Deck 11: Collisions

Question 1

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

Answer 1

30 J

Question 2

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

Answer 2

24 J

Question 3

A 3.0-kg ball with an initial velocity of m/s collides with a wall and rebounds with a velocity of m/s. What is the impulse exerted on the ball by the wall?

A)+24 N s
B)−24 N s
C)+18 N s
D)−18 N s
E)+8.0 N s

Answer 3

−24 N s

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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.

Question 22

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.

Question 23

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.

Question 24

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.

Question 25

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.

Question 26

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).
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

Question 27

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.

Question 28

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.

Question 29

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.

Question 30

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.

Question 31

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.

Question 32

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

Question 33

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) .
C) .
D)1
E) .

Question 34

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

Question 35

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.

Question 36

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.

Question 37

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

Question 38

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.

Question 39

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.

Question 40

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.

Question 41

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.

Question 42

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).
What is the horizontal component of their momentum, in , immediately after the collision?

A)0
B)6.1
C)7.5
D)13
E)15

Question 43

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).
What is the magnitude of their velocity, in m/s, immediately after the collision?

A)0
B)13
C)15
D)26
E)30