Deck 11: Impulse and Momentum

Question 1

A shell explodes into two fragments,one fragment 25 times heavier than the other.If any gas from the explosion has negligible mass,then

A)the momentum change of the lighter fragment is 25 times as great as the momentum change of the heavier fragment.
B)the momentum change of the heavier fragment is 25 times as great as the momentum change of the lighter fragment.
C)the momentum change of the lighter fragment is exactly the same as the momentum change of the heavier fragment.
D)the kinetic energy change of the heavier fragment is 25 times as great as the kinetic energy change of the lighter fragment.
E)the kinetic energy change of the lighter fragment is 25 times as great as the kinetic energy change of the heavier fragment.

Answer 1

the momentum change of the lighter fragment is exactly the same as the momentum change of the heavier fragment.

Question 2

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

A)The truck experiences the greater average force.
B)The small car experiences the greater average force.
C)The small car and the truck experience the same average force.
D)It is impossible to tell since the masses are not given.
E)It is impossible to tell since the velocities are not given.

Answer 2

The small car and the truck experience the same average force.

Question 3

A time-varying horizontal force F(t)= At⁴ + Bt² acts for 0.500 s on a 12.25-kg object,starting at time t = 1.00 s.In the SI system,A has the numerical value 4.50 and B has the numerical value 8.75.
(a)What are the SI units of A and B?
(b)What impulse does this force impart to the object?

Answer 3

(a)A: N/s⁴ = kg ∙ m/s⁶ ,B: N/s² = kg ∙ m/s⁴ (b)12.9 N ∙ s,horizontally

Question 4

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 off the thing it hits,and the collision time is the same in both cases.Which of these two situations would result in the greatest impact force?

A)hitting the other car
B)hitting the brick wall
C)The force would be the same in both cases.
D)We cannot answer this question without more information.
E)None of these is true.

Question 5

A baseball is thrown vertically upward and feels no air resistance.As it is rising

A)both its momentum and its mechanical energy are conserved.
B)its momentum is not conserved,but its mechanical energy is conserved.
C)both its momentum and its kinetic energy are conserved.
D)its kinetic energy is conserved,but its momentum is not conserved.
E)its gravitational potential energy is not conserved,buts its momentum is conserved.

Question 6

A firecracker breaks up into several pieces,one of which has a mass of 200 g and flies off along the x-axis with a speed of 82.0 m/s.A second piece has a mass of 300 g and flies off along the y-axis with a speed of 45.0 m/s.What are the magnitude and direction of the total momentum of these two pieces?

A)361 kg ∙ m/s at 56.3° from the x-axis
B)93.5 kg ∙ m/s at 28.8° from the x-axis
C)21.2 kg ∙ m/s at 39.5° from the x-axis
D)361 kg ∙ m/s at 0.983° from the x-axis
E)21.2 kg ∙ m/s at 56.3° from the x-axis

Question 7

In a collision between two objects having unequal masses,how does magnitude of the impulse imparted to the lighter object by the heavier one compare with the magnitude of the impulse imparted to the heavier object by the lighter one?

A)The lighter object receives a larger impulse.
B)The heavier object receives a larger impulse.
C)Both objects receive the same impulse.
D)The answer depends on the ratio of the masses.
E)The answer depends on the ratio of the speeds.

Question 8

A 2.50-kg stone is dropped from rest at a height of 3.75 m.What impulse does gravity impart to this stone from the instant it is dropped until it hits the ground,assuming negligible air resistance?

Question 9

On a smooth horizontal floor,an object slides into a spring which is attached to another mass that is initially stationary.When the spring is most compressed,both objects are moving at the same speed.Ignoring friction,what is conserved during this interaction?

A)momentum and mechanical energy
B)momentum only
C)kinetic energy only
D)momentum and kinetic energy
E)momentum and potential energy

Question 10

In a perfectly ELASTIC collision between two perfectly rigid objects

A)the momentum of each object is conserved.
B)the kinetic energy of each object is conserved.
C)the momentum of the system is conserved but the kinetic energy of the system is not conserved.
D)both the momentum and the kinetic energy of the system are conserved.
E)the kinetic energy of the system is conserved,but the momentum of the system is not conserved.

Question 11

As a tile falls from the roof of a building to the ground its momentum is conserved.

Question 12

In an INELASTIC collision between two objects

A)the momentum of each object is conserved.
B)the kinetic energy of each object is conserved.
C)the momentum of the system is conserved but the kinetic energy of the system is not conserved.
D)both the momentum and the kinetic energy of the system are conserved.
E)the kinetic energy of the system is conserved,but the momentum of the system is not conserved.

Question 13

A 1.0-kg block and a 2.0-kg block are pressed together on a horizontal frictionless surface with a compressed very light spring between them.They are not attached to the spring.After they are released and have both moved free of the spring

A)the lighter block will have more kinetic energy than the heavier block.
B)the heavier block will have more kinetic energy than the lighter block.
C)both blocks will both have the same amount of kinetic energy.
D)both blocks will have equal speeds.
E)the magnitude of the momentum of the heavier block will be greater than the magnitude of the momentum of the lighter block.

Question 14

Jacques and George meet in the middle of a lake while paddling in their canoes.They come to a complete stop and talk for a while.When they are ready to leave,Jacques pushes George's canoe with a force to separate the two canoes.What is correct to say about the final momentum and kinetic energy of the system if we can neglect any resistance due to the water?

A)The final momentum is in the direction of but the final kinetic energy is zero.
B)The final momentum is in the direction opposite of but the final kinetic energy is zero.
C)The final momentum is in the direction of and the final kinetic energy is positive.
D)The final momentum is zero and the final kinetic energy is zero.
E)The final momentum is zero but the final kinetic energy is positive.

Question 15

A stationary 1.67-kg object is struck by a stick.The object experiences a horizontal force given by F = at - bt²,where t is the time in milliseconds from the instant the stick first contacts the object.If a = 1500 N/(ms)and b = 20 N/(ms)²,what is the speed of the object just after it comes away from the stick at t = 2.74 ms?

A)3.3 m/s
B)22 m/s
C)3.7 m/s
D)25 m/s

Question 16

A small glider is coasting horizontally when suddenly a very heavy piece of cargo falls out of the bottom of the plane.You can neglect air resistance.Just after the cargo has fallen out

A)the plane speeds up and the cargo slows down.
B)the plane speeds up but the cargo does not change speed.
C)neither the cargo nor the plane change speed.
D)the cargo slows down but the plane does not change speed.
E)both the cargo and the plane speed up.

Question 17

A 0.500-kg ball traveling horizontally on a frictionless surface approaches a very massive stone at 20.0 m/s perpendicular to wall and rebounds with 70.0% of its initial kinetic energy.What is the magnitude of the change in momentum of the stone?

A)18.4 kg ∙ m/s
B)14.0 kg ∙ m/s
C)3.00 kg ∙ m/s
D)1.63 kg ∙ m/s
E)0.000 kg ∙ m/s

Question 18

A 620-g object traveling at 2.1 m/s collides head-on with a 320-g object traveling in the opposite direction at 3.8 m/s.If the collision is perfectly elastic,what is the change in the kinetic energy of the 620-g object?

A)It loses 0.23 J.
B)It gains 0.69 J.
C)It loses 0.47 J.
D)It loses 1.4 J.
E)It doesn't lose any kinetic energy because the collision is elastic.

Question 19

You are standing on a skateboard,initially at rest.A friend throws a very heavy ball towards you.You can either catch the object or deflect the object back towards your friend (such that it moves away from you with the same speed as it was originally thrown).What should you do in order to MINIMIZE your speed on the skateboard?

A)Catch the ball.
B)Deflect the ball.
C)Your final speed on the skateboard will be the same regardless whether you catch the ball or deflect the ball.

Question 20

During a collision with a wall,the velocity of a 0.200-kg ball changes from 20.0 m/s toward the wall to 12.0 m/s away from the wall.If the time the ball was in contact with the wall was 60.0 ms,what was the magnitude of the average force applied to the ball?

A)40.0 N
B)107 N
C)16.7 N
D)26.7 N
E)13.3 N

Question 21

A block of mass m = 8.40 kg,moving on a horizontal frictionless surface with a speed 4.20 m/s,makes a perfectly elastic collision with a block of mass M at rest.After the collision,the 8.40 block recoils with a speed of 0.400 m/s.In the figure,the blocks are in contact for 0.200 s.The magnitude of the average force on the 8.40-kg block,while the two blocks are in contact,is closest to

A)193 N.
B)185 N.
C)176 N.
D)168 N.
E)160 N.

Question 22

A 900-kg car traveling east at 15.0 m/s collides with a 750-kg car traveling north at 20.0 m/s.The cars stick together.Assume that any other unbalanced forces are negligible.
(a)What is the speed of the wreckage just after the collision?
(b)In what direction does the wreckage move just after the collision?

Question 23

A 10.0-kg shell is traveling horizontally to the right at 25.0 m/s relative to the ground when it explodes into two fragments,one of mass 3.00 kg and the other of mass 7.00 kg.The lighter fragment goes directly forward,and the explosion releases 1.50 × 10³ J of mechanical energy to the fragments.Find the magnitude and direction of the velocity of the heavier fragment relative to the ground just after the explosion.Ignore the effect of any ejected gases.

Question 24

A 480-kg car moving at 14.4 m/s hits from behind a 570-kg car moving at 13.3 m/s in the same direction.If the new speed of the heavier car is 14.0 m/s,what is the speed of the lighter car after the collision,assuming that any unbalanced forces on the system are negligibly small?

A)13.6 m/s
B)10.5 m/s
C)19.9 m/s
D)5.24 m/s

Question 25

A car of mass 1689 kg collides head-on with a parked truck of mass 2000 kg.Spring mounted bumpers ensure that the collision is essentially elastic.If the velocity of the truck is 17 km/h (in the same direction as the car's initial velocity)after the collision,what was the initial speed of the car?

A)19 km/h
B)38 km/h
C)29 km/h
D)10 km/h

Question 26

Two objects of the same mass move along the same line in opposite directions.The first mass is moving with speed v.The objects collide,stick together,and move with speed 0.100v in the direction of the velocity of the first mass before the collision.What was the speed of the second mass before the collision?

A)1.20v
B)10.0v
C)0.900v
D)0.800v
E)0.00v

Question 27

A 5.00-kg ball is hanging from a long but very light flexible wire when it is struck by a 1.50-kg stone traveling horizontally to the right at 12.0 m/s.The stone rebounds to the left with a speed of 8.50 m/s,and the ball swings to a maximum height h above its original level.The value of h is closest to

A)0.0563 m.
B)1.10 m.
C)1.93 m.
D)2.20 m.
E)3.69 m.

Question 28

A billiard ball traveling at 3.00 m/s collides perfectly elastically with an identical billiard ball initially at rest on the level table.The initially moving billiard ball deflects 30.0° from its original direction.What is the speed of the initially stationary billiard ball after the collision?

A)2.00 m/s
B)0.866 m/s
C)1.50 m/s
D)2.59 m/s
E)0.750 m/s

Question 29

A 2.3-kg object traveling at 6.1 m/s collides head-on with a 3.5-kg object traveling in the opposite direction at 4.8 m/s.If the collision is perfectly elastic,what is the final speed of the 2.3-kg object?

A)0.48 m/s
B)7.1 m/s
C)3.8 m/s
D)4.3 m/s
E)6.6 m/s

Question 30

Two ice skaters push off against one another starting from a stationary position.The 45.0-kg skater acquires a speed of 0.375 m/s.What speed does the 60.0-kg skater acquire? Assume that any other unbalanced forces during the collision are negligible.

A)0.500 m/s
B)0.281 m/s
C)0.375 m/s
D)0.750 m/s
E)0.000 m/s

Question 31

A pool player is attempting a fancy shot.He hits the cue ball giving it a speed of 5.57 m/s and directs its center on a path tangent to the surface of the target ball having the same mass as the cue ball.After the collision (on a frictionless table)the initially-stationary ball moves with a speed of 4.82 m/s.After the collision,the new speed of the cue ball and the relative direction of the balls are closest to

A)2.79 m/s,at 90° to each other.
B)2.79 m/s,at 60° to each other.
C)8.34 m/s,at 90° to each other.
D)8.34 m/s,at 60° to each other.

Question 32

An 8.0-g bullet is shot into a 4.0-kg block,at rest on a frictionless horizontal surface (see the figure).The bullet remains lodged in the block.The block moves into an ideal massless spring and compresses it by 8.7 cm.The spring constant of the spring is 2400 N/m.The initial velocity of the bullet is closest to

A)1100 m/s.
B)1200 m/s.
C)900 m/s.
D)1300 m/s.
E)1000 m/s.

Question 33

In the figure,determine the character of the collision.The masses of the blocks,and the velocities before and after are given.The collision is

A)perfectly elastic.
B)partially inelastic.
C)completely inelastic.
D)characterized by an increase in kinetic energy.
E)not possible because momentum is not conserved.

Question 34

A 2.00-kg object traveling east at 20.0 m/s collides with a 3.00-kg object traveling west at 10.0 m/s.After the collision,the 2.00-kg object has a velocity 5.00 m/s to the west.How much kinetic energy was lost during the collision?

A)0.000 J
B)458 J
C)516 J
D)91.7 J
E)175 J

Question 35

A 15-g bullet is shot vertically into an 2-kg block.The block lifts upward 8.0 mm (see the figure).The bullet penetrates the block and comes to rest in it in a time interval of 0.0010 s.Assume the force on the bullet is constant during penetration and that air resistance is negligible.The initial kinetic energy of the bullet is closest to

A)21 J.
B)14 J.
C)10 J.
D)0.0012 J.
E)0.16 J.

Question 36

A 1000-kg car approaches an intersection traveling north at 20.0 m/s.A 1200-kg car approaches the same intersection traveling east at 22.0 m/s.The two cars collide at the intersection and lock together.Ignoring any external forces that act on the cars during the collision,what is the velocity of the cars immediately after the collision?

A)29.7 m/s in a direction 47.7° east of north
B)21.1 m/s in a direction 47.7° west of south
C)15.1 m/s in a direction 52.8° east of north
D)21.1 m/s in a direction 52.8° east of north
E)21.1 m/s in a direction 47.7° east of north

Question 37

On a frictionless horizontal table,two blocks (A of mass 2.00 kg and B of mass 3.00 kg)are pressed together against an ideal massless spring that stores 75.0 J of elastic potential energy.The blocks are not attached to the spring and are free to move free of it once they are released from rest.The maximum speed achieved by each block is closest to

A)6.71 m/s (A),4.47 m/s (B).
B)4.47 m/s (A),6.71 m/s (B).
C)5.48 m/s for both.
D)6.12 m/s (A),5.00 m/s (B).
E)5.00 m/s (A),6.12 m/s (B).

Question 38

Two automobiles traveling at right angles to each other collide and stick together.Car A has a mass of 1200 kg and had a speed of 25 m/s before the collision.Car B has a mass of 1600 kg.The skid marks show that,immediately after the collision,the wreckage was moving in a direction making an angle of 40° with the original direction of car A.What was the speed of car B before the collision,assuming that any other unbalanced forces are negligible?

A)16 m/s
B)18 m/s
C)11 m/s
D)21 m/s
E)14 m/s

Question 39

A car heading north collides at an intersection with a truck of the same mass as the car heading east.If they lock together and travel at 28 m/s at 46° north of east just after the collision,how fast was the car initially traveling? Assume that any other unbalanced forces are negligible.

A)40 m/s
B)20 m/s
C)80 m/s
D)30 m/s

Question 40

In the figure,determine the character of the collision.The masses of the blocks,and the velocities before and after are given,and no other unbalanced forces act on these blocks.The collision is

A)perfectly elastic.
B)partially inelastic.
C)completely inelastic.
D)characterized by an increase in kinetic energy.
E)not possible because momentum is not conserved.

Question 41

A 1.2-kg spring-activated toy bomb slides on a smooth surface along the x-axis with a speed of 0.50 m/s.At the origin 0,the bomb explodes into two fragments.Fragment 1 has a mass of 0.40 kg and a speed of 0.90 m/s along the negative y-axis.In the figure,the angle θ,made by the velocity vector of fragment 2 and the x-axis,is closest to

A)31°.
B)37°.
C)38°.
D)53°.
E)59°.

Question 42

A 1.2-kg spring-activated toy bomb slides on a smooth surface along the x-axis with a speed of 0.50 m/s.At the origin 0,the bomb explodes into two fragments.Fragment 1 has a mass of 0.40 kg and a speed of 0.90 m/s along the negative y-axis.In the figure,the energy released by the explosion is closest to

A)0.20 J.
B)0.24 J.
C)0.28 J.
D)0.32 J.
E)0.36 J.

Question 43

A plate falls vertically to the floor and breaks up into three pieces,which slide along the floor.Immediately after the impact,a 320-g piece moves along the x-axis with a speed of 2.00 m/s and a 355-g piece moves along the y-axis with a speed of 1.50 m/s.The third piece has a mass of 100 g.In what direction does the third piece move? You can neglect any horizontal forces during the crash.

A)216.9° from the x-axis
B)219.8° from the x-axis
C)36.9° from the x-axis
D)39.9° from the x-axis
E)39.8° from the x-axis