Exam 2 Flashcards
What is the equation for centripetal (radial) acceleration?
a(R) = v^2/r
The direction of the force needed to keep an object revolving in a circle is pointed
toward the center of the circle
What is the equation for the magnitude of the gravitational force
F(G) = G(m1m2/r^2)
m1 and m2: the masses of the two particles
r: distance between them
G: 6.67 x 10^-11 N*m^2/kg^2
What is the equation for the period (T) of an object revolving around a circle?
T = 1/f
f: frequency
What is the equation for the net force in the radial direction (circular motion) that acts on an object?
∑F(r) = ma(R) = m(v^2/r)
T or F? There is no outward force on a revolving object
T
The gravitational force F(grav) or F(G) exerted by the Earth on any object decreases with the ____ from the Earth’s center
square of its distance r
What is the equation for the acceleration of gravity at the Earth’s surface?
g = G(m(E)/r(E)^2)
What is the mass of Earth (m(E))?
m(E) = 5.98 x 10^24 kg
What is Kepner’s first law?
The path of each planet around the Sun is an ellipse with the Sun at one focus
What is Kepner’s second law?
Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time
What is Kepner’s third law?
The ratio of the squares of the periods T of any two planets revolving around the Sun is equal to the ratio of the cubes of their mean distances from the Sun
(T1/T2)^2 = (s1/s2)^3
T1 and T2: periods (time needed for one rev around the Sun)
s1 and s2: mean distances from the Sun
Equation for velocity of circular motion?
v = 2πr/ T
Newton’s laws are causal laws. This means that
one occurrence can causes another
Energy and momentum are
conserved
Work and energy have no ___ associated with them
direction
What does work describe?
what is accomplished when a force acts on an object, and the object moves through a distance
What is the equation for work?
W = F||d
What is another equation for work?
W = Fd cosθ
What is the unit for work?
joule
1 J = 1 N * m
You need both a ___ and a ___ to do work
force; displacement
When a particular force is perpendicular to the displacement,
no work is done by that force
What is the equation for translational kinetic energy?
KE = 1/2mv^2
What is the equation for net work?
W(net) = 1/2mv2^2 - 1/2mv1^2 W(net) = ΔKE
What does the work energy principle state?
the net work done on an object is equal to the change in the object’s kinetic energy
If positive net work (W) is done on an object, the object’s kinetic energy
increases by an amount W
If negative net work (W) is done on an object, the object’s kinetic energy
decreases by an amount W
Energy is measured in
joules
What is the formula for external work?
W(ext) = mg(y2-y1)
What is the formula for gravitational potential energy?
PE(G) = mgy
mg: object’s weight
y: height above some reference level
What is the change in gravitational potential energy?
equal to the negative of the work done by gravity
ΔPE(G) = -W(G)
What is the equation for elastic potential energy?
PE(el) = 1/2kx^2
k: spring stiffness constant
x: final amount stretched
What is characteristic of conservative forces?
work done does not depend on the path taken but only on the initial and final positions
What is characteristic of nonconservative forces?
work done depends on the path taken
Potential energy can only be defined for a ___ force
conservative
net work is the sum of
work done by conservative forces and nonconservative forces
W(net) = W(C) + W(NC)
What is the equation for conservation of mechanical energy?
KE2 + PE2 = KE1 + PE1
If only conservative forces do work, mechanical energy is
conserved
What is the equation for total mechanical energy (gravity only)?
1/2mv1^2 + mgy1 = 1/2mv2^2 + mgy2
What is the equation for total mechanical energy (elastic PE only)?
1/2mv1^2 + 1/2kx1^2 = 1/2mv2^2 + 1/2kx2^2
Work is done when
energy is transferred from one object to another
What are dissipative forces?
forces that reduce mechanical energy but not total energy
What is the equation for total mechanical energy (when friction is acting)?
1/2mv1^2 + mgy1 = 1/2mv2^2 + mgy2 + F(fr)d
What is the equation for power?
P = w/t
w: work
t: time
One horsepower equals
746 watts
Power is measured in
watts
Another equation for power involving net force?
P(ave) = Fv(ave)
What is efficiency?
the ratio of the useful power output of the engine (P(out)), to the power input, (P(in))
e = P(out)/P(in)
What is the equation for momentum?
p = mv
The direction is momentum is ___ the momentum of the velocity
the same as
What is the unit of momentum?
kg x m/s
The more momentum an object has
- the harder it will be to stop it
- the greater effect it will have on another object if it is brought to rest by striking that object
What does Newton’s Second Law state?
the rate of change of momentum of an object is equal to the net force applied to it
What is the equation of net force that involved change in momentum?
ΣF = Δp/Δt
What is the equation for the conservation of momentum when there is no net external forces acting on a system?
mAvA + mBvB = mAvA’ + mBvB’
What does the law of conservation of momentum state?
the total momentum of an isolated system of objects remains constant
What is an impulse?
a change in momentum
impulse = FΔt
What is the equation for the law of conservation of total kinetic energy for an elastic collision?
1/2mAvA^2 + 1/2mBvB^2 = 1/2mAvA’^2 + 1/2mBvB’^2
In an inelastic collision
kinetic energy is not conserved
What is the equation for a head on elastic collision?
vA - vB = -(v’A - v’B)
For any elastic head-on collision, the relative speed of two objects after the collision ___ as before the collision, no matter what the masses are
has the same magnitude (but opposite direction)
If two objects stick together as a result of a collision, the collision is said to be
completely inelastic
What is the center of mass?
the one point of an object that moves in the same path that a particle would move
What is the equation for the x coordinate of the center of mass?
x(CM) = (mAxA + mBxB)/(mA + mB)
If one mass is greater than the other, the CM
is closer to the larger mass
What is the y coordinate for the center of mass?
y(CM) = (mAyA + mByB)/(mA + mB)
Center of mass and center of gravity are
the same thing
What is the equation of Newton’s Second Law for a system?
Ma(CM) = Fnet
M: total mass of the system
a(CM): the acceleration of its center of mass of the system
What is meant by “purely rotational motion”?
that all points in the object move in circles, and that the center of these circles all lie on one line called the axis of rotation
What is the equation for θ in radians?
θ = l/r
r: radius of circle
l: the arc length subtended by the angle θ
How many radians does one revolution equal?
1 rev = 2Π radians
What is the equation for angular displacement?
Δθ = θ2 - θ1
What is the equation of average angular velocity?
ω(ave) = Δθ/Δt
What are the units for angular velocity?
radians per second (rad/s)
What is the equation for average angular acceleration?
α(ave) = Δω/Δt
How are linear velocity (v) and angular velocity (ω) related?
v = rω
How are angular acceleration and linear acceleration related?
a(tan) = rα
a(tan): linear acceleration
α: angular acceleration
The total linear acceleration of a point is the sum of
the radial (centripetal) acceleration and the linear acceleration
a = a(tan) + a(R)
a(tan): linear acceleration
a(R): radial (centripetal) acceleration
What is the relationship between centripetal acceleration and angular velocity?
a(R) = ω^2r
Centripetal acceleration is ___ the farther you are from the axis of rotation
greater
What is the relationship between angular velocity and frequency?
ω = 2Πf
What is the unit for frequency?
Hertz (1 Hz = 1 rev/s)
What is the equation for the velocity of an object that is rolling without slipping?
v = rω
Angular acceleration is proportional to the
product of the force times the lever arm (torque)
What are the two equations that can describe torque?
τ= r⊥F τ= rFsinθ
mr^2 represents an object’s
moment of inertia (Ι)
When a mass is concentrated farther from the axis of rotation, the rotational inertia is
greater
Rotational kinetic energy can be expressed by
1/2Ιω^2
What are the units for rotational kinetic energy?
joules
Total kinetic energy equals
KE = 1/2Mv(CM)^2 + 1/2I(CM)ω^2
What is the equation for the work done by torque?
W = τΔθ
What is the equation for the power of torque?
P = τω
What is the equation for angular momentum (L)?
L = Iω
What does the law of conservation of angular momentum state?
the total angular momentum of a rotating object remains constant if the net torque acting on it is zero
Which of the following statements is NOT TRUE about work done on a laptop as a student moves it by sliding from one side of a desk to the other?
-The normal force exerted by the desk on the laptop does no work.
-The force of friction does negative work.
-The net work is zero.
-The force of gravity does positive work.
The work done by the student is positive.
The force of gravity does positive work.
A conveyor moves a carton up an incline at constant speed from the first floor to the second floor of a factory. Pick the statement below which is true.
- The normal force acting on the carton does work.
- The force of friction acting on the carton does no work because the carton is not sliding.
- The work done on the carton by the force of gravity does not depend on the angle of the incline.
- The work done by the force of friction depends on the speed of the conveyor.
The work done on the carton by the force of gravity does not depend on the angle of the incline.
Two satellites follow circular orbits about the earth. The orbital radius of Satellite 1 is 4 times the orbital radius of Satellite 2. The mass of Satellite 1 is twice the mass of Satellite 2. All but one of the following statements is true. Pick the statement which is FALSE.
- The speed of Satellite 1 is half the speed of Satellite 2.
- The gravitational force acting on Satellite 2 is 8 times greater than the gravitational force acting on Satellite 1.
- The centripetal accelerations of Satellites 1 and 2 are independent of their respective masses.
- The centripetal acceleration of Satellite 1 is one eighth the centripetal acceleration of Satellite 2.
The centripetal acceleration of Satellite 1 is one eighth the centripetal acceleration of Satellite 2.
Which of the following statements is INCORRECT?
- The power delivered to a falling rock by the gravitational pull of the earth increases as the speed of the rock increases.
- Power has the units of energy.
- Power is the rate at which work is being done.
Power has the units of energy.
Which of the following statements is incorrect in the case that one or more non-conservative forces is acting on a system?
- Total energy is conserved.
- The mechanical energy of the system is conserved.
- The thermal energy of the system may be changing.
- The net work done by non-conservative forces depends on the path followed by the system
The mechanical energy of the system is conserved
If there are no non-conservative forces acting on a system, which of the following quantities is conserved?
mechanical energy
The net work done on a crate as it is sliding down a ramp is zero. Which of the following statements always holds?
- A worker must be applying a force on the crate which has a component in the direction up the ramp in order to keep the crate from accelerating.
- The work done by the force of friction is positive.
- The work done by the force of gravity is negative.
- The net work is zero because the normal force is doing no work.
- The crate is sliding down the ramp at constant speed.
The crate is sliding down the ramp at constant speed.
A ball is thrown straight up. Neglecting air resistance, which statement is NOT TRUE regarding the energy of the ball?
- The kinetic energy decreases while the ball is going up.
- The potential energy decreases while the ball is going up.
- The potential energy decreases when the ball is coming down.
- The sum of the kinetic energy and potential energy is constant.
- The kinetic energy increases when the ball is coming down.
The potential energy decreases while the ball is going up.
Two balls are thrown from the roof of Gallalee Hall. Both are thrown at the same speed, but Ball 1 is thrown horizontally and Ball 2 is thrown downward at an angle of 45 degrees below the horizontal. Which ball has the greater speed when it reaches the ground? Neglect air resistance.
- Ball 2.
- Both balls have the same speed.
- Ball 1.
Both balls have the same speed.
A constant net force is applied to Block 1. After it has been displaced a distance d, its speed is v. The same net force is then applied to Block 2 and after some displacement its speed is 2v. Block 2 is twice as massive as Block 1. How far was Block 2 displaced? (Both blocks start from rest.)
- d/2.
- d.
- 8d.
- 4d.
- 2d.
- d/4.
8d
A fork lift is used to carry a loaded pallet up a ramp at a constant speed of 4 mph. If the operator were instead to drive the fork lift at 8 mph, how would the power delivered by the fork lift to the pallet change?
- The power would quadruple because the kinetic energy would quadruple
- The power would double because the rate at which energy is being delivered to the pallet by the fork lift would double.
- The power would be the same because the force exerted by the fork lift is the same at both speeds.
- The power would decrease by a factor of two because it would take half as long to climb the ramp.
The power would double because the rate at which energy is being delivered to the pallet by the fork lift would double.
Which of the following statements is not correct?
- In a collision between an insect and a truck, the insect exerts the same force on the truck as the truck exerts on the insect.
- Another way of stating Newton’s Second Law is that the net force is equal to the rate at which momentum is changing.
- In an inelastic collision, the total kinetic energy decreases.
- Total momentum is conserved if the net external force acting on a system is zero.
- Momentum is the product of mass and speed.
Momentum is the product of mass and speed.
Two cars traveling in opposite directions at the same speed of 10 mph collide head-on. Immediately after the collision, the cars move together in the same direction as the first car but at 5 mph. Which of the following statements is correct?
- Kinetic energy is conserved in the collision because the sum of the speeds of the cars after the collision is equal to the speed of the cars before the collision.
- The second car is twice as heavy as the first car.
- The first car is twice as heavy as the second car.
- None of the statements can be judged correct or incorrect because not enough information is given.
- The first car is three times as heavy as the second car.
The first car is three times as heavy as the second car.
Two blocks, initially at rest, are each acted upon by the same net force over the same interval in time. At the end of the interval, Block 1 is moving twice as fast as Block 2. Which of the following statements is true?
- The mass of Block 2 is half the mass of Block 1.
- The force of friction acting on Block 2 is greater than the force of friction acting on Block 1.
- The mass of Block 2 is twice the mass of Block 1.
- Block 1 and Block 2 have the same kinetic energy at the end of the interval.
- The average force acting on Block 1 is twice as great as the average force acting on Block 2.
The mass of Block 2 is twice the mass of Block 1.
Which of the following statements is NOT CORRECT about an elastic collision between two objects?
- The net external force on the two-object system is zero.
- The two objects do not stick together as a result of the collision.
- The direction of the relative velocity between the two objects after the collision is opposite the direction of the relative velocity before the collision.
- The total kinetic energy of the two objects is the same before and after the collision.
- In the case where the colliding objects have unequal masses and the heavier object is at rest before the collision, the direction of the lighter object is reversed by the collision.
- The magnitude of the relative velocity between the two objects may change as a result of the collision.
The magnitude of the relative velocity between the two objects may change as a result of the collision.
Which of the following statements is correct?
- A ring and a uniform disk have the same mass and radius. They therefore have the same rotational inertia.
- Two rings have the same mass but one ring has a diameter twice as large as the the other. The same force F is applied to each ring on the circumference of the ring and and in the direction tangent to the ring. -The smaller ring will experience the smaller angular acceleration.
- The rotational inertia is independent of the location of the axis about which the rotation occurs.
- The torque which a force exerts depends on the position at which the force is applied.
The torque which a force exerts depends on the position at which the force is applied.
A disk undergoing constant angular acceleration starting from rest undergoes two complete revolutions in time t. The time it took for it to complete the first revolution is
- More than t/2.
- t/2.
- Less than t/2.
- unknown because not enough information is given.
More than t/2.
Which of the following quantities is not required to calculate the buoyant force exerted by a fluid on an object partially submerged in it?
- The density of the fluid
- The acceleration of gravity
- The fraction of the object’s volume submerged in the fluid
- The density of the object
- The volume of the object
-The density of the object
Which of the following statements is not correct? Assume the fluid is incompressible.
- If the pressure is increased at one point in a fluid, the pressure increases at every other point in the fluid by an amount which depends on the depth
- The pressure in a fluid increases linearly with depth.
- The upward force that a fluid exerts on an object submerged in it is equal to the weight of the fluid displaced by the object.
- Pressure is force per unit area.
If the pressure is increased at one point in a fluid, the pressure increases at every other point in the fluid by an amount which depends on the depth
