Question 1

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.

Accepted Answer

According to Newton's third law of motion, when two bodies collide, they exert equal and opposite forces on each other. This means that the impulses they exert on each other are also equal and opposite. Therefore, the correct option is B, which states that the impulses are equal but opposite for all collisions.

Question 2

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.

Accepted Answer

The answer of In an elastic collision between two bodies...

Question 3

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  , 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.

Accepted Answer

When the two cars start, they are at the same point, so the center of mass is at the center of the circle. As they move in opposite directions, the center of mass remains fixed, since the two movements cancel each other out.

When each car has traveled a quarter of the circle, they are diametrically opposite each other. At this point, the center of mass is still fixed, since the two cars are equidistant from it.

When each car has traveled a distance less than a quarter of the circle, the center of mass is still fixed, since the two cars have not yet moved far enough to cause a significant shift.

However, once each car has traveled a distance greater than a quarter of the circle, the center of mass will shift towards the faster car. This is because the faster car covers a greater distance in the same amount of time, causing it to "catch up" with the slower car.

Since each car travels for a distance less than a quarter of the circle, the center of mass remains fixed at the center of the circle.

However, the question asks about the movement of the center of mass while each car travels a distance less than 11eb6adc_ed01_322b_b0cf_fbe08d79c216_TB8245_11, one quarter of the circle. At this distance, the two cars have not yet moved far enough to cause a significant shift in the center of mass.

Therefore, the center of mass remains fixed at the center of the circle, which is also a diameter. Since the two cars are moving in opposite directions along the circumference of the circle, the center of mass is moving along the diameter of the circle at a constant speed v', which is equal to 0.

Question 4

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: m₁v₁_i0 = m₁v₁_f cosθ + m₂v₂_f sinφ = m₁v₁_f sinθ + m₂v₂_f cosφ What error(s) has the student made? A) In the first equation, m₂v₂_f sinφ should be m₂v₂_f cosφ. B) In the second equation, m₂v₂_f cosφ should be m₂v₂_f 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.

Accepted Answer

The answer of In an elastic collision between two bodies...

Question 5

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.

Accepted Answer

The law of conservation of momentum is based on Newton's third law, which states that for every action, there is an equal and opposite reaction. This means that in a collision, the two bodies exert equal and opposite forces on each other, ensuring that the total momentum before the collision is equal to the total momentum after the collision.

Question 6

A ball of mass m_B is released from rest and acquires velocity of magnitude v_B before hitting the ground. The ratio of the impulse delivered to the Earth to the impulse delivered to the ball is A) 0. B) . C) . D) 1 E) .

Accepted Answer

The answer of A ball of mass m_B is released...

Question 7

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.

Accepted Answer

The canoe and the boys will experience equal and opposite forces from the ball each time it is thrown. This will cause the canoe to oscillate back and forth, always moving in the opposite direction of the ball because of the conservation of momentum. However, since there are two boys in the canoe and they are both throwing the ball, the oscillation may be more complex and erratic.

Question 8

An exam paper contains the following equation for rocket propulsion: . The error in the equation is that, instead of (v + v_e), the velocity of the fuel relative to the ground should be A) −v_e. B) +v_e. C) v − v_e. D) v_e − v. E) 2v_e.

Accepted Answer

The correct velocity of the fuel relative to the ground should be subtracted from the velocity of the rocket (v), as both velocities are in opposite directions. Therefore, the correct equation should be v - v_e. This is option C.

Question 9

A ball of mass m_B is released from rest and acquires velocity of magnitude v_B before hitting the ground. The ratio of the kinetic energy the Earth acquires to the kinetic energy the ball acquires is A) 0. B) . C) . D) 1 E) .

Accepted Answer

The answer of A ball of mass m_B is released...

Question 10

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.

Accepted Answer

When the rate of burn and the exhaust velocity are constant, the mass of the rocket decreases as fuel is consumed, leading to an increase in acceleration due to the conservation of momentum and Newton's second law.

Question 11

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

Accepted Answer

In an elastic collision, when masses are equal (ii), they exchange speeds, so $v_{1} = v_{2}$. If $m_{1} > m_{2}$ (i), $m_{1}$ slows down but is still faster than $m_{2}$ after the collision, hence $v_{1} < v_{2}$. If $m_{1} < m_{2}$ (iii), $m_{1}$ bounces back with a greater speed than $m_{2}$ moves forward, so $v_{1} > v_{2}$.

Question 12

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.

Accepted Answer

This is due to Newton's third law of motion. When the astronaut pulls the hammer back, they exert a force on the hammer towards themselves, causing a reaction force that moves them towards the spaceship. When they swing the hammer forward, the opposite occurs: they exert a force on the hammer away from themselves, and the reaction force moves them away from the spaceship.

Question 13

A ball of mass m_B is released from rest and acquires velocity of magnitude v_B 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) . C) . D) 1 E) .

Accepted Answer

The answer of A ball of mass m_B is released...

Question 14

Refer to Exhibit 9-1. What is the magnitude of their total momentum, in  , immediately after the collision?
A) 0
B) 6.5
C) 7.5
D) 13
E) 15

Accepted Answer

The answer of Refer to Exhibit 9-1. What is the...

Question 15

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.

Accepted Answer

Momentum is always conserved in the ball-earth system regardless of the height h' the ball reaches after bouncing. This is because the law of conservation of momentum applies to all interactions, assuming no external forces act on the system.

Question 16

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.

Accepted Answer

According to Newton's third law, for every action, there is an equal and opposite reaction, which means the force each body exerts on the other during the collision is equal in magnitude and opposite in direction (B). Also, since momentum is conserved in collisions, the change in momentum of one body is equal in magnitude and opposite in direction to the change in momentum of the other body (A). However, the changes in kinetic energy are not necessarily equal, as kinetic energy is not conserved in inelastic collisions where bodies stick together. Therefore, options (A) and (B) are correct.

Question 17

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.

Accepted Answer

Impulse is the change in momentum of a body. So, if you know the impulse that has acted on a body of mass m, you can calculate the change in its velocity.

Question 18

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.

Accepted Answer

The value of the momentum of a system remains constant (is conserved) if there are no external forces acting on the system. This is a direct consequence of Newton's third law of motion and the principle of conservation of momentum. Internal forces, regardless of their nature (collisional or non-collisional), do not change the total momentum of the system; it is the external forces that can change the system's total momentum.

Question 19

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

Accepted Answer

The answer of Refer to Exhibit 9-1. What is the...

Question 20

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.

Accepted Answer

Rachel's argument is supported by all the given reasons: A) Newton's third law ensures that forces between the two bodies are equal and opposite, B) these forces act for the same amount of time, and C) the conservation of momentum is indeed a vector equation, meaning it applies in all directions, not just for head-on collisions.

Quiz 9: Linear Momentum and Collisions

When two bodies of different masses collide, the impulses they exert on each other are

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

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 , one quarter circle, the center of mass of the two cars

The law of conservation of momentum applies to a collision between two bodies since

A ball of mass m_B is released from rest and acquires velocity of magnitude v_B before hitting the ground. The ratio of the impulse delivered to the Earth to the impulse delivered to the ball is

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.

An exam paper contains the following equation for rocket propulsion: . The error in the equation is that, instead of (v + v_e) , the velocity of the fuel relative to the ground should be

A ball of mass m_B is released from rest and acquires velocity of magnitude v_B before hitting the ground. The ratio of the kinetic energy the Earth acquires to the kinetic energy the ball acquires is

When the rate of burn and the exhaust velocity are constant, a rocket ascends with

An astronaut outside a spaceship hammers a loose rivet back in place. What happens to the astronaut as he swings the hammer?

A ball of mass m_B is released from rest and acquires velocity of magnitude v_B 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

Refer to Exhibit 9-1. What is the magnitude of their total momentum, in , immediately after the collision?

A ball falls to the ground from height h and bounces to height h'. Momentum is conserved in the ball-earth system

Two bodies of equal mass m collide and stick together. The quantities that always have equal magnitude for both masses during the collision are

If you know the impulse that has acted on a body of mass m you can calculate

The value of the momentum of a system is the same at a later time as at an earlier time if there are no

Refer to Exhibit 9-1. What is the magnitude of their velocity, in m/s, immediately after the collision?

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

Quiz 9: Linear Momentum and Collisions

When two bodies of different masses collide, the impulses they exert on each other are

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

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 , one quarter circle, the center of mass of the two cars

The law of conservation of momentum applies to a collision between two bodies since

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

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.

An exam paper contains the following equation for rocket propulsion: . The error in the equation is that, instead of (v + ve) , the velocity of the fuel relative to the ground should be

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

When the rate of burn and the exhaust velocity are constant, a rocket ascends with

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.

An astronaut outside a spaceship hammers a loose rivet back in place. What happens to the astronaut as he swings the hammer?

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

Refer to Exhibit 9-1. What is the magnitude of their total momentum, in , immediately after the collision?

A ball falls to the ground from height h and bounces to height h'. Momentum is conserved in the ball-earth system

Two bodies of equal mass m collide and stick together. The quantities that always have equal magnitude for both masses during the collision are

If you know the impulse that has acted on a body of mass m you can calculate

The value of the momentum of a system is the same at a later time as at an earlier time if there are no

Refer to Exhibit 9-1. What is the magnitude of their velocity, in m/s, immediately after the collision?

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 ball of mass m_B is released from rest and acquires velocity of magnitude v_B before hitting the ground. The ratio of the impulse delivered to the Earth to the impulse delivered to the ball is

An exam paper contains the following equation for rocket propulsion: . The error in the equation is that, instead of (v + v_e) , the velocity of the fuel relative to the ground should be

A ball of mass m_B is released from rest and acquires velocity of magnitude v_B before hitting the ground. The ratio of the kinetic energy the Earth acquires to the kinetic energy the ball acquires is

A ball of mass m_B is released from rest and acquires velocity of magnitude v_B 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