-kg object is given by v = (2t) m/s, where t is in s. At what rate is the resultant force on this object doing work at t = 1 s? a. 48 W b. 40 W c. 32 W d. 56 W e. 16 W

e. 16 W

A 3.0-kg block is on a frictionless horizontal surface. The block is at rest when, at t = 0, a force (magnitude P = 2.0 N) acting at an angle of 22° above the horizontal is applied to the block. At what rate is the force P doing work at t = 2.0 s? a. 2.3 W b. 2.0 W c. 1.4 W d. 1.7 W e. 1.2 W

a. 2.3 W

A 1.6-kg block slides down a plane (inclined at 25° with the horizontal) at a constant speed of 2.0 m/s. At what rate is the frictional force changing the mechanical energy of the block? a. +28 W b. +13 W c. −13 W d. −28 W e. +6.5 W

c. −13 W

A 3.0-kg block is on a horizontal surface. The block is at rest when, at t = 0, a force (magnitude P = 12 N) acting parallel to the surface is applied to the block causing it to accelerate. The coefficient of kinetic friction between the block and the surface is 0.20. At what rate is the force P doing work on the block at t = 2.0 s? a. 54 W b. 49 W c. 44 W d. 59 W e. 24 W

b. 49 W

Starting from rest at t = 0, a 5.0-kg block is pulled across a horizontal surface by a constant horizontal force having a magnitude of 12 N. If the coefficient of friction between the block and the surface is 0.20, at what rate is the 12-N force doing work at t = 5.0 s? a. 0.13 kW b. 0.14 kW c. 0.12 kW d. 26 W e. 12 W

d. 26 W

Two equal masses are raised at constant velocity by ropes that run over pulleys, as shown below. Mass B is raised twice as fast as mass A. The magnitudes of the forces are FA and FB, while the power supplied is respectively PA and PB. Which statement is correct? a. FB = FA; PB = PA. b. FB = FA; PB = 2 PA. c. FB = 2 FA; PB = PA. d. FB = 2 FA; PB = 2 PA. e. PA = FA; PB = FB.

b. FB = FA; PB = 2 PA.

A rain cloud contains 2.66 × 107 kg of water vapor. How long would it take for a 2.0 kW pump to lift the same amount of water to an altitude of 2 000 m?

8.26 years

A surprising demonstration involves dropping an egg from a third-floor window to land on a foam-rubber pad 2 in (5 cm) thick without breaking. If a 56-gram egg falls 12 m, and the foam pad stops the egg in 6.25 ms, by how much is the pad compressed?

4.8 cm

A 70-kg high jumper leaves the ground with a vertical velocity of 6.0 m/s. How high can he jump?

1.84 m

. A simple pendulum, 2.0 m in length, is released from rest when the support string is at an angle of 25° from the vertical. What is the speed of the suspended mass at the bottom of the swing?

1.9 m/s

While running, a person dissipates about 0.6 J of mechanical energy per step per kilogram of body mass. If a 60-kg person runs with a power of 70 Watts during a race, how fast is the person running? Assume a running step is 1.5 m long.

2.92 m/s

When an automobile moves with constant velocity the power developed is used to overcome the frictional forces exerted by the air and the road. If the power developed in an engine is 50.0 hp, what total frictional force acts on the car at 55 mph (24.6 m/s)? One horsepower equals 746 W.

1520 N

. A 2000-kg truck traveling at a speed of 6.0 m/s makes a 90° turn in a time of 4.0 s and emerges from this turn with a speed of 4.0 m/s. What is the magnitude of the average resultant force on the truck during this turn? a. 4.0 kN b. 5.0 kN c. 3.6 kN d. 6.4 kN e. 0.67 kN

c. 3.6 kN

A 1.2-kg object moving with a speed of 8.0 m/s collides perpendicularly with a wall and emerges with a speed of 6.0 m/s in the opposite direction. If the object is in contact with the wall for 2.0 ms, what is the magnitude of the average force on the object by the wall? a. 9.8 kN b. 8.4 kN c. 7.7 kN d. 9.1 kN e. 1.2 kN

b. 8.4 kN

A 1.5-kg playground ball is moving with a velocity of 3.0 m/s directed 30° below the horizontal just before it strikes a horizontal surface. The ball leaves this surface 0.50 s later with a velocity of 2.0 m/s directed 60° above the horizontal. What is the magnitude of the average resultant force on the ball? a. 14 N b. 11 N c. 18 N d. 22 N e. 3.0 N

b. 11 N

The only force acting on a 2.0-kg object moving along the x axis is shown. If the velocity vx is −2.0 m/s at t = 0, what is the velocity at t = 4.0 s? a. −2.0 m/s b. −4.0 m/s c. −3.0 m/s d. +1.0 m/s e. +5.0 m/s

c. −3.0 m/s

The only force acting on a 2.0-kg object moving along the x axis is shown. If the velocity vx is +2.0 m/s at t = 0, what is the velocity at t = 4.0 s? a. +4.0 m/s b. +5.0 m/s c. +6.0 m/s d. +7.0 m/s e. +2.0 m/s

a. +4.0 m/s

The speed of a 2.0-kg object changes from 30 m/s to 40 m/s during a 5.0-s time interval. During this same time interval, the velocity of the object changes its direction by 90°. What is the magnitude of the average total force acting on the object during this time interval? a. 30 N b. 20 N c. 40 N d. 50 N e. 6.0 N

b. 20 N

. A 3.0-kg ball with an initial velocity of (4 + 3 ) m/s collides with a wall and rebounds with a velocity of (−4 + 3 ) m/s. What is the impulse exerted on the ball by the wall? a. +24i N*s b. −24i N*s c. +18i N*s d. −18i N*s e. +8.0i N*s

b. −24i N*s

A 2.4-kg ball falling vertically hits the floor with a speed of 2.5 m/s and rebounds with a speed of 1.5 m/s. What is the magnitude of the impulse exerted on the ball by the floor? a. 9.6 N*s b. 2.4 N*s c. 6.4 N*s d. 1.6 N*s e. 1.0 N*s

a. 9.6 N*s

An 8.0-kg object moving 4.0 m/s in the positive x direction has a one-dimensional collision with a 2.0-kg object moving 3.0 m/s in the opposite direction. The final velocity of the 8.0-kg object is 2.0 m/s in the positive x direction. What is the total kinetic energy of the two-mass system after the collision? a. 32 J b. 52 J c. 41 J d. 25 J e. 29 J

c. 41 J

A 1.6-kg ball is attached to the end of a 0.40-m string to form a pendulum. This pendulum is released from rest with the string horizontal. At the lowest point of its swing, when it is moving horizontally, the ball collides with a 0.80-kg block initially at rest on a horizontal frictionless surface. The speed of the block just after the collision is 3.0 m/s. What is the speed of the ball just after the collision? a. 1.7 m/s b. 1.1 m/s c. 1.5 m/s d. 1.3 m/s e. 2.1 m/s

d. 1.3 m/s

A 4.0-kg particle is moving horizontally with a speed of 5.0 m/s when it strikes a vertical wall. The particle rebounds with a speed of 3.0 m/s. What is the magnitude of the impulse delivered to the particle? a. 24 N⋅s b. 32 N⋅s c. 40 N⋅s d. 30 N⋅s e. 8.0 N⋅s

b. 32 N⋅s

A 2.0-kg object moving with a velocity of 5.0 m/s in the positive x direction strikes and sticks to a 3.0-kg object moving with a speed of 2.0 m/s in the same direction. How much kinetic energy is lost in this collision? a. 2.4 J b. 9.6 J c. 5.4 J d. 0.6 J e. 6.0 J

c. 5.4 J

A 10-g bullet moving 1000 m/s strikes and passes through a 2.0-kg block initially at rest, as shown. The bullet emerges from the block with a speed of 400 m/s. To what maximum height will the block rise above its initial position? a. 78 cm b. 66 cm c. 56 cm d. 46 cm e. 37 cm

d. 46 cm

A 12-g bullet moving horizontally strikes and remains in a 3.0-kg block initially at rest on the edge of a table. The block, which is initially 80 cm above the floor, strikes the floor a horizontal distance of 120 cm from its initial position. What was the initial speed of the bullet? a. 0.68 km/s b. 0.75 km/s c. 0.81 km/s d. 0.87 km/s e. 0.41 km/s

b. 0.75 km/s

A 6.0-kg object moving 5.0 m/s collides with and sticks to a 2.0-kg object. After the collision the composite object is moving 2.0 m/s in a direction opposite to the initial direction of motion of the 6.0-kg object. Determine the speed of the 2.0-kg object before the collision. a. 15 m/s b. 7.0 m/s c. 8.0 m/s d. 23 m/s e. 11 m/s

d. 23 m/s

A 2.0-kg object moving 5.0 m/s collides with and sticks to an 8.0-kg object initially at rest. Determine the kinetic energy lost by the system as a result of this collision. a. 20 J b. 15 J c. 30 J d. 25 J e. 5.0 J

a. 20 J

A 1.6-kg block is attached to the end of a 2.0-m string to form a pendulum. The pendulum is released from rest when the string is horizontal. At the lowest point of its swing when it is moving horizontally, the block is hit by a 10-g bullet moving horizontally in the opposite direction. The bullet remains in the block and causes the block to come to rest at the low point of its swing. What was the magnitude of the bullet's velocity just before hitting the block? a. 1.0 km/s b. 1.6 km/s c. 1.2 km/s d. 1.4 km/s e. 1.8 km/s

a. 1.0 km/s

A 3.0-kg mass sliding on a frictionless surface has a velocity of 5.0 m/s east when it undergoes a one-dimensional inelastic collision with a 2.0-kg mass that has an initial velocity of 2.0 m/s west. After the collision the 3.0-kg mass has a velocity of 1.0 m/s east. How much kinetic energy does the two-mass system lose during the collision? a. 22 J b. 24 J c. 26 J d. 20 J e. 28 J

b. 24 J

A 3.0-kg mass is released from rest at point A of a circular frictionless track of radius 0.40 m as shown in the figure. The mass slides down the track and collides with a 1.4-kg mass that is initially at rest on a horizontal frictionless surface. If the masses stick together, what is their speed after the collision? a. 2.1 m/s b. 1.7 m/s c. 1.9 m/s d. 1.5 m/s e. 2.3 m/s

c. 1.9 m/s

A 3.0-kg mass is sliding on a horizontal frictionless surface with a speed of 3.0 m/s when it collides with a 1.0-kg mass initially at rest as shown in the figure. The masses stick together and slide up a frictionless circular track of radius 0.40 m. To what maximum height, h, above the horizontal surface will the masses slide? a. 0.18 m b. 0.15 m c. 0.21 m d. 0.26 m e. 0.40 m

d. 0.26 m

A 10-g bullet moving horizontally with a speed of 2.0 km/s strikes and passes through a 4.0-kg block moving with a speed of 4.2 m/s in the opposite direction on a horizontal frictionless surface. If the block is brought to rest by the collision, what is the kinetic energy of the bullet as it emerges from the block? a. 0.51 kJ b. 0.29 kJ c. 0.80 kJ d. 0.13 kJ e. 20 kJ

a. 0.51 kJ

A 10-g bullet moving horizontally with a speed of 1.8 km/s strikes and passes through a 5.0-kg block initially at rest on a horizontal frictionless surface. The bullet emerges from the block with a speed of 1.0 km/s. What is the kinetic energy of the block immediately after the bullet emerges? a. 8.0 J b. 6.4 J c. 5.3 J d. 9.4 J e. 10 J

b. 6.4 J

A pendulum consists of a 2.0-kg block hanging on a 1.5-m length string. A 10-g bullet moving with a horizontal velocity of 900 m/s strikes, passes through, and emerges from the block (initially at rest) with a horizontal velocity of 300 m/s. To what maximum height above its initial position will the block swing? a. 32 cm b. 38 cm c. 46 cm d. 27 cm e. 9 cm

c. 46 cm

A 1.0-kg ball is attached to the end of a 2.5-m string to form a pendulum. This pendulum is released from rest with the string horizontal. At the lowest point in its swing when it is moving horizontally, the ball collides elastically with a 2.0-kg block initially at rest on a horizontal frictionless surface. What is the speed of the block just after the collision? a. 2.3 m/s b. 4.7 m/s c. 3.5 m/s d. 3.0 m/s e. 7.0 m/s

b. 4.7 m/s

A 3.0-kg object moving in the positive x direction has a one-dimensional elastic collision with a 5.0-kg object initially at rest. After the collision the 5.0-kg object has a velocity of 6.0 m/s in the positive x direction. What was the initial speed of the 3.0 kg object? a. 6.0 m/s b. 7.0 m/s c. 4.5 m/s d. 8.0 m/s e. 5.5 m/s

d. 8.0 m/s

. A 3.0-kg object moving 8.0 m/s in the positive x direction has a one-dimensional elastic collision with an object (mass = M) initially at rest. After the collision the object of unknown mass has a velocity of 6.0 m/s in the positive x direction. What is M? a. 7.5 kg b. 5.0 kg c. 6.0 kg d. 4.2 kg e. 8.0 kg

b. 5.0 kg

A 6.0-kg object moving 2.0 m/s in the positive x direction has a one-dimensional elastic collision with a 4.0-kg object moving 3.0 m/s in the opposite direction. What is the total kinetic energy of the two-mass system after the collision? a. 30 J b. 62 J c. 20 J d. 44 J e. 24 J

a. 30 J

Two blocks with masses 2.0 kg and 3.0 kg are placed on a horizontal frictionless surface. A light spring is placed in a horizontal position between the blocks. The blocks are pushed together, compressing the spring, and then released from rest. After contact with the spring ends, the 3.0-kg mass has a speed of 2.0 m/s. How much potential energy was stored in the spring when the blocks were released? a. 15 J b. 3.0 J c. 6.0 J d. 12 J e. 9.0 J

a. 15 J

An 80-g particle moving with an initial speed of 50 m/s in the positive x direction strikes and sticks to a 60-g particle moving 50 m/s in the positive y direction. How much kinetic energy is lost in this collision? a. 96 J b. 89 J c. 175 J d. 86 J e. 110 J

d. 86 J

A 2.0-kg object moving 3.0 m/s strikes a 1.0-kg object initially at rest. Immediately after the collision, the 2.0-kg object has a velocity of 1.5 m/s directed 30° from its initial direction of motion. What is the x component of the velocity of the 1.0-kg object just after the collision? a. 3.7 m/s b. 3.4 m/s c. 1.5 m/s d. 2.4 m/s e. 4.1 m/s

b. 3.4 m/s

A 2.0-kg object moving 3.0 m/s strikes a 1.0-kg object initially at rest. Immediately after the collision, the 2.0-kg object has a velocity of 1.5 m/s directed 30° from its initial direction of motion. What is the y component of the velocity of the 1.0-kg object just after the collision? a. −3.7 m/s b. −3.4 m/s c. −1.5 m/s d. −2.4 m/s e. −4.1 m/s

c. −1.5 m/s

A 6.0-kg object, initially at rest in free space, "explodes" into three segments of equal mass. Two of these segments are observed to be moving with equal speeds of 20 m/s with an angle of 60° between their directions of motion. How much kinetic energy is released in this explosion? a. 2.4 kJ b. 2.9 kJ c. 2.0 kJ d. 3.4 kJ e. 1.2 kJ

c. 2.0 kJ

A 5.0-g particle moving 60 m/s collides with a 2.0-g particle initially at rest. After the collision each of the particles has a velocity that is directed 30° from the original direction of motion of the 5.0-g particle. What is the speed of the 2.0-g particle after the collision? a. 72 m/s b. 87 m/s c. 79 m/s d. 94 m/s e. 67 m/s

b. 87 m/s

A 1.0-kg object moving 9.0 m/s collides with a 2.0-kg object moving 6.0 m/s in a direction that is perpendicular to the initial direction of motion of the 1.0-kg object. The two masses remain together after the collision, and this composite object then collides with and sticks to a 3.0-kg object. After these collisions, the final composite (6.0-kg) object remains at rest. What was the speed of the 3.0-kg object before the collisions? a. 15 m/s b. 10 m/s c. 5.0 m/s d. 20 m/s e. 25 m/s

c. 5.0 m/s

A 3.0-kg mass sliding on a frictionless surface explodes into three 1.0-kg masses. After the explosion the velocities of the three masses are: (1) 9.0 m/s, north; (2) 4.0 m/s, 30° south of west; and (3) 4.0 m/s, 30° south of east. What was the magnitude of the original velocity of the 3.0-kg mass? a. 1.7 m/s b. 1.0 m/s c. 1.3 m/s d. 2.0 m/s e. 2.8 m/s

a. 1.7 m/s

A 3.0-kg mass moving in the positive x direction with a speed of 10 m/s collides with a 6.0-kg mass initially at rest. After the collision, the speed of the 3.0-kg mass is 8.0 m/s, and its velocity vector makes an angle of 35° with the positive x axis. What is the magnitude of the velocity of the 6.0-kg mass after the collision? a. 2.2 m/s b. 2.9 m/s c. 4.2 m/s d. 3.5 m/s e. 4.7 m/s

b. 2.9 m/s

A 5.0-kg mass with an initial velocity of 4.0 m/s, east collides with a 4.0-kg mass with an initial velocity of 3.0 m/s, west. After the collision the 5.0-kg mass has a velocity of 1.2 m/s, south. What is the magnitude of the velocity of the 4.0-kg mass after the collision? a. 2.0 m/s b. 1.5 m/s c. 1.0 m/s d. 2.5 m/s e. 3.0 m/s

d. 2.5 m/s

A 4.0-kg mass has a velocity of 4.0 m/s, east when it explodes into two 2.0-kg masses. After the explosion one of the masses has a velocity of 3.0 m/s at an angle of 60° north of east. What is the magnitude of the velocity of the other mass after the explosion? a. 7.9 m/s b. 8.9 m/s c. 7.0 m/s d. 6.1 m/s e. 6.7 m/s

c. 7.0 m/s

A 4.2-kg object, initially at rest, "explodes" into three objects of equal mass. Two of these are determined to have velocities of equal magnitudes (5.0 m/s) with directions that differ by 90°. How much kinetic energy was released in the explosion? a. 70 J b. 53 J c. 60 J d. 64 J e. 35 J

a. 70 J

A 4.0-kg mass, initially at rest on a horizontal frictionless surface, is struck by a 2.0-kg mass moving along the x axis with a speed of 8.0 m/s. After the collision, the 2.0-kg mass has a speed of 4.0 m/s at an angle of 37° from the positive x axis. What is the speed of the 4.0-kg mass after the collision? a. 2.0 m/s b. 2.7 m/s c. 4.9 m/s d. 2.4 m/s e. 3.6 m/s

b. 2.7 m/s

At an instant when a particle of mass 50 g has an acceleration of 80 m/s2 in the positive x direction, a 75-g particle has an acceleration of 40 m/s2 in the positive y direction. What is the magnitude of the acceleration of the center of mass of this two-particle system at this instant? a. 60 m/s2 b. 56 m/s2 c. 40 m/s2 d. 50 m/s2 e. 46 m/s2

c. 40 m/s2

At an instant when a particle of mass 80 g has a velocity of 25 m/s in the positive y direction, a 75-g particle has a velocity of 20 m/s in the positive x direction. What is the speed of the center of mass of this two-particle system at this instant? a. 16 m/s b. 45 m/s c. 23 m/s d. 20 m/s e. 36 m/s

a. 16 m/s

Three particles are placed in the xy plane. A 40-g particle is located at (3, 4) m, and a 50-g particle is positioned at (−2, −6) m. Where must a 20-g particle be placed so that the center of mass of this three-particle system is located at the origin? a. (−1, −3) m b. (−1, 2) m c. (−1, 12) m d. (−1, 7) m e. (−1, 3) m

d. (−1, 7) m

A rocket engine consumes 450 kg of fuel per minute. If the exhaust speed of the ejected fuel is 5.2 km/s, what is the thrust of the rocket? a. 42 kN b. 39 kN c. 45 kN d. 48 kN e. 35 kN

b. 39 kN

A rocket with an initial mass of 1000 kg adjusts its thrust by varying the rate at which mass is ejected. The ejection speed relative to the rocket is 40 km/s. If the acceleration of the rocket is to have a magnitude of 20 m/s2 at an instant when its mass is 80% of the original mass, at what rate is mass being ejected at that instant? Ignore any external forces on the rocket. a. 0.40 kg/s b. 0.50 kg/s c. 0.60 kg/s d. 0.70 kg/s e. 0.80 kg/s

a. 0.40 kg/s

A rocket moving in outer space maintains a constant acceleration (magnitude = 20 m/s2) while ejecting fuel at a speed of 15 km/s relative to the rocket. If the initial mass of the rocket is 3 000 kg, what is the magnitude of the thrust after 800 kg of fuel have been consumed? a. 56 kN b. 48 kN c. 52 kN d. 44 kN e. 36 kN

d. 44 kN

Three particles are placed in the xy plane. A 30-g particle is located at (3, 4) m, and a 40-g particle is located at (−2, −2) m. Where must a 20-g particle be placed so that the center of mass of the three-particle system is at the origin? a. (−3, −1) m b. (+1, +3) m c. (+3, −1) m d. (−1, −3) m e. (−0.5, −2) m

e. (−0.5, −2) m

At the instant a 2.0-kg particle has a velocity of 4.0 m/s in the positive x direction, a 3.0-kg particle has a velocity of 5.0 m/s in the positive y direction. What is the speed of the center of mass of the two-particle system? a. 3.8 m/s b. 3.4 m/s c. 5.0 m/s d. 4.4 m/s e. 4.6 m/s

b. 3.4 m/s

Two 0.20-kg balls, moving at 4 m/s east, strike a wall. Ball A bounces backwards at the same speed. Ball B stops. Which statement correctly describes the change in momentum of the two balls? a. |ΔPB| < |ΔPA| b. |ΔPB| = |ΔPA| c. |ΔPB|> |ΔPA| d. ΔPB = ΔPA. e. ΔPB > ΔPA.

a. |ΔPB| < |ΔPA|

Two bodies with masses m1 and m2 are both moving east with velocities of magnitudes v1 and v2, where v1 is less than v2. The magnitude of the velocity of the center of mass of this system of two bodies is a. less than v1. b. equal to v1. c. equal to the average of v1 and v2. d. greater than v1 and less than v2. e. greater than v2.

d. greater than v1 and less than v2.

A car of mass m1 traveling at velocity v passes a car of mass m2 parked at the side of the road. The momentum of the system of two cars is a. 0. b. m1v. c. (m1 − m2)v. d. e. (m1 + m2)v.

b. m1v.

. Car A rear ends Car B, which has twice the mass of A, on an icy road at a speed low enough so that the collision is essentially elastic. Car B is stopped at a light when it is struck. Car A has mass m and speed v before the collision. After the collision a. each car has half the momentum. b. car A stops and car B has momentum mv. c. car A stops and car B has momentum 2mv. d. the momentum of car B is four times as great in magnitude as that of car A. e. each car has half of the kinetic energy.

d. the momentum of car B is four times as great in magnitude as that of car A.

A 3.00-kg stone is dropped from a 39.2 m high building. When the stone has fallen 19.6 m, the magnitude of the impulse it has received from the gravitational force is a. 9.80 N*s. b. 19.6 N*s. c. 29.4 N*s. d. 58.8 N*s. e. 118 N*s.

d. 58.8 N*s

A 3.00-kg stone is dropped from a 39.2 m high building. When the stone has fallen 19.6 m, the magnitude of the impulse the Earth has received from the gravitational force exerted by the stone is a. 9.80 N*s. b. 19.6 N*s. c. 29.4 N*s. d. 58.8 N*s. e. 118 N*s.

d. 58.8 N s.

Assume that the average mass of each of the approximately 1 billion people in China is 55 kg. Assume that they all gather in one place and climb to the top of 2 m high ladders. The center of mass of the Earth (mE = 5.90 1024 kg) is then displaced a. 0 m. b. 1.84 × 10−23 m. c. 1.84 × 10−14 m. d. 1.80 × 10−13 m. e. 2 m.

c. 1.84 × 10−14 m.

A 0.28-kg stone you throw rises 34.3 m in the air. The magnitude of the impulse the stone received from your hand while being thrown is a. 0.27 N s. b. 2.7 N s. c. 7.3 N s. d. 9.6 N s. e. 34.3 N s.

c. 7.3 N s.

A 0.28-kg stone you throw rises 34.3 m in the air. The impulse your hand receives from the stone while it throws the stone is a. 2.7 N s, up. b. 2.7 N s, down. c. 7.3 N s, up. d. 7.3 N s, down. e. 9.6 N s, up.

d. 7.3 N s, down.

A 0.28-kg stone you throw rises 34.3 m in the air. The impulse the stone receives from your hand while being thrown is a. 2.7 N s, up. b. 2.7 N s, down. c. 7.3 N s, up. d. 7.3 N s, down. e. 9.6 N s, up.

c. 7.3 N s, up.

A catapult fires an 800-kg rock with an initial velocity of 100 m/s at a 40° angle to the ground. The magnitude of the horizontal impulse the catapult receives from the rock is a. 5.1 × 104 N s. b. 6.1 × 104 N s. c. 8.0 × 104 N s. d. 5.0 × 105 N s. e. 6.0 × 105 N s.

b. 6.1 × 104 N s.

A catapult fires an 800-kg rock with an initial velocity of 100 m/s at a 40° angle to the ground. The magnitude of the vertical impulse the catapult receives from the rock is a. 5.1 × 104 N s. b. 6.1 × 104 N s. c. 8.0 × 104 N s. d. 5.0 × 105 N s. e. 6.0 × 105 N s.

a. 5.1 × 104 N s.

A ball falls to the ground from height h and bounces to height h'. Momentum is conserved in the ball-earth system a. no matter what height h' it reaches. b. only if h' < h. c. only if h' = h. d. only if h' > h. e. only if h' ≥ h.

a. no matter what height h' it reaches.

The law of conservation of momentum applies to a collision between two bodies since a. they exert equal and opposite forces on each other. b. they exert forces on each other respectively proportional to their masses. c. they exert forces on each other respectively proportional to their velocities. d. they exert forces on each other respectively inversely proportional to their masses. e. their accelerations are proportional to their masses.

a. they exert equal and opposite forces on each other.

When two bodies of different masses collide, the impulses they exert on each other are a. equal for all collisions. b. equal but opposite for all collisions. c. equal but opposite only for elastic collisions. d. equal but opposite only for inelastic collisions. e. equal but opposite only when the bodies have equal but opposite accelerations.

b. equal but opposite for all collisions.

If you know the impulse that has acted on a body of mass m you can calculate a. its initial velocity. b. its final velocity. c. its final momentum. d. the change in its velocity. e. its acceleration during the impulse.

d. the change in its velocity.

Two boys in a canoe toss a baseball back and forth. What effect will this have on the canoe? Neglect (velocity-dependent) frictional forces with water or air. a. None, because the ball remains in the canoe. b. The canoe will drift in the direction of the boy who throws the ball harder each time. c. The canoe will drift in the direction of the boy who throws the ball with less force each time. d. The canoe will oscillate back and forth always moving opposite to the ball. e. The canoe will oscillate in the direction of the ball because the canoe and ball exert forces in opposite directions upon the person throwing the ball.

d. The canoe will oscillate back and forth always moving opposite to the ball.

An astronaut outside a spaceship hammers a loose rivet back in place. What happens to the astronaut as he swings the hammer? a. Nothing. The spaceship takes up the momentum of the hammer. b. He moves away from the spaceship. c. He moves towards the spaceship. d. He moves towards the spaceship as he pulls the hammer back and moves away from it as he swings the hammer forward. e. He moves away from the spaceship as he pulls the hammer back and moves toward it as he swings the hammer forward.

d. He moves towards the spaceship as he pulls the hammer back and moves away from it as he swings the hammer forward.

The value of the momentum of a system is the same at a later time as at an earlier time if there are no a. collisions between particles within the system. b. inelastic collisions between particles within the system. c. changes of momentum of individual particles within the system. d. internal forces acting between particles within the system. e. external forces acting on particles of the system.

e. external forces acting on particles of the system.

When the rate of burn and the exhaust velocity are constant, a rocket ascends with a. decreasing acceleration. b. decreasing velocity. c. constant velocity. d. constant acceleration. e. increasing acceleration.

e. increasing acceleration.

. Two cars start at the same point, but travel in opposite directions on a circular path of radius R, each at speed v. While each car travels a distance less than pi/2R, one quarter circle, the center of mass of the two cars a. remains at the initial point. b. travels along a diameter of the circle at speed v' < v. c. travels along a diameter of the circle at speed v' = v. d. travels along a diameter of the circle at speed v' > v. e. remains at the center of the circle.

b. travels along a diameter of the circle at speed v' < v.

. A ball of mass mB is released from rest and acquires velocity of magnitude vB before hitting the ground. The ratio of the magnitude of the momentum the Earth acquires to the magnitude of the momentum the ball acquires is a. 0. b. (mB/mE)^2 c. mB/mE d. 1 e. mE/mB

d. 1

A ball of mass mB is released from rest and acquires velocity of magnitude vB before hitting the ground. The ratio of the kinetic energy the Earth acquires to the kinetic energy the ball acquires is a. 0. b. (mB/mE)^2 c. mB/mE d. 1 e. mE/mB

c. mB/mE

A ball of mass mB is released from rest and acquires velocity of magnitude vB before hitting the ground. The ratio of the impulse delivered to the Earth to the impulse delivered to the ball is a. 0. b. (mB/mE)^2 c. mB/mE d. 1 e. mE/mB

d. 1

Two bodies of equal mass m collide and stick together. The quantities that always have equal magnitude for both masses during the collision are a. their changes in momentum. b. the force each exerts on the other. c. their changes in kinetic energy. d. all of the above. e. only (a) and (b) above.

e. only (a) and (b) above.

A steel ball bearing of mass m1 and speed of magnitude v1 has a head-on elastic collision with a steel ball bearing of mass m2 at rest. Rank the speed v1 of m1 relative to v2, the magnitude of the speed of m2, after the collision when i) m1 > m2; ii) m1 = m2; and iii) m1 < m2. a. v1 < v2; v1 < v2; v1 < v2 b. v1 < v2; v1 = v2; v1 > v2 c. v1 < v2; v1 > v2; v1 > v2 d. v1 > v2; v1 = v2; v1 < v2 e. v1 > v2; v1 > v2; v1 > v2

b. v1 < v2; v1 = v2; v1 > v2

Stan argues that momentum cannot be conserved when a collision is not a head-on collision. Rachel insists it is conserved because each body receives an impulse of equal magnitude. Rachel is correct because a. each body exerts an equal and opposite force on the other during the collision. b. the forces act during equal time intervals. c. the law of conservation of momentum for an isolated system is a vector equation. d. of all of the above. e. of only (a) and (b) above.

d. of all of the above.

In an elastic collision between two bodies of equal mass, with body 2 initially at rest, body 1 moves off at angle θ relative to the direction of its initial velocity and body 2 at angle φ. The sine of the sum of θ and φ, sin(θ + φ), is equal to a. 0. b. 0.500. c. 0.707. d. 0.866. e. 1.00.

e. 1.00.

An exam paper contains the following equation for rocket propulsion: (M + Δm)v = M(v+Δv) + Δm(v+ve) The error in the equation is that, instead of (v + ve), the velocity of the fuel relative to the ground should be a. −ve. b. +ve. c. v − ve. d. ve − v. e. 2ve.

c. v − ve.

. In an elastic collision between two bodies of mass m1 and m2, with m2 initially at rest, mass 1 moves off at angle θ relative to the direction of its initial velocity and mass 2 at angle φ. An exam paper shows the equations below: m1v1i 0 = m1v1f cosθ + m2v2f sinφ = m1v1f sinθ + m2v2f cosφ What error(s) has the student made? a. In the first equation, m2v2f sinφ should be m2v2f cosφ. b. In the second equation, m2v2f cosφ should be m2v2f sinφ. c. In the second equation, the plus sign between the terms on the right should be a minus sign. d. All of the errors listed above. e. Only errors (a) and (b) above.

d. All of the errors listed above.

Exhibit 9-1 Two birds of prey hurtling after the same mouse collide in mid-air and grab each other with their talons. Each 250-g bird is flying at 30 m/s at a 60° angle to the ground. Use this exhibit to answer the following question(s). 79. Refer to Exhibit 9-1. What is the magnitude of their total momentum, in kg*m / s, immediately after the collision? a. 0 b. 6.5 c. 7.5 d. 13 e. 15

d. 13

Refer to Exhibit 9-1. What is the magnitude of their velocity, in m/s, immediately after the collision? a. 0 b. 13 c. 15 d. 26 e. 30

d. 26

Refer to Exhibit 9-What is the horizontal component of their momentum, in kg*m / s , immediately after the collision? a. 0 b. 6.1 c. 7.5 d. 13 e. 15

a. 0

A 500-g firework explodes into two pieces of equal mass at an instant when it is traveling straight up at 10 m/s. If one half shoots off horizontally to the left at 20 m/s, what is the velocity, in m/s, of the other half immediately after the explosion? (The x axis is directed right; the y axis up.) a. -20i-20j b. -20i+20j c. +20i-20j d. +20i+20j e. -20i+20k

d. +20i+20j

The linear density of a rod, in g/m, is given by mew = 40.0 + 30.0x. The rod extends from the origin to x = 0.400 m. What is the mass of the rod? a. 0.213 g b. 3.50 g c. 3.84 g d. 18.4 g e. 20.8 g

d. 18.4 g

The linear density of a rod, in g/m, is given by mew = 40.0 + 30.0x. The rod extends from the origin to x = 0.400 m. What is the location of the center of mass of the rod? a. x = 0.213 m b. x = 0.315 m c. x = 0.384 m d. x = 0.184 m e. x = 0.208 m

a. x = 0.213 m

A child bounces a 50-gram superball on the sidewalk. The velocity of the superball changes from 21 m/s downward to 19 m/s upward. If the contact time with the sidewalk is 1/800 s, what is the magnitude of the force exerted on the superball by the sidewalk?

1600 N

High-speed stroboscopic photographs show that the head of a golf club of mass 200 grams is traveling at 55.0 m/s just before it strikes a 46.0-gram golf ball at rest on a tee. After the collision, the clubhead travels (in the same direction) at 40.0 m/s. Find the speed of the golf ball just after impact.

65.2 m/s

A pitcher claims he can throw a baseball with as much momentum as a 3.00-g bullet moving with a speed of 1500 m/s. A baseball has a mass of 0.145 kg. What must be its speed if the pitcher's claim is valid?

31.0 m/s

2.56 * 10^5 m/s

A uniform thin wire has a length and is bent into a semicircular arc of radius R. If the wire starts at (x, y) = (R, 0) and curves counterclockwise to (x, y) = (−R, 0), what is the y coordinate of its center of mass?

0.637 R

At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s. Two seconds later it has turned through 5.0 complete revolutions. What is the angular acceleration of this wheel? a. 17 rad/s2 b. 14 rad/s2 c. 20 rad/s2 d. 23 rad/s2 e. 13 rad/s2

b. 14 rad/s2

At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration of −0.40 rad/s2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad. What is the angular position of the wheel at t = 2.0 s? a. 4.9 rad b. 4.7 rad c. 4.5 rad d. 4.3 rad e. 4.1 rad

c. 4.5 rad

A wheel rotating about a fixed axis has an angular position given by θ = 3.0 − 2.0t3, where θ is measured in radians and t in seconds. What is the angular acceleration of the wheel at t = 2.0 s? a. −1.0 rad/s2 b. −24 rad/s2 c. −2.0 rad/s2 d. −4.0 rad/s2 e. −3.5 rad/s2

b. −24 rad/s2

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 turns through 2.4 revolutions during a 2.0-s time interval. What is the angular velocity at the end of this time interval? a. 9.5 rad/s b. 9.7 rad/s c. 9.3 rad/s d. 9.1 rad/s e. 8.8 rad/s

a. 9.5 rad/s

The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off. The turntable comes to rest 2.5 s after being turned off. Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration. a. 12 rad b. 8.0 rad c. 10 rad d. 16 rad e. 6.8 rad

c. 10 rad

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity increases to 40 rad/s. Assume that the angular acceleration was constant during the 5.0-s interval. How many revolutions does the wheel turn through during the 5.0-s interval? a. 20 rev b. 24 rev c. 32 rev d. 28 rev e. 39 rev

b. 24 rev

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval? a. 95 rad b. 85 rad c. 65 rad d. 75 rad e. 125 rad

d. 75 rad

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis. It completes the first revolution 6.0 s after it started. How long after it started will the wheel complete the second revolution? a. 9.9 s b. 7.8 s c. 8.5 s d. 9.2 s e. 6.4 s

c. 8.5 s

A thin uniform rod (length = 1.2 m, mass = 2.0 kg) is pivoted about a horizontal, frictionless pin through one end of the rod. (The moment of inertia of the rod about this axis is ML2/3.) The rod is released when it makes an angle of 37° with the horizontal. What is the angular acceleration of the rod at the instant it is released? a. 9.8 rad/s2 b. 7.4 rad/s2 c. 8.4 rad/s2 d. 5.9 rad/s2 e. 6.5 rad/s2

a. 9.8 rad/s2

A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s2. In a 4.0-s interval the wheel turns through an angle of 80 radians. Assuming the wheel started from rest, how long had it been in motion at the start of the 4.0-s interval? a. 2.5 s b. 4.0 s c. 3.5 s d. 3.0 s e. 4.5 s

d. 3.0 s

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 starts from rest at t = 0. The wheel has a diameter of 20 cm. What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s? a. 0.25 m/s2 b. 0.50 m/s2 c. 0.14 m/s2 d. 0.34 m/s2 e. 0.20 m/s2

a. 0.25 m/s2

A wheel rotates about a fixed axis with a constant angular acceleration of 4.0 rad/s2. The diameter of the wheel is 40 cm. What is the linear speed of a point on the rim of this wheel at an instant when that point has a total linear acceleration with a magnitude of 1.2 m/s2? a. 39 cm/s b. 42 cm/s c. 45 cm/s d. 35 cm/s e. 53 cm/s

b. 42 cm/s

A disk (radius = 8.0 cm) that rotates about a fixed axis starts from rest and accelerates at a constant rate to an angular velocity of 4.0 rad/s in 2.0 s. What is the magnitude of the total linear acceleration of a point on the rim of the disk at the instant when the angular velocity of the disk is 1.5 rad/s? a. 24 cm/s2 b. 16 cm/s2 c. 18 cm/s2 d. 34 cm/s2 e. 44 cm/s2

a. 24 cm/s2

A mass (M1 = 5.0 kg) is connected by a light cord to a mass (M2 = 4.0 kg) which slides on a smooth surface, as shown in the figure. The pulley (radius = 0.20 m) rotates about a frictionless axle. The acceleration of M2 is 3.5 m/s2. What is the moment of inertia of the pulley? a. 0.29 kg⋅m2 b. 0.42 kg⋅m2 c. 0.20 kg⋅m2 d. 0.62 kg⋅m2 e. 0.60 kg⋅m2

c. 0.20 kg⋅m2

A wheel (radius = 0.20 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50-kg object, as shown in the figure. When released from rest the object falls with a downward acceleration of 5.0 m/s2. What is the moment of inertia of the wheel? a. 0.023 kg⋅m2 b. 0.027 kg⋅m2 c. 0.016 kg⋅m2 d. 0.019 kg⋅m2 e. 0.032 kg⋅m2

d. 0.019 kg⋅m2

A wheel (radius = 0.25 m) is mounted on a frictionless, horizontal axis. The moment of inertia of the wheel about the axis is 0.040 kg⋅m2. A light cord wrapped around the wheel supports a 0.50-kg object as shown in the figure. The object is released from rest. What is the magnitude of the acceleration of the 0.50-kg object? a. 3.0 m/s2 b. 3.4 m/s2 c. 4.3 m/s2 d. 3.8 m/s2 e. 2.7 m/s2

c. 4.3 m/s2

A mass m = 4.0 kg is connected, as shown, by a light cord to a mass M = 6.0 kg, which slides on a smooth horizontal surface. The pulley rotates about a frictionless axle and has a radius R = 0.12 m and a moment of inertia I = 0.090 kg⋅m2. The cord does not slip on the pulley. What is the magnitude of the acceleration of m? a. 2.4 m/s2 b. 2.8 m/s2 c. 3.2 m/s2 d. 4.2 m/s2 e. 1.7 m/s2

a. 2.4 m/s2

A cylinder rotating about its axis with a constant angular acceleration of 1.6 rad/s2 starts from rest at t = 0. At the instant when it has turned through 0.40 radian, what is the magnitude of the total linear acceleration of a point on the rim (radius = 13 cm)? a. 0.31 m/s2 b. 0.27 m/s2 c. 0.35 m/s2 d. 0.39 m/s2 e. 0.45 m/s2

b. 0.27 m/s2

A wheel (radius = 0.20 m) starts from rest and rotates with a constant angular acceleration of 2.0 rad/s2. At the instant when the angular velocity is equal to 1.2 rad/s, what is the magnitude of the total linear acceleration of a point on the rim of the wheel? a. 0.40 m/s2 b. 0.29 m/s2 c. 0.69 m/s2 d. 0.49 m/s2 e. 0.35 m/s2

d. 0.49 m/s2

A horizontal disk with a radius of 10 cm rotates about a vertical axis through its center. The disk starts from rest at t = 0 and has a constant angular acceleration of 2.1 rad/s2. At what value of t will the radial and tangential components of the linear acceleration of a point on the rim of the disk be equal in magnitude? a. 0.55 s b. 0.63 s c. 0.69 s d. 0.59 s e. 0.47 s

c. 0.69 s

Two particles (m1 = 0.20 kg, m2 = 0.30 kg) are positioned at the ends of a 2.0-m long rod of negligible mass. What is the moment of inertia of this rigid body about an axis perpendicular to the rod and through the center of mass? a. 0.48 kg⋅m2 b. 0.50 kg⋅m2 c. 1.2 kg⋅m2 d. 0.80 kg⋅m2 e. 0.70 kg⋅m2

a. 0.48 kg⋅m2

Four identical particles (mass of each = 0.24 kg) are placed at the vertices of a rectangle (2.0 m × 3.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the center of mass of the body and is parallel to the shorter sides of the rectangle? a. 2.4 kg⋅m2 b. 2.2 kg⋅m2 c. 1.9 kg⋅m2 d. 2.7 kg⋅m2 e. 8.6 kg⋅m2

b. 2.2 kg⋅m2

Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.5 m × 4.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the shorter sides and is parallel to the longer sides? a. 2.2 kg⋅m2 b. 2.8 kg⋅m2 c. 2.5 kg⋅m2 d. 3.1 kg⋅m2 e. 1.6 kg⋅m2

c. 2.5 kg⋅m2

. Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.0 m × 3.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the longer sides and is parallel to the shorter sides? a. 2.7 kg⋅m2 b. 3.6 kg⋅m2 c. 3.1 kg⋅m2 d. 4.1 kg⋅m2 e. 1.6 kg⋅m2

b. 3.6 kg⋅m2

The rigid object shown is rotated about an axis perpendicular to the paper and through point P. The total kinetic energy of the object as it rotates is equal to 1.4 J. If M = 1.3 kg and L = 0.50 m, what is the angular velocity of the object? Neglect the mass of the connecting rods and treat the masses as particles. a. 1.3 rad/s b. 1.5 rad/s c. 1.7 rad/s d. 1.2 rad/s e. 2.1 rad/s

c. 1.7 rad/s

If M = 0.50 kg, L = 1.2 m, and the mass of each connecting rod shown is negligible, what is the moment of inertia about an axis perpendicular to the paper through the center of mass? Treat the mass as particles. a. 3.7 kg⋅m2 b. 2.8 kg⋅m2 c. 3.2 kg⋅m2 d. 2.3 kg⋅m2 e. 3.9 kg⋅m2

d. 2.3 kg⋅m2

Three particles, each of which has a mass of 80 g, are positioned at the vertices of an equilateral triangle with sides of length 60 cm. The particles are connected by rods of negligible mass. What is the moment of inertia of this rigid body about an axis that is parallel to one side of the triangle and passes through the respective midpoints of the other two sides? a. 0.018 kg⋅m2 b. 0.020 kg⋅m2 c. 0.016 kg⋅m2 d. 0.022 kg⋅m2 e. 0.032 kg⋅m2

c. 0.016 kg⋅m2

A uniform rod (mass = 2.0 kg, length = 0.60 m) is free to rotate about a frictionless pivot at one end. The rod is released from rest in the horizontal position. What is the magnitude of the angular acceleration of the rod at the instant it is 60° below the horizontal? a. 15 rad/s2 b. 12 rad/s2 c. 18 rad/s2 d. 29 rad/s2 e. 23 rad/s2

b. 12 rad/s2

. Particles (mass of each = 0.20 kg) are placed at the 40-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the initial angular acceleration of the body? a. 12 rad/s2 b. 5.9 rad/s2 c. 8.4 rad/s2 d. 5.4 rad/s2 e. 17 rad/s2

a. 12 rad/s2

Particles (mass of each = 0.40 kg) are placed at the 60-cm and 100-cm marks of a meter stick of negligible mass. This rigid body is free to rotate about a frictionless pivot at the 0-cm end. The body is released from rest in the horizontal position. What is the magnitude of the initial linear acceleration of the end of the body opposite the pivot? a. 15 m/s2 b. 9.8 m/s2 c. 5.8 m/s2 d. 12 m/s2 e. 4.7 m/s2

d. 12 m/s2

A wheel (radius = 12 cm) is mounted on a frictionless, horizontal axle that is perpendicular to the wheel and passes through the center of mass of the wheel. A light cord wrapped around the wheel supports a 0.40-kg object. If released from rest with the string taut, the object is observed to fall with a downward acceleration of 3.0 m/s2. What is the moment of inertia (of the wheel) about the given axle? a. 0.023 kg⋅m2 b. 0.013 kg⋅m2 c. 0.020 kg⋅m2 d. 0.016 kg⋅m2 e. 0.035 kg⋅m2

b. 0.013 kg⋅m2

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 30° above the horizontal. What is the angular acceleration of the rod at the instant it is released? a. 4.7 rad/s2 b. 6.9 rad/s2 c. 6.4 rad/s2 d. 5.6 rad/s2 e. 4.2 rad/s2

c. 6.4 rad/s2

A uniform rod is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at the horizontal position. What is the angular acceleration of the rod at the instant the rod makes an angle of 70° with the horizontal? a. 3.7 rad/s2 b. 1.3 rad/s2 c. 2.5 rad/s2 d. 4.9 rad/s2 e. 1.9 rad/s2

c. 2.5 rad/s2

A uniform rod of mass M = 1.2 kg and length L = 0.80 m, lying on a frictionless horizontal plane, is free to pivot about a vertical axis through one end, as shown. The moment of inertia of the rod about this axis is given by (1/3)ML2. If a force (F = 5.0 N, θ = 40°) acts as shown, what is the resulting angular acceleration about the pivot point? a. 16 rad/s2 b. 12 rad/s2 c. 14 rad/s2 d. 10 rad/s2 e. 33 rad/s2

d. 10 rad/s2

A uniform meter stick is pivoted to rotate about a horizontal axis through the 25-cm mark on the stick. The stick is released from rest in a horizontal position. The moment of inertia of a uniform rod about an axis perpendicular to the rod and through the center of mass of the rod is given by (1/12)ML2. Determine the magnitude of the initial angular acceleration of the stick. a. 17 rad/s2 b. 13 rad/s2 c. 15 rad/s2 d. 19 rad/s2 e. 23 rad/s2

a. 17 rad/s2

A uniform rod (length = 2.0 m) is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through the rod at a point 0.50 m from one end of the rod. If the rod is released from rest in a horizontal position, what is the angular speed of the rod as it rotates through its lowest position? a. 3.5 rad/s b. 3.8 rad/s c. 4.1 rad/s d. 2.0 rad/s e. 5.6 rad/s

c. 4.1 rad/s

Identical particles are placed at the 50-cm and 80-cm marks on a meter stick of negligible mass. This rigid body is then mounted so as to rotate freely about a pivot at the 0-cm mark on the meter stick. If this body is released from rest in a horizontal position, what is the angular speed of the meter stick as it swings through its lowest position? a. 4.2 rad/s b. 5.4 rad/s c. 4.6 rad/s d. 5.0 rad/s e. 1.7 rad/s

b. 5.4 rad/s

A uniform rod (mass = 1.5 kg) is 2.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest in a horizontal position. What is the angular speed of the rod when the rod makes an angle of 30° with the horizontal? (The moment of inertia of the rod about the pin is 2.0 kg⋅m2). a. 2.2 rad/s b. 3.6 rad/s c. 2.7 rad/s d. 3.1 rad/s e. 1.8 rad/s

c. 2.7 rad/s

A uniform rod is 3.0 m long. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 27° above the horizontal. What is the angular speed of the rod as it passes through the horizontal position? a. 3.0 rad/s b. 2.8 rad/s c. 2.1 rad/s d. 2.5 rad/s e. 3.4 rad/s

c. 2.1 rad/s

A uniform rod of length (L = 2.0 m) and mass (M = 1.5 kg) is pivoted about a horizontal frictionless pin through one end. The rod is released from rest at an angle of 30° below the horizontal. What is the angular speed of the rod when it passes through the vertical position? (The moment of inertia of the rod about the pin is 2.0 kg⋅m2.) a. 3.5 rad/s b. 2.7 rad/s c. 3.1 rad/s d. 2.3 rad/s e. 1.6 rad/s

b. 2.7 rad/s

A nonuniform 2.0-kg rod is 2.0 m long. The rod is mounted to rotate freely about a horizontal axis perpendicular to the rod that passes through one end of the rod. The moment of inertia of the rod about this axis is 4.0 kg⋅m2. The center of mass of the rod is 1.2 m from the axis. If the rod is released from rest in the horizontal position, what is its angular speed as it swings through the vertical position? a. 3.4 rad/s b. 4.4 rad/s c. 4.3 rad/s d. 5.8 rad/s e. 6.8 rad/s

a. 3.4 rad/s

The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper. If M = 2.0 kg and L = 80 cm, what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod and treat the masses as particles. a. 18 J b. 15 J c. 12 J d. 23 J e. 26 J

c. 12 J

The rigid body shown is rotated about an axis perpendicular to the paper and through the point P. If M = 0.40 kg, a = 30 cm, and b = 50 cm, how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles. a. 2.9 J b. 2.6 J c. 3.1 J d. 3.4 J e. 1.6 J

b. 2.6 J

A uniform rod (length = 2.4 m) of negligible mass has a 1.0-kg point mass attached to one end and a 2.0-kg point mass attached to the other end. The rod is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through a point 1.0 m from the 2.0-kg mass. The rod is released from rest when it is horizontal. What is the angular velocity of the rod at the instant the 2.0-kg mass passes through its low point? a. 1.7 rad/s b. 2.2 rad/s c. 2.0 rad/s d. 1.5 rad/s e. 3.1 rad/s

a. 1.7 rad/s

A campus bird spots a member of an opposing football team in an amusement park. The football player is on a ride where he goes around at angular velocity ω at distance R from the center. The bird flies in a horizontal circle above him. Will a dropping the bird releases while flying directly above the person's head hit him? a. Yes, because it falls straight down. b. Yes, because it maintains the acceleration of the bird as it falls. c. No, because it falls straight down and will land behind the person. d. Yes, because it maintains the angular velocity of the bird as it falls. e. No, because it maintains the tangential velocity the bird had at the instant it started falling.

e. No, because it maintains the tangential velocity the bird had at the instant it started falling.

Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars. If the two cars are in line at t = 0, and moving at 3ω and ω respectively, at what time will they next pass each other? a. t = 0. b. t = pi/2w c. t = pi/w d. t = 2pi/w e. t = 3pi/w

c. t = pi/w

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track. Through how many radians does the car travel in the first 10 minutes? a. 30 b. 50 c. 70 d. 90 e. 100

c. 70

The graphs below show angular velocity as a function of time. In which one is the magnitude of the angular acceleration constantly decreasing?

+ Exponential Curve

You throw a Frisbee of mass m and radius r so that it is spinning about a horizontal axis perpendicular to the plane of the Frisbee. Ignoring air resistance, the torque exerted about its center of mass by gravity is a. 0. b. mgr. c. 2mgr. d. a function of the angular velocity. e. small at first, then increasing as the Frisbee loses the torque given it by your hand.

a. 0.

Two forces of magnitude 50 N, as shown in the figure below, act on a cylinder of radius 4 m and mass 6.25 kg. The cylinder, which is initially at rest, sits on a frictionless surface. After 1 second, the velocity and angular velocity of the cylinder in m/s and rad/s are respectively a. v = 0; ω = 0. b. v = 0; ω = 4. c. v = 0; ω = 8. d. v = 8; ω = 8. e. v = 16; ω = 8.

b. v = 0; ω = 4.

Two cylinders made of the same material roll down a plane inclined at an angle θ with the horizontal. Each travels the same distance. The radius of cylinder B is twice the radius of cylinder A. In what order do they reach the bottom? a. A reaches the bottom first because it has the greater acceleration. b. A reaches the bottom first because it has a smaller moment of inertia. c. B reaches the bottom first because is experiences a larger torque. d. B reaches the bottom first because it travels a larger distance in one rotation. e. They both reach the bottom at the same time, because each has the same linear acceleration.

e. They both reach the bottom at the same time, because each has the same linear acceleration.

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s). 52. Refer to Exhibit 10-1. What is her angular displacement (in rad) in the first 8 minutes? a. 0 b. π c. 4π d. 8π e. 16π

e. 16π

Refer to Exhibit 10-1. What is her angular displacement (in rad) in the first 12 minutes? a. 0 b. 2π c. 4π d. 16π e. 32π

e. 32π

Refer to Exhibit 10-1. What is her angular displacement (in rad) in the 16 minute period shown in the graph? a. 0 b. 16π c. 32π d. 40π e. 64π

d. 40π

Refer to Exhibit 10-1. How many revolutions does she complete in the first 12 minutes? a. 4 b. 8 c. 12 d. 16 e. 32

d. 16

Refer to Exhibit 10-1. How many revolutions does she complete in the 16 minute period? a. 8 b. 12 c. 16 d. 20 e. 40

d. 20

A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere, as shown below. The moment of inertia of the sphere about this axis is a. 2/5MR^2 b. 2/3MR^2 c. 5/7MR^2 d. 7/5MR^2 e. 3/2MR^2

d. 7/5MR^2

A uniform cylinder of radius R, mass M, and length L rotates freely about a horizontal axis parallel and tangent to the cylinder, as shown below. The moment of inertia of the cylinder about this axis is a. 1/2MR^2 b. 2/3MR^2 c. MR^2 d. 3/2MR^2 e. 7/5MR^2

d. 3/2MR^2

The angular speed of the minute hand of a clock, in rad/s, is a. 1/1800π b. 1/60π c. 1/30π d. π. e. 120π.

c. 1/30π

The angular speed of the hour hand of a clock, in rad/s, is a. 1/7200π b. 1/1800π c. 1/30π d. 1 800π. e. 7 200π.

b. 1/1800π

The angular speed of the hour hand of a clock, in rad/min, is a. 1/1800π b. 1/60π c. 1/30π d. π. e. 120π.

c. 1/30π

Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s). Refer to Exhibit 10-2. What is his average angular acceleration, in rad/s2, in the first 10 minutes? a. 0 b. -pi/150 c. -pi/75 d. +pi/75 e. +pi/150

c. -pi/75

Refer to Exhibit 10-2. What is his average angular acceleration, in rad/s2, in the period from t = 6 min to t = 8 min? a. 0 b. -pi/90 c. -pi/30 d. +pi/30 e. +pi/90

c. -pi/30

Which of the following diagrams shows the greatest magnitude net torque with a zero net force? All the rods, of length 2r, rotate about an axis that is perpendicular to the rod and fixed in the center of the rod. All the forces are of magnitude F or 2F and all distances from the axis are r or r/2.

b. stick with one arrow at very top and one arrow at very bottom

A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod. Relative to the positive direction of the axis of rotation, the angular positions of the sphere are positive, its angular velocity is positive, and its angular acceleration is negative. The sphere is a. rotating clockwise and slowing down. b. rotating counterclockwise and slowing down. c. rotating clockwise and speeding up. d. rotating counterclockwise and speeding up. e. first rotating clockwise and then counterclockwise.

b. rotating counterclockwise and slowing down.

A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod. Relative to the positive direction of the axis of rotation, the angular positions of the sphere are negative, its angular velocity is negative, and its angular acceleration is positive. The sphere is a. rotating clockwise and slowing down. b. rotating counterclockwise and slowing down. c. rotating clockwise and speeding up. d. rotating counterclockwise and speeding up. e. first rotating counterclockwise and then clockwise.

a. rotating clockwise and slowing down.

A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod. Relative to the positive direction of the axis of rotation, the angular positions of the sphere are negative, its angular velocity is negative, and its angular acceleration is negative. The sphere is a. rotating clockwise and slowing down. b. rotating counterclockwise and slowing down. c. rotating clockwise and speeding up. d. rotating counterclockwise and speeding up. e. first rotating counterclockwise and then clockwise.

c. rotating clockwise and speeding up.

Exhibit 10-3 The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s. Use this exhibit to answer the following question(s). Refer to Exhibit 10-3. The change in angular position, Δθ, during the 7-second period is a. 21 rad, CW. b. 21 rad, CCW. c. 30 rad, CW. d. 30 rad, CCW. e. 39 rad, CCW.

d. 30 rad, CCW.

Refer to Exhibit 10-3. The angular position, θ, at t = 0 s is 3.0 rad, clockwise. The angular position, θ, at t = 7 s is a. 27 rad, CW. b. 27 rad, CCW. c. 33 rad, CW. d. 33 rad, CCW. e. 36 rad, CCW.

b. 27 rad, CCW.

The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s. The change in angular velocity, Δω, during this 8-second period is a. 18 rad/s CW. b. 18 rad/s CCW. c. 23 rad/s CW. d. 23 rad/s CCW. e. 31 rad/s CW.

c. 23 rad/s CW.

When a wheel is rolling without slipping, the magnitude of its velocity relative to the ground is greatest at a. the point in contact with the ground. b. the point at the center of the wheel. c. the point at the top of the wheel opposite to the point in contact with the ground. d. the point farthest forward from the center of mass of the wheel. e. the point farthest behind the center of mass of the wheel.

c. the point at the top of the wheel opposite to the point in contact with the ground.

The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s. The angular velocity at t = 0 s is , CCW. The angular velocity, ω, at t = 8 s is a. 18 rad/s CW. b. 18 rad/s CCW. c. 23 rad/s CW. d. 23 rad/s CCW. e. 43 rad/s CW.

a. 18 rad/s CW.

A rigid rod of length l rotates about an axis perpendicular to the rod, with one end of the rod fixed to the axis. Which of the following are equal at all points on the rod? I. the angular position II. the angular velocity III. the angular acceleration IV. the centripetal acceleration V. the tangential acceleration a. I and II b. I, II, and III c. I, II, III and IV d. I, II, III, IV and V e. I, II and IV.

b. I, II, and III

When the sum of the external forces and the sum of the external torques on a body are both zero, we can conclude that a. the body is moving at constant velocity but is not rotating. b. the body is rotating at constant angular velocity but has no linear velocity. c. the body has neither linear nor angular velocity. d. the body may have constant linear or angular velocity, but not both simultaneously. e. the body may have constant linear or constant angular velocity, or both simultaneously.

e. the body may have constant linear or constant angular velocity, or both simultaneously.

When the center of a bicycle wheel has linear velocity relative to the ground, the velocity relative to the ground of point P' at the top of the wheel is a. 0. b. V cm c. 2V cm d. -V cm e. -2V cm

c. 2V cm

A solid sphere, a solid cylinder, and a hoop all have the same mass and radius. Each are sent down identical inclined planes starting from rest. Their kinetic energies at the bottom of the incline are Ksphere, Kcylinder, and Khoop. Which of the following is true? a. Ksphere > Kcylinder b. Khoop > Ksphere c. Khoop > Kcylinder d. Kcylinder > Khoop e. No answer above is correct.

e. No answer above is correct.

A solid sphere, a solid cylinder, a spherical shell, and a hoop all have the same mass and radius. Each are rolling on a horizontal surface with the same center of mass speed, and then they roll up identical inclines. Which one goes the greatest distance up its incline? a. the hoop b. the solid sphere c. the spherical shell d. the cylinder e. They all go the same distance up their inclines.

a. the hoop

The net work done in accelerating a propeller from rest to an angular velocity of 200 rad/s is 3 000 J. What is the moment of inertia of the propeller?

0.15 kg*m^2

A horizontal force of magnitude 6.5 N is exerted tangentially on a Frisbee of mass 32 grams and radius 14.3 cm. Assuming the Frisbee, a uniform disk, is originally at rest and the force is exerted for 0.08 s, determine the angular velocity of rotation about the central axis when the Frisbee is released.

227 rad/s

1590 km

A uniform solid sphere rolls without slipping along a horizontal surface. What fraction of its total kinetic energy is in the form of rotational kinetic energy about the CM?

2/7

A rod of length 1.00 m has a mass per unit length given by , where is in kg/m. The rod is placed on the x axis going from x = 0.00 m to x = 1.00 m. What is the moment of inertia of the rod in kg m2 about the y axis?

0.867

Two vectors lying in the xy plane are given by the equations A = 5i+2j and B=2i-3j . The value of A*B is a. 19k b. −11k c. −19k d. 11k e. 10i-j

c. −19k

Two vectors lying in the xz plane are given by the equations A=2i+3k and B=-i+2k . The value of A*B is a. j b. -j c. 7k d. −7j e. i+5j

d. −7j

. A particle located at the position vector r = (i+j) m has a force F = (2i+3j) N acting on it. The torque about the origin is a. (1k )N⋅m b. (5k )N⋅m c. (−1k )N⋅m d. (−5k )N⋅m e. (2i + 3j )N⋅m

a. (1k )N⋅m

A car of mass 1 000 kg moves with a speed of 50 m/s on a circular track of radius 100 m. What is the magnitude of its angular momentum (in kg⋅m2/s) relative to the center of the race track? a. 5.0 × 10^2 b. 5.0 × 10^6 c. 2.5 × 10^4 d. 2.5 × 10^6 e. 5.0 × 10^3

b. 5.0 × 10^6

A solid cylinder of radius R = 1.0 m and mass 10 kg rotates about its axis. When its angular velocity is 10 rad/s, its angular momentum (in kg⋅m2/s) is a. 50. b. 20. c. 40. d. 25. e. 70.

a. 50.

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s in the x direction along the line y = 5. What is its angular momentum (in kg⋅m2/s) relative to the origin? a. −30k b. 30k c. −15k d. 15k e. 45k

a. −30k

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s along the direction r = i+j . What is its angular momentum (in kg⋅m2/s) relative to the origin? a. 0k b. 6sqrt2k c. -6sqrt2k d. 6k e. −6k

a. 0k

A particle whose mass is 2.0 kg moves in the xy plane with a constant speed of 3.0 m/s along the direction r = i+j . What is its angular momentum (in kg⋅m2/s) relative to the point (0, 5.0) meters? a. 12k b. 11k c. 13k d. 14k e. 21k

e. 21k

In the figure, a 1.6-kg weight swings in a vertical circle at the end of a string having negligible weight. The string is 2 m long. If the weight is released with zero initial velocity from a horizontal position, its angular momentum (in kg⋅m2/s) at the lowest point of its path relative to the center of the circle is approximately a. 40 b. 10 c. 30 d. 20 e. 50

d. 20

A massless rope is wrapped around a uniform cylinder that has radius R and mass M, as shown in the figure. Initially, the unwrapped portion of the rope is vertical and the cylinder is horizontal. The linear acceleration of the cylinder is a. (2/3)g b. (1/2)g c. (1/3)g d. (1/6)g e. (5/6)g

a. (2/3)g

Two blocks, m1 = 1.0 kg and m2 = 2.0 kg, are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its moment of inertia is 5.0 kg⋅m2, the acceleration of the system is a. (1/6)g b. (3/8)g c. (1/8)g d. (1/2)g e. (5/8)g

c. (1/8)g

A puck on a frictionless air hockey table has a mass of 5.0 kg and is attached to a cord passing through a hole in the surface as in the figure. The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s. The angular momentum of the puck (in kg⋅m2/s) is a. 80 b. 20 c. 30 d. 60 e. 50

d. 60

A pendulum bob of mass m is set into motion in a circular path in a horizontal plane as shown in the figure. The square of the angular momentum of the bob about the vertical axis through the point P is a. m2 gl3 sin4 θ/cos θ b. m2 gl3 sin3 θ/cos θ c. m2 gl3 sin2 θ/cos θ d. m2 gl3 sin θ/cos θ e. m2 gl3 sin2 θ

a. m2 gl3 sin4 θ/cos θ

A puck on a frictionless air hockey table has a mass of 5.0 g and is attached to a cord passing through a hole in the surface as in the figure. The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s. The cord is then pulled from below, shortening the radius to 1.0 m. The new angular velocity (in rad/s) is a. 4.0 b. 6.0 c. 12 d. 2.0 e. 8.0

c. 12

A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in the figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is a. (m + M/3)(vL/2) b. (m + M/12)(vL/2) c. (m + M/6)(vL/2) d. mvL/2 e. mvL

d. mvL/2

A particle of mass m = 0.10 kg and speed v0 = 5.0 m/s collides and sticks to the end of a uniform solid cylinder of mass M = 1.0 kg and radius R = 20 cm. If the cylinder is initially at rest and is pivoted about a frictionless axle through its center, what is the final angular velocity (in rad/s) of the system after the collision? a. 8.1 b. 2.0 c. 6.1 d. 4.2 e. 10

d. 4.2

A skater extends her arms horizontally, holding a 5-kg mass in each hand. She is rotating about a vertical axis with an angular velocity of one revolution per second. If she drops her hands to her sides, what will the final angular velocity (in rev/s) be if her moment of inertia remains approximately constant at 5 kg⋅m2, and the distance of the masses from the axis changes from 1 m to 0.1 m? a. 6 b. 3 c. 9 d. 4 e. 7

b. 3

A merry-go-round of radius R = 2.0 m has a moment of inertia I = 250 kg⋅m2, and is rotating at 10 rpm. A child whose mass is 25 kg jumps onto the edge of the merry-go-round, heading directly toward the center at 6.0 m/s. The new angular speed (in rpm) of the merry-go-round is approximately a. 10 b. 9.2 c. 8.5 d. 7.1 e. 6.4

d. 7.1

A solid sphere (radius R, mass M) rolls without slipping down an incline as shown in the figure. The linear acceleration of its center of mass is a. (5/7)g sin θ b. (3/5)g sin θ c. (2/3)g sin θ d. (1/2)g sin θ e. (4/5)g sin θ

a. (5/7)g sin θ

A solid cylinder rolls without slipping down an incline as shown in the figure. The linear acceleration of its center of mass is a. (5/7)g sin θ b. (1/2)g sin θ c. (2/3)g sin θ d. (3/5)g sin θ e. (4/5)g sin θ

c. (2/3)g sin θ

A cylindrical shell rolls without slipping down an incline as shown in the figure. The linear acceleration of its center of mass is a. (5/7)g sin θ b. (1/2)g sin θ c. (3/5)g sin θ d. (2/3)g sin θ e. (4/5)g sin θ

b. (1/2)g sin θ

A solid sphere, spherical shell, solid cylinder and a cylindrical shell all have the same mass m and radius R. If they are all released from rest at the same elevation and roll without slipping, which reaches the bottom of an inclined plane first? a. solid sphere b. spherical shell c. solid cylinder d. cylindrical shell e. all take the same time

a. solid sphere

Stars originate as large bodies of slowly rotating gas. Because of gravity, these clumps of gas slowly decrease in size. The angular velocity of a star increases as it shrinks because of a. conservation of angular momentum b. conservation of linear momentum c. conservation of energy d. the law of universal gravitation e. conservation of mass

a. conservation of angular momentum

Five objects of mass m move at velocity at a distance r from an axis of rotation perpendicular to the page through point A, as shown below. The one that has zero angular momentum about that axis is

d. A* vector v pointing to the corner

The object shown below has mass m and velocity v . The direction of its angular momentum vector with respect to an axis perpendicular to the page through point O is a. downwards. b. to the right. c. into the page. d. up out of the page. e. counterclockwise.

c. into the page.

Two objects of mass m1 = 2m and m2 = m move around a rotation axis A in parallel circles of radii r1 = r and r2 = 2r with equal tangential speeds. As they rotate, forces of equal magnitude are applied opposite to their velocities to stop them. Which statement is correct? a. m2 will stop first because it has the larger initial angular velocity. b. m1 will stop first because it has the smaller radius. c. m2 will stop first because the torque on it is greater. d. m1 will stop first because it has the smaller moment of inertia. e. Both objects will stop at the same time because the angular accelerations are equal.

c. m2 will stop first because the torque on it is greater.

A torque can be exerted on a body with a fixed axis of rotation a. only by a centripetal force. b. only by a force directed radially outwards. c. only by a tangential force. d. only by a force with a component directed radially outwards. e. by any force not pointing directly toward or away from the axis of rotation.

e. by any force not pointing directly toward or away from the axis of rotation.

Five identical cylinders are each acted on by forces of equal magnitude. Which force exerts the biggest torque about the central axes of the cylinders?

a. cylinder with F pointing STRAIGHT to the right

The diagram below shows five cylinders, each cylinder rotating with constant angular velocity about its central axis. The magnitude of the tangential speed of one point of each cylinder is shown, along with each cylinder's radius and mass. Which cylinder has the largest angular momentum?

v = 4 m/s r = 2 m M = 20 kg

The diagram below shows five thin cylindrical shells, each shell rotating with constant angular velocity about its central axis. The magnitude of the tangential speed of one point of each cylinder is shown, along with each cylinder's radius and mass. Which cylindrical shell has the largest angular momentum?

v = 4 m/s r = 2 m M = 20 kg

The diagram below shows five 20-kg rods of the same 2.0-m length free to rotate about axes through the rods, as indicated. Which rod experiences the greatest magnitude gravitational torque?

Ruler with dot on 2.0

A force is applied to a cylindrical roll of paper of radius R and mass M by pulling on the paper as shown. The acceleration of the center of mass of the roll of paper (when it rolls without slipping) is a. 1/2 F/M b. F/M c. 3/2 F/M d. 4/3 F/M e. 2F/M

d. 4/3 F/M

A 0.5 kg fish, hooked as shown below, starts to swim away at a speed of 3 m/s. The angular momentum of the fish relative to the hand holding the fishing rod is about a. 3 kgm^2/s b. 6 kgm^2/s c. 17 kgm^2/s d. 30 kgm^2/s e. 60 kgm^2/s

a. 3 kgm^2/s

Exhibit 11-1 Two blocks of masses m1 and m2 are connected by a light cord that passes over a pulley of mass M, as shown. Block m2 slides on a frictionless horizontal surface. The blocks and pulley are initially at rest. When m1 is released, the blocks accelerate and the pulley rotates. The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is Use this exhibit to answer the following question(s). Refer to Exhibit 11-1. The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is a. the same at all times. b. proportional to l1, the length of string from the pulley to m1. c. proportional to l2, the length of string from the pulley to m2. d. conserved because the Earth doesn't move. e. proportional to the speed of the blocks.

e. proportional to the speed of the blocks.

. Refer to Exhibit 11-1. The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is a. proportional to the radius of the pulley. b. proportional to the speed of the blocks. c. proportional to the length of the string. d. to all of the above. e. only to (a) and (b) above.

b. proportional to the speed of the blocks.

When an object is effectively isolated from external torques, like an ice skater twirling on the tip of one skate, the angular momentum of the object a. can be increased by shifting mass out away from the axis of rotation. b. can be decreased by shifting mass out away from the axis of rotation. c. can be increased by shifting mass in toward the axis of rotation. d. can be decreased by shifting mass in toward the axis of rotation. e. cannot be changed except by friction at the point of contact.

e. cannot be changed except by friction at the point of contact.

A hockey puck traveling at speed v on essentially frictionless ice collides elastically with one end of a straight stick lying flat on the ice. In this collision a. momentum is conserved. b. angular momentum is conserved. c. energy is conserved. d. all of the above are conserved. e. only momentum and angular momentum are conserved.

d. all of the above are conserved.

A hockey puck traveling at speed v on essentially frictionless ice collides with one end of a straight stick lying flat on the ice and sticks to that end. In this collision a. momentum is conserved. b. angular momentum is conserved. c. energy is conserved. d. all of the above are conserved. e. only momentum and angular momentum are conserved.

e. only momentum and angular momentum are conserved.

A space station out beyond the solar system is rotating with constant angular velocity. A spaceship heading into the station along a diameter of the station, uses its rockets to brake, and then docks inside the station at its center. When the spaceship docks, the angular momentum of the system consisting of the station and ship a. is less than the original angular momentum of the station. b. is the same as the original angular momentum of the station. c. is greater than the original angular momentum of the station. d. is less than the original angular momentum of the station, but the angular velocity increases. e. is greater than the original angular momentum of the station, but the angular velocity decreases.

b. is the same as the original angular momentum of the station.

A top is set spinning so that the rotation is counterclockwise around its axis when viewed from above. When the top is placed on a level surface it happens that its axis of rotation is not quite vertical. Viewed from above, which way does the rotational axis of the top precess? a. clockwise b. counterclockwise c. It’s random, if it starts clockwise it will continue clockwise, and vice versa, i.e., a 50% chance either way. d. The direction depends on the little shove given to the axis when the top is placed on the surface. e. In the northern hemisphere it will be clockwise, in the southern hemisphere it will be counterclockwise.

b. counterclockwise

A 3.0-kg particle has a position vector given by r = (2.0t^2i + 3.0j) where r is in meters and t is in seconds. What is the angular momentum of the particle, in kg⋅m2/s, about the origin at t = 2 s? a. 72k b. −72k c. 24k d. −24k e. 22k

b. −72k

If L represents angular momentum, I represents moment of inertia, p represents linear momentum, m represents mass, and r represents a distance, which of the following can represent kinetic energy? a. p2/2m b. L2/2I c. rpI d. all of the above e. both (a) and (b)

e. both (a) and (b)

Halley's comet moves about the sun in an elliptical orbit with its closest approach to the sun being 0.59 A.U. and its furthest distance being 35 A.U. [1 Astronomical Unit (A.U.) is the Earth-sun distance.] If the comet's speed at closest approach is 54 km/s, what is its speed when it is farthest from the sun?

910 m/s

What is the angular momentum of the moon about the Earth? The mass of the moon is 7.35 × 1022 kg, the center-to-center separation of the Earth and the moon is 3.84 × 105 km, and the orbital period of the moon is 27.3 days. Ignore the small offset of the center of mass of the system from the center of the Earth in your calculation.

2.89 * 10^34 kgm^2/s

A regulation basketball has a 25.0-cm diameter and a mass of 0.560 kg. It may be approximated as a thin spherical shell with a moment of inertia MR2. Starting from rest, how long will it take a basketball to roll without slipping 4.00 m down an incline at 30.0° to the horizontal?

1.65 s

A coin with a diameter 3.00 cm rolls up a 30.0° inclined plane. The coin starts out with an initial angular speed of 60.0 rad/s and rolls in a straight line without slipping. If the moment of inertia of the coin is MR2, how far will the coin roll up the inclined plane?

12.4 cm