chapter 7: linear momentum Flashcards
linear momentum
an object is the product of its mass and velocity, can be expressed using F=ma
Momentum is a vector quantity…
magnitude and direction are both important
SI units for momentum -
kg * m/s
A constant friction force of 25 N acts on a 65 kg skier for 15 seconds. What is the skier’s change in velocity?
Using Newtons 2nd law (force and momentum relationship):
(-25 N because friction is in the opposite direction)
A system of particles is known to have a total kinetic energy of zero. What can you say about the total momentum of the system?
The total momentum of the system is zero
- KE cannot be negative
A system of particles is known to have a total momentum of zero. What can you say about the KE of the system?
You cannot say anything about the KE of the system.
* could be positive or negative depending on the circumstance
A child in a boat throws a 5.70 kg package out horizontally with a speed of v = 10.0 m/s. Calculate velocity of the boat and child, Vg, immediately after the throw, assuming it was initially as rest. The mass of the child is 24.0 kg and that of the boat is 35 kg.
Initial momentum= 0
Final momentum= MpV + (Mboat + Mchild)Vb
Impulse
product of the force of collision and time interval during which it acts, change in momentum due to the collision
A small bean bag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater impulse to the floor when it hits?
The rubber ball, has a greater change in momentum
the ball bounces back up with nearly the same speed as it hit
Which of the following is a way of correctly expressing momentum in SI units?
N * s
When a cannon fires a cannonball, the cannon will recoil backward because the ________
momentum of the cannonball and cannon is conserved.
A freight car moves along a frictionless level railroad track at constant speed. The car is open on top. A large load of coal is suddenly dumped into the car. What happens to the forward velocity of the car?
It decreases.
A rubber ball and a lump of putty have equal mass. They are thrown with equal speed against a wall. The ball bounces back with nearly the same speed with which it hit. The putty sticks to the wall. Which objects experiences the greater momentum change after the collision?
the ball
A 3.0-kg object moves to the right at 4.0 m/s. It collides head-on with a 6.0-kg object moving to the left at 2.0 m/s. Which statement is correct?
The total momentum both before and after the collision is zero.
In which collision type is kinetic energy conserved?
in elastic collisions
When a light beach ball rolling with a speed of 6.0 m/s collides with a heavy exercise ball at rest, the beach ball’s speed after the collision will be, approximately, _________
6.0 m/s.
In an inelastic collision, if the momentum is conserved, then which of the following statements is true about kinetic energy?
Kinetic energy is lost.
Two objects collide and stick together. The kinetic energy of the system ________
is definitely not conserved
A 30.0-kg object moves to the right at 4.0 m/s. It collides in a perfectly inelastic collision with a 3.0 kg object at rest. What is the total kinetic energy before the collision?
240 J
KE= (0.5)(30 kg)(4 m/s)^2
A 30.0-kg object moves to the right at 4.0 m/s. It collides in a perfectly inelastic collision with a 3.0 kg object at rest. What is the total kinetic energy after the collision, and what percent of the initial KE remains after the collision?
220 J, 91%
A 3.0-kg object moves to the right at 4.0 m/s. It collides in a perfectly inelastic collision with a 30.0 kg object at rest. What is the total kinetic energy before the collision?
24 J
A 3.0-kg object moves to the right at 4.0 m/s. It collides in a perfectly inelastic collision with a 30.0 kg object at rest. What is the total kinetic energy after the collision and what percent of the KE is remaining after the collision?
2 J, 9%
Consider two unequal masses, M and m. Which of the following statements is false?
If a uniform rod of mass m were to join the two masses, this would not alter the position of the center of mass of the system without the rod present.
What is the momentum of a 2000-kg truck traveling at 35 m/s?
7.0 x 10^4 kgm/s
(2000 kg) x (35 m/s)
A handball of mass 0.10 kg, traveling horizontally at 30 m/s, strikes a wall and rebounds at 24 m/s. What is the impulse (change in the momentum) of the ball?
5.4 kg * m/s
A 1000-kg car traveling at 25 m/s runs into the rear end of a stopped car of mass 1500 kg and they stick together. What is the speed of the cars after the collision?
10 m/s
A constant 9.0-N net force acts for 2.0 s on a 6.0-kg object. What is the object’s change of velocity?
3.0 m/s
Which of the following is an accurate statement?
If an object is acted on by a non-zero net external force, its momentum will not remain constant.
A ball of mass 0.10 kg is dropped from a height of 12 m. Its momentum when it strikes the ground is _________
1.5 kg m/s.
A railroad freight car of mass 15,000 kg is allowed to coast along a level track at a speed of 2.0 m/s. It collides and couples with a 50,000-kg freight car, initially at rest and with its brakes released. What is the speed of the two cars after coupling?
0.46 m/s
Tightrope walkers walk with a long flexible rod in order to ________
lower their center of mass.
A 4.00-kg mass sits at the origin, and a 10.0-kg mass sits at x = + 21.0 m. Where along the x-axis is the center of mass located?
+15.0 m
The center of mass of a two-particle system is at the origin. The smaller particle has a mass of 2.0 kg and is located at x = +3.0 m, y = 0 m. What is the location of the second particle if its mass is 3.0 kg?
x = -2.0 m, y = 0 m
A constant friction force of 25 N acts on a 65-kg skier for 15 s.
What is the skier’s change in velocity?
In the absence of a net external force, the total momentum of a system of masses is ____?
conserved
A system of particles is known to have a total kinetic energy of zero. What can you say about the total momentum of the system?
Total momentum of the system is zero.
*Kinetic energy cannot be negative, so the only way the total kinetic energy can be zero is if nothing is moving, in which case the total momentum will also be zero.
A system of particles is known to have a total momentum of zero. What can you say about the total kinetic energy of the system?
You cannot say anything about the kinetic energy of the system.
*Total momentum may be zero if either 1) nothing is moving or 2) if the particles are moving in opposite directions with equal magnitudes of momentum. This doesn’t give us enough information to say anything about kinetic energy.
A 0.060-kg tennis ball, moving with a speed of 4.50 m/s, has a head-on collision with a
0.090-kg ball initially moving in the same direction at a speed of 3.00 m/s. Assuming a
perfectly elastic collision, determine the speed and direction of each ball after the
collision.
Consider two elastic collisions: 1) A golf ball with speed 𝑣𝑣 hits a stationary bowling ball head-on. 2) A bowling ball with speed 𝑣𝑣 hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision?
Situation 2 - In both situations the relative speed before and after collisions must be the same.
In the first situation the bowling ball will almost remain at rest, and the golf ball will bounce back with speed close to 𝑣. In case 2 the bowling ball will keep going with speed close to 𝑣, hence the golf ball will rebound with speed close to 2𝑣
inelastic collision
some of the initial kinetic energy is lost to heat, sound, deformation of the objects, etc., so total mechanical energy is not conserved
completely inelastic collision
occurs when the two colliding objects stick together and move as one after the collision
A small car and a large truck collide head-on and stick together. They both then move together in the direction the truck was originally heading. Which one experiences the greater magnitude momentum change?
They both have the same momentum change.
A projectile of mass 𝑚 is fired into a large block of wood of mass 𝑀, which is suspended like a pendulum. As a result of the collision, the pendulum and projectile together swing up to a maximum height ℎ. Determine the relationship between the initial horizontal speed of the
projectile, 𝑣, and the maximum height ℎ.
one point on an object that moves
along the same path that a particle would move if subjected to the same net force
center of mass (CM)
A mallet consists of a uniform cylindrical head of mass 2.80 kg and a diameter of 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown below. If this mallet is tossed, spinning, how far above the bottom of the handle is the point that will follow a parabolic trajectory?
Two equal-mass particles (A and B) are located at some distance from each other. Particle A is held stationary while B is moved away at speed 𝑣. What happens to the center of mass of the two-particle system?
It moves away from A with speed 1/2v
*Since the particles have equal masses, the CM will always be located halfway between the two particles. If particle B travels 10 m away from A, the CM will travel 5 m, so the CM must be moving away from A at speed 1/2 𝑣.
