Question 1

A very light Ping-Pong ball moving east at a speed of 4 m/s collides with a very heavy stationary bowling ball.The Ping-Pong ball bounces back to the west,and the bowling ball moves very slowly to the east.On which object is the greater magnitude impulse exerted during the collision?
A)Neither; the same magnitude impulse was exerted on both.
B)On the Ping-Pong ball
C)On the bowling ball
D)It is impossible to tell since the actual mass values are not given.
E)It is impossible to tell since the velocities after the collision are unknown.

Accepted Answer

The law of conservation of momentum and Newton's third law (for every action, there is an equal and opposite reaction) imply that the magnitude of impulse (change in momentum) is the same for both objects during their interaction, regardless of their masses or the velocities after the collision.

Question 2

A rocket explodes into two fragments,one 25 times heavier than the other.The magnitude of the momentum change of the lighter fragment is
A)25 times as great as the momentum change of the heavier fragment.
B)The same as the momentum change of the heavier fragment.
C)1/25 as great as the momentum change of the heavier fragment.
D)5 times as great as the momentum change of the heavier fragment.
E)1/4 as great as the momentum change of the heavier fragment.

Accepted Answer

The law of conservation of momentum states that the total momentum of a closed system is constant if no external forces act on it. When the rocket explodes, the momentum of the system (rocket) before the explosion is equal to the sum of the momenta of the fragments after the explosion. Since momentum is a vector quantity, the momentum change of the lighter fragment must be equal in magnitude and opposite in direction to the momentum change of the heavier fragment to conserve the total momentum of the system.

Question 3

Three cars,car X,car Y,and car Z,begin accelerating from rest at the same time.Car X is more massive than car Y,which is more massive than car Z.The net accelerating force exerted on each car is identical.After 10 seconds,which car has the most amount of momentum?
A)They all have the same amount of momentum.
B)Car X
C)Car Y
D)Car Z

Accepted Answer

Since the net accelerating force and the time period are the same for all cars, according to the equation of motion (momentum = mass x velocity) and Newton's second law (F = ma), each car will gain the same amount of momentum. The difference in mass is compensated by the difference in acceleration.

Question 4

A 2.0-kg ball moving eastward at 3.0 m/s suddenly collides with and sticks to a 4.0-kg ball moving northward at 2.0 m/s.What is the magnitude of the momentum of this system just after the collision?
A)14 kg ∙ m/s
B)2.0 kg ∙ m/s
C)10 kg ∙ m/s
D)6.0 kg ∙ m/s
E)8.0 kg ∙ m/s

Accepted Answer

Before the collision, the momentum of the 2.0-kg ball is (2.0 kg)(3.0 m/s)east = 6.0 kg∙m/s east, and the momentum of the 4.0-kg ball is (4.0 kg)(2.0 m/s)north = 8.0 kg∙m/s north. Since only the direction matters, we can represent these momenta as vectors: 6.0 east and 8.0 north.

After the collision, the two balls stick together and move as a single system, conserving momentum. To find the total momentum, we just add the vectors:

(6.0 east) + (8.0 north) = √(6.0² + 8.0²) = 10 kg∙m/s

Therefore, the magnitude of the momentum of the system just after the collision is 10 kg∙m/s.

Question 5

During World War I,Germany used a "Big Bertha" cannon to hurl shells into Paris 30 miles away.This gun also had a very long barrel.What was the reason for using a long barrel in these guns?
A)to exert a larger force on the shells
B)to reduce frictional losses
C)to allow the expanding gases from the gunpowder to exert a force on the bullets for a longer time
D)to increase the force exerted on the bullet by the expanding gases from the gunpowder
E)to reduce the force exerted on the bullet by the expanding gases from the gunpowder

Accepted Answer

A longer barrel allows the expanding gases from the gunpowder to exert a force on the bullets for a longer time, thus increasing the velocity of the shell. This is known as the principle of conservation of momentum.

Question 6

Consider two less-than-desirable options.In the first you are driving 30 mph and crash head-on into an identical car also going 30 mph.In the second option you are driving 30 mph and crash head-on into a stationary brick wall.In neither case does your car bounce back from the thing it hits,and the collision time is the same in both cases.Which of these two situations would result in the greater impact force exerted on your car?
A)hitting the other car
B)hitting the brick wall
C)The force would be the same in both cases.
D)None of the above choices are correct.

Accepted Answer

The force exerted on your car would be the same in both cases because the change in momentum and the collision time are the same, according to Newton's third law of motion.

Question 7

A small car meshes with a large truck in a head-on collision.Which of the following statements concerning the magnitude of the momentum change during the collision is correct? (There could be more than one correct choice.)
A)The truck has the greater magnitude momentum change.
B)The small car has the greater magnitude momentum change.
C)The small car and the truck have the same magnitude momentum change.
D)The magnitude of the momentum change of each one is inversely proportional to its mass.
E)The magnitude of the momentum change of each one is directly proportional to its mass.

Accepted Answer

According to the law of conservation of momentum, the magnitude of momentum change is the same for both the truck and the small car during the collision. This is because the force exerted on each other is equal in magnitude and opposite in direction for the same duration, leading to equal and opposite changes in momentum.

Question 8

A small car meshes with a large truck in a head-on collision.Which of the following statements concerning the magnitude of the average force during the collision is correct?
A)There is a greater average force exerted on the truck.
B)There is a greater average force exerted on the small car.
C)There is the same magnitude average force exerted on both the small car and the truck.
D)The force exerted on each object is inversely proportional to its mass.
E)The force exerted on each object is directly proportional to its mass.

Accepted Answer

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. In this collision, the small car exerts a force on the truck, and the truck exerts an equal and opposite force on the small car. Therefore, the magnitude of the average force exerted on both the small car and the truck is the same. The force exerted on each object is not affected by the mass of the object. Therefore, options D and E can be eliminated. Option A and B cannot be correct as they suggest a different magnitude of force on each object, which goes against Newton's third law.

Question 9

Two friends are standing on opposite ends of a canoe that is initially at rest with respect to a frictionless lake.The person in the front throws a very massive ball toward the back,and the person in the back catches it.After the ball is caught,the canoe is
A)moving backward.
B)stationary.
C)moving forward.

Accepted Answer

The answer of Two friends are standing on opposite ends...

Question 10

You are standing on a skateboard,initially at rest.A friend throws a very heavy ball towards you.You have two choices about what to do with the ball: either catch the ball or deflect it back toward your friend with the same speed as it was originally thrown.Which choice should you make in order to maximize your speed on the skateboard?
A)Catch the ball.
B)Deflect the ball back.
C)Your final speed on the skateboard will be the same regardless whether you catch the ball or deflect the ball.

Accepted Answer

According to the law of conservation of momentum, the momentum of the ball when thrown is equal and opposite to the momentum of the skateboard when you deflect the ball back towards your friend. Since the ball is very heavy, it has a larger momentum compared to the skateboard. Hence, when you deflect the ball back towards your friend with the same speed as it was originally thrown, the momentum gained by the skateboard will be larger compared to when you catch the ball. Therefore, the best choice is to deflect the ball back towards your friend.

Question 11

Which of the following quantities are units of momentum? (There could be more than one correct choice.) A)N ∙ m B)kg ∙ s/m C)kg ∙ m/s D)N ∙ s E)kg ∙ m²/s²

Accepted Answer

Momentum is defined as the product of mass and velocity, which is represented by the unit kg ∙ m/s, making choice C correct. Additionally, since a Newton-second (N ∙ s) is equivalent to kg ∙ m/s when considering Newton's second law (F = ma), choice D is also a correct representation of momentum.

Question 12

A 0.14-kg baseball is dropped from rest from a height of 2.0 m above the ground.What is the magnitude of its momentum just before it hits the ground if we neglect air resistance?
A)0.28 kg ∙ m/s
B)0.88 kg ∙ m/s
C)0.44 kg ∙ m/s
D)0.62 kg ∙ m/s
E)1.4 kg ∙ m/s

Accepted Answer

To find the momentum just before the baseball hits the ground, we first calculate its velocity using the equation for gravitational potential energy (PE) and kinetic energy (KE), assuming no air resistance. The potential energy at the height of 2.0 m is converted entirely into kinetic energy just before the ball hits the ground. $$PE = KE$$$$mgh = \frac{1}{2}mv^2$$Solving for $v$, we get:$$v = \sqrt{2gh}$$Substituting $g = 9.8 \, m/s^2$ and $h = 2.0 \, m$, we find:$$v = \sqrt{2 \times 9.8 \times 2.0} = \sqrt{39.2} \approx 6.26 \, m/s$$The momentum ($p$) is given by $p = mv$, where $m = 0.14 \, kg$ and $v = 6.26 \, m/s$, so:$$p = 0.14 \times 6.26 \approx 0.876 \, kg \cdot m/s$$Rounding to two significant figures, the momentum is approximately $0.88 \, kg \cdot m/s$, which corresponds to choice B.

Question 13

Identical forces are exerted for the same length of time on two different objects.The magnitude of the change in momentum of the lighter object is
A)smaller than the magnitude of the change in momentum of the larger mass object, but not zero.
B)larger than the magnitude of the change in momentum of the larger mass object.
C)exactly equal to the magnitude of the change in momentum of the larger mass object.
D)zero.
E)There is not enough information to answer the question.

Accepted Answer

According to the law of conservation of momentum, the change in momentum of an object is equal to the force applied on it multiplied by the time for which the force was applied. As the forces applied are identical and act for the same length of time on both objects, the change in momentum of each object will be directly proportional to its mass. Therefore, the change in momentum of the lighter object will be smaller than the change in momentum of the larger mass object but exactly equal in magnitude, as stated in choice C.

Question 14

A small car meshes with a large truck in a head-on collision.Which of the following statements concerning the momentum during the collision are correct? (There could be more than one correct choice.)
A)The momentum of the truck is constant.
B)The momentum of the car is constant.
C)The car and the truck must undergo the same change in speed.
D)The momentum of the car and the momentum of the truck are each constant.
E)The momentum of the car-truck system is constant, but the momentum of each one separately is not constant.

Accepted Answer

During a collision, the law of conservation of momentum states that the total momentum of the system (in this case, the car and the truck) remains constant. However, the momentum of each object individually is not constant, as they experience an impulse that changes their momentum. Therefore, statement E is correct.

Statement A is incorrect because the momentum of the truck changes during the collision.

Statement B is incorrect because the momentum of the car changes during the collision.

Statement C is incorrect because the change in speed of the car and the truck depends on their masses and the forces involved in the collision. They may undergo different changes in speed.

Statement D is incorrect because it implies that the momentum of each object individually is constant, which is not the case during a collision.

Question 15

What is the magnitude of the momentum of a 0.140 kg baseball traveling at 45.0 m/s?

Accepted Answer

The answer of What is the magnitude of the momentum...

Question 16

A tiger is running in a straight line.If we double both the mass and speed of the tiger,the magnitude of its momentum will increase by what factor?
A) $\sqrt { 2 }$
B)2
C)4
D)8
E)16

Accepted Answer

Momentum is given by the product of mass and velocity. If both mass and velocity are doubled, the new momentum will be 2(mass) * 2(velocity) = 4 times the original momentum.

Question 17

A very elastic rubber ball is dropped from a certain height and hits the floor with a downward speed v.Since it is so elastic,the ball bounces back with the same speed v going upward.Which of the following statements about the bounce are correct? (There could be more than one correct choice.)
A)The ball had the same momentum just before and just after the bounce.
B)The magnitude of the ball's momentum was the same just before and just after the bounce.
C)The ball's momentum was conserved during the bounce.
D)None of the above statements are correct.

Accepted Answer

CThe magnitude of the ball's momentum is the same just before and just after the bounce because momentum is mass times velocity, and only the direction of the velocity changes, not its magnitude. Momentum is conserved during the bounce because the change in momentum (which involves the ball going from downward to upward motion) is equal and opposite, assuming no external forces act on the system other than the normal force from the floor, which is an internal force for the system consisting of the ball and the Earth.

Question 18

Which of the following quantities are units of impulse? (There could be more than one correct choice.) A)N ∙ m B)kg ∙ s/m C)kg ∙ m/s D)N ∙ s E)kg ∙ m²/s²

Accepted Answer

The answer of Which of the following quantities are units...

Question 19

In a collision between two objects of unequal mass,which object receives a greater magnitude impulse?
A)the object of larger mass
B)the object of smaller mass
C)They receive equal magnitude impulses.

Accepted Answer

In a collision, both objects receive impulses of equal magnitude but in opposite directions, according to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.

Question 20

A rubber ball and a lump of clay 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 clay sticks to the wall.Which one of these objects has the greater momentum change?
A)the ball
B)the clay
C)Both of them have the same non-zero momentum change.
D)Both of them have zero momentum change.

Accepted Answer

Momentum change is given by Δp = mΔv, where Δv is the change in velocity. Since both objects are thrown with equal speed, the initial velocity is the same. When they hit the wall, both objects experience the same force and thus the same momentum change. However, since the ball bounces back with nearly the same speed, its final velocity is much greater than that of the clay, which stuck to the wall. Therefore, the ball has a greater change in velocity and hence a greater momentum change.

Quiz 6: Impulse and Linear Momentum

A very light Ping-Pong ball moving east at a speed of 4 m/s collides with a very heavy stationary bowling ball.The Ping-Pong ball bounces back to the west,and the bowling ball moves very slowly to the east.On which object is the greater magnitude impulse exerted during the collision?

A rocket explodes into two fragments,one 25 times heavier than the other.The magnitude of the momentum change of the lighter fragment is

Three cars,car X,car Y,and car Z,begin accelerating from rest at the same time.Car X is more massive than car Y,which is more massive than car Z.The net accelerating force exerted on each car is identical.After 10 seconds,which car has the most amount of momentum?

A 2.0-kg ball moving eastward at 3.0 m/s suddenly collides with and sticks to a 4.0-kg ball moving northward at 2.0 m/s.What is the magnitude of the momentum of this system just after the collision?

During World War I,Germany used a "Big Bertha" cannon to hurl shells into Paris 30 miles away.This gun also had a very long barrel.What was the reason for using a long barrel in these guns?

A small car meshes with a large truck in a head-on collision.Which of the following statements concerning the magnitude of the momentum change during the collision is correct? (There could be more than one correct choice.)

A small car meshes with a large truck in a head-on collision.Which of the following statements concerning the magnitude of the average force during the collision is correct?

Two friends are standing on opposite ends of a canoe that is initially at rest with respect to a frictionless lake.The person in the front throws a very massive ball toward the back,and the person in the back catches it.After the ball is caught,the canoe is

Which of the following quantities are units of momentum? (There could be more than one correct choice.)

A 0.14-kg baseball is dropped from rest from a height of 2.0 m above the ground.What is the magnitude of its momentum just before it hits the ground if we neglect air resistance?

Identical forces are exerted for the same length of time on two different objects.The magnitude of the change in momentum of the lighter object is

A small car meshes with a large truck in a head-on collision.Which of the following statements concerning the momentum during the collision are correct? (There could be more than one correct choice.)

What is the magnitude of the momentum of a 0.140 kg baseball traveling at 45.0 m/s?

A tiger is running in a straight line.If we double both the mass and speed of the tiger,the magnitude of its momentum will increase by what factor?

A very elastic rubber ball is dropped from a certain height and hits the floor with a downward speed v.Since it is so elastic,the ball bounces back with the same speed v going upward.Which of the following statements about the bounce are correct? (There could be more than one correct choice.)

Which of the following quantities are units of impulse? (There could be more than one correct choice.)

In a collision between two objects of unequal mass,which object receives a greater magnitude impulse?

A rubber ball and a lump of clay 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 clay sticks to the wall.Which one of these objects has the greater momentum change?