Deck 6: Linear Momentum and Collisions

Question 1

Define linear momentum.

Answer 1

The linear momentum of an object is the product of its mass and velocity.

Question 2

Discuss similarities and differences between KINETIC ENERGY and MOMENTUM.

Answer 2

K is a scalar whereas P is a vector. Both depend upon mass and speed, however K depends upon the square of the speed but P is simply proportional to velocity. Momentum is always conserved for an isolated system, but K might change if it changes to/from other energy forms.

Question 3

Momentum of a system isn't always constant. What condition assures that momentum is conserved for a system?

Answer 3

Momentum is conserved for an "isolated" system; i.e., if the net external force acting on the system is zero.

Question 4

In space, a 4.0 kg metal ball moving 30. m/s has a head-on collision with a stationary second ball of equal mass. After the elastic collision, what are the velocities of the balls?

Question 5

What is the difference between "center of gravity" (cg) (cm)? When are they the same?

Question 6

Why does ion propulsion, which expels material much faster than ordinary chemical rockets, hold such promise for future space travel?

Question 7

In an inelastic collision, the initial kinetic energy is less than the final kinetic energy.

Question 8

Momentum is conserved during a completely inelastic collision.

Question 9

The center of mass of an object must always be located where the physical material of the object is located.

Question 10

Which of the following has units of momentum?

A) N-m
B) J-s/m
C) kg-m²/s²
D) kg-s/m
E) kg- m²/s

Question 11

Figure 6-1, an Olympic diver dives off the high-diving platform.


-See Figure 6-1. The magnitude of his momentum will be a maximum at which point (A, B, C or D)?

A) A
B) B
C) C
D) D

Question 12

Figure 6-1, an Olympic diver dives off the high-diving platform.


-See Figure 6-1. After leaving the platform, the diver's momentum will be least at which point?

A) A
B) B
C) C
D) D

Question 13

Figure 6-1, an Olympic diver dives off the high-diving platform.


-See Figure 6-1. The area under the curve on a F - t graph represents

A) impulse.
B) average mass.
C) momentum.
D) power.
E) work.

Question 14

A Ping-Pong ball moving East at a speed of 4 m/s collides with a stationary bowling ball. The Ping-Pong ball bounces back to the West, and the bowling ball moves very slowly to the East. Which object experiences the greater magnitude impulse during the collision?

A) the bowling ball
B) It's impossible to tell since the velocities after the collision are unknown.
C) Neither; both experienced the same magnitude impulse.
D) the Ping-Pong ball

Question 15

When a cannon fires a cannonball, the cannon will recoil backward because the

A) energy of the cannonball and cannon is conserved.
B) momentum of the cannon is greater than the energy of the cannonball.
C) energy of the cannon is greater than the energy of the cannonball.
D) momentum of the cannon is conserved.
E) momentum of the cannonball and cannon is conserved.

Question 16

Two cars suffer a head-on collision. What is conserved in the collision?

A) mechanical energy and momentum
B) momentum
C) (Neither energy nor momentum is conserved.)
D) kinetic energy

Question 17

Suppose a bug spatters upon your windshield as you drive down the road. Which sustains the greater change of momentum?

A) the car
B) both the same
C) the bug
D) insufficient information

Question 18

Automobile air bags reduce what during a collision?

A) the impulse exerted upon the passenger
B) speed of the automobile
C) the forces exerted upon the passenger
D) the kinetic energy transferred to the passenger

Question 19

Two equal mass balls (one blue and the other gold) are dropped from the same height, and rebound off the floor. The blue ball rebounds to a higher position. Which ball is subjected to the greater magnitude impulse during its collision with the floor?

A) It's impossible to tell since the time intervals and forces are unknown.
B) Both balls were subjected to the same magnitude impulse.
C) the gold ball
D) the blue ball

Question 20

Some automobiles have air bags installed on their dashboards as a safety measure. The impact of a collision causes the bag to inflate, and it then cushions a passenger's head when he is thrown forward in the car. Suppose that such a bag could lengthen the collision time between one's head and the dashboard by a factor of 10. What effect would this have on the force exerted on the head?

A) The force would be reduced by a factor of about 100.
B) The force would be reduced by a factor of about 1000.
C) The force would be reduced by a factor of about 10.
D) The force would be reduced by a factor of about 3.
E) The force would not be reduced, but the energy transferred to the head would be, thereby minimizing the damage done.

Question 21

A sailboat of mass m is moving with a momentum p. Which of the following represents its kinetic energy?

A) p²/2m
B) 1/2 mp²
C) mp
D) mp/3
E) mp/2

Question 22

If you pitch a baseball with twice the kinetic energy you gave it in a previous pitch, the magnitude of its momentum is

A) 2 times as much.
B) times as much.
C) the same.
D) 4 times as much.
E) doubled.

Question 23

A car hits another and the two bumpers lock together during the collision. Is this an elastic or inelastic collision?

A) inelastic
B) insufficient information (It could be either.)
C) elastic

Question 24

In an inelastic collision, the final total momentum is

A) the same as the initial momentum.
B) more than the initial momentum.
C) less than the initial momentum.
D) insufficient information to answer

Question 25

When a car, moving at velocity v, collides head on with a light volley ball, initially at rest, the ball bounces off with velocity

A) -v.
B) -1.5v.
C) -v/2.
D) -2v.
E) -4v.

Question 26

A car of mass M, traveling with a velocity V, strikes a parked station wagon, whose mass is 2M. The bumpers lock together in this head-on inelastic collision. What fraction of the initial kinetic energy is lost in this collision?

A) 1/4
B) 1/3
C) 2/3
D) 1/2
E) 1/9

Question 27

A golf ball traveling 3 m/s to the right collides in a head-on collision with a stationary bowling ball in a friction-free environment. If the collision is almost perfectly elastic, the speed of the golf ball immediately after the collision is

A) slightly greater than 3 m/s.
B) much less than 3 m/s.
C) equal to 3 m/s.
D) slightly less than 3 m/s.

Question 28

A proton, of mass m and speed v, strikes an alpha-particle (which consists of 2 protons and 2 neutrons) at rest. If the collision is completely elastic, what speed will the $\alpha$ -particle have after the collision? (Assume the neutron's mass equals the proton's mass.)

A) 5/3 v
B) zero
C) 2/5 v
D) 2/3 v
E) 3/2 v

Question 29

In a game of pool, the white cue ball hits the 5 ball and stops, while the 5 ball moves away with the same velocity as the cue ball had originally. The type of collision is

A) inelastic.
B) elastic.
C) elastic or inelastic, depending on the mass of the balls.
D) completely inelastic.

Question 30

A 100 kg football linebacker moving at 2 m/s tackles head-on an 80 kg halfback running 3 m/s. Neglecting the effects due to digging in of cleats

A) the linebacker will drive the halfback backward.
B) the halfback will drive the linebacker backward.
C) neither player will drive the other backward.
D) this is a simple example of an elastic collision.

Question 31

Tightrope walkers walk with a long flexible rod in order to

A) allow both hands to hold onto something.
B) increase their total weight.
C) lower their center of mass.
D) move faster along the rope.

Question 32

Consider two unequal masses, M and m. Which of the following statements is false?

A) 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.
B) It is possible for the center of mass to lie within one of the objects.
C) The center of mass lies on the line joining the centers of each mass.
D) The center of mass is closer to the larger mass.

Question 33

The center of mass and the center of gravity coincide

A) only if the object is symmetrical and it is in a uniform gravitational field.
B) at all times.
C) if the object is in a uniform gravitational field.
D) only if the object is symmetrical.

Question 34

Two cars collide head-on on a level friction-free road. The collision was completely inelastic and both cars quickly came to rest during the collision. What is true about the velocity of this system's center of mass?

A) It was never zero.
B) It was not initially zero, but ended up zero.
C) It was always zero.

Question 35

An arrow of mass 20. g is shot horizontally into a bale of hay, striking the hay with a constant velocity of 60. m/s. It penetrates a depth of 20. cm before stopping. What is the average stopping force acting on the arrow?

Question 36

A machine gun, of mass 35. kg, fires 50. gram bullets, with a muzzle velocity of 750. m/s, at the rate of 300. rounds per minute. What is the average force exerted on the machine gun mount?

Question 37

A 0.32 kg ball is moving horizontally 30. m/s just before bouncing off a wall, thereafter moving 25. m/s in the opposite direction.
(a) What is the magnitude of its change in momentum?
(b) What percentage of the kinetic energy was lost in the collision?

Question 38

An empty coal-car (mass 20,000.kg) of a train coasts along at 10.m/s. An unfortunate 3000. kg elephant falls from a bridge and drops vertically into the car. Determine the speed of the car immediately after the elephant is added to its contents.

Question 39

A 60. kg person walks along a 100. kg log at the rate of 0.8 m/s (with respect to the log). With what speed does the log move, with respect to the shore?

Question 40

A mine railroad car, of mass 200 kg, rolls with negligible friction on a horizontal track with a speed of 10.0 m/s. A 70. kg stunt man drops straight down a distance of 4.0 m, and lands in the car. How fast will the car be moving after this happens?

Question 41

As shown in Figure 6-2, a car (mass = 1500 kg) and a small truck (mass = 2000 kg) collide at right angles at an icy intersection. The car was traveling East at 20 m/s and the truck was traveling North at 20 m/s when the collision took place.

What is the speed of the combined wreck, assuming a completely inelastic collision?

Question 42

A 2200. kg auto moving at 12.0 m/s runs into a 3800. kg truck which is moving in the same direction at 5.00 m/s. The collision is perfectly inelastic.
(a) What is the speed of the auto immediately after the collision?
(b) What percentage kinetic energy did the truck gain in the collision?

Question 43

Consider the Sun and its largest planet Jupiter. Where on the line joining them is their center mass? Is it within or outside the Sun?
(Sun-Jupiter avg distance 778.million km;
Solar mass/Jupiter mass = 1.0 × 10³;
Solar diameter 1.4 million km)

Question 44

Three masses are positioned at the following coordinates:
3.0 kg at (3,2) What are the coordinates of the center of mass of the system?

Question 45

1.0 kg is at ( -2.0, 2.0); 2.0 kg is at ( 2.0, -4.0); and 3.0 kg is at ( 2.0, 0.0).
(a) What is the x coordinate of the center of mass?
(b) What is the y coordinate of the center of mass?

Question 46

A 1200. kg ferryboat is moving south at 20. m/s. Its momentum is

A) 24. kN-s
B) 2.4 × 10³ kg-m/s
C) 1.2 × 10³ kg-m/s
D) 6.0 × 10² kg-m/s
E) 1.7 × 10^-3 N-s

Question 47

A ball, of mass 100. g, is dropped from a height of 12. m. Its momentum when it strikes the ground is

A) 1.5 kg.m/s.
B) 1.8 kg.m/s.
C) 4.8 kg.m/s.
D) 3.3 kg.m/s.
E) 2.4 kg.m/s.

Question 48

A handball of mass 0.10 kg, traveling horizontally at 25. m/s, strikes a wall and rebounds at 19. m/s. What is the change in the momentum of the ball?

A) 4.4 N-s
B) 1.8 N-s
C) 72 N-s
D) 5.4 N-s
E) 1.2 N-s

Question 49

A bullet of mass 20. g, traveling at 350. m/s, strikes a steel plate at an angle of 30.° with the plane of the plate. It ricochets off at the same angle, at a speed of 320. m/s, as shown in Figure 6-3. What is the magnitude of the impulse that the wall gives to the bullet?
Figure 6-3

A) 4.3 N-s
B) 0.52 N-s
C) 0.30 kN-s
D) 6.7 N-s
E) 0.30 N-s

Question 50

A toy rocket, of mass 60 g, achieves a velocity of 80 m/s after 3.0 s when fired straight up. What average thrust force does the rocket engine exert?

A) 3.3 N
B) 3.4 N
C) 1.2 N
D) 2.2 N
E) 1.6 N

Question 51

A fire hose is turned on the door of a burning building in order to knock the door down. This requires a force of 1000. N. If the hose delivers 40. liters per second, what is the maximum velocity of the stream needed, assuming the water doesn't bounce back?

A) 50. m/s
B) 25 m/s
C) 15. m/s
D) 40. m/s
E) 30. m/s

Question 52

A 60. gram toy rocket achieves a speed of 80. m/s after 3.0 s, when fired straight up. What is the average total force on the rocket during the 3 s?

A) 2.2 N
B) 3.2 N
C) 1.6 N
D) 1.2 N
E) 3.4 N

Question 53

Water runs out of a horizontal drainpipe at the rate of 120. liters per minute. It falls 3.20 m to the ground. Assuming the water doesn't splash up, what average force does it exert on the ground?

A) 15.8 N
B) 6.20 N
C) 8.88 N
D) 12.0 N
E) 19.6 N

Question 54

A 2000. kg car, traveling to the right at 30. m/s, collides with a brick wall and comes to rest in 0.20 s. The average force the car exerts on the wall is

A) 30. kN.
B) 600 kN.
C) 300 kN.
D) 60. kN.
E) 12. kN.

Question 55

A 2.0 kg softball is pitched to you at 20. m/s. You hit the ball back along the same path, and at the same speed. If the bat was in contact with the ball for 0.10 s, the average force the bat exerted was

A) 0.40 kN.
B) zero.
C) 40. N.
D) 0.65 kN.
E) 0.80 kN.

Question 56

A rope is towing a 100-kg rock, from rest, with a force that varies with time, as shown in Figure 6-4.
Figure 6-4

At the end of 8.0 s, the velocity of the rock is

A) -20 m/s.
B) +80 m/s.
C) +40 m/s.
D) +20 m/s.
E) zero.

Question 57

From the graph, determine the change in momentum after 10 seconds of a 100. kg object.

A) -100. N-s
B) 75.N-s
C) -25.N-s
D) 25.N-s
E) -75.N-s

Question 58

A crane lifts up a 100. kg box, from rest, with a force that varies with time, as shown on the graph.

What is the instantaneous velocity of the box at t = 10. s?

A) +0.25 m/s
B) +0.75 m/s
C) -0.25 m/s
D) zero
E) -0.75 m/s

Question 59

Daisy (50. kg mass) skates on ice at 4.0 m/s to greet her friend (70. kg mass), who is standing still, with open arms. As they collide, while holding each other, with what speed do they both move off together?

A) zero
B) 2.5 m/s
C) 5.0 m/s
D) 1.7 m/s

Question 60

A 3. kg ball of putty moving at 1 m/s collides and sticks to a 2 kg ball initially at rest. The putty and ball then move with a momentum of

A) 0 N-s.
B) 3 N-s.
C) 4 N-s.
D) 2 N-s.
E) 1 N-s.

Question 61

A small bomb, of mass 10. kg, is moving toward the North with a velocity of 5.0 m/s. It explodes into three fragments: a 5.0 kg fragment moving West with a speed of 8.0 m/s; a 4.0 kg fragment moving East with a speed of 10. m/s; and a third fragment with a mass of 1.0 kg. What is the velocity of the third fragment? (Neglect air friction.)

A) 40 m/s North
B) zero
C) 50.m/s North
D) 4.0 m/s North
E) 5.0 m/s South

Question 62

Car A (mass = 1000 kg) moves to the right along a level, straight road at a speed of 6.0 m/s. It collides directly with car B (mass = 200 kg) in a completely inelastic collision. What is the momentum after the collision if car B was initially at rest?

A) 10. KN-s to the right
B) 8.0 KN-s to the left
C) 6.0 KN-s to the right
D) 2.0 KN-s to the right
E) zero

Question 63

Car A (mass = 1000 kg) moves to the right along a level, straight road at a speed of 6.0 m/s. It collides directly with car B (mass = 200 kg) in a completely inelastic collision. What is the speed of the car immediately after the collision?

A) 5.0 m/s
B) 6.0 m/s
C) 4.0 m/s
D) 3.0 m/s
E) zero

Question 64

A 2.0 kg mass moving to the East at a speed of 4.0 m/s collides head-on in an inelastic collision with a stationary 2.0 kg mass. How much kinetic energy is lost during this collision?

A) 8.0 J
B) 16. J
C) 2.0 J
D) zero
E) 4.0 J

Question 65

When a light beach ball rolling with a speed of 6 m/s collides with a heavy exercise ball at rest, the beach ball's speed after the collision will be approximately

A) 3 m/s.
B) 0.
C) 6 m/s.
D) 18 m/s.
E) 12 m/s.

Question 66

A 30. kg child stands at one end of a floating 20. kg canoe that is 10. ft long. The child walks to the other end of the canoe. How far does the canoe move in the water assuming water friction is negligible?

A) 4.0 ft
B) 2.0 ft
C) 8.0 ft
D) 10. ft
E) 6.0 ft

Question 67

A right isosceles triangle is cut out from a piece of sheet metal. The two equal sides are 1.0 m long each. How far is the center of gravity from the right angle (90. °) vertex of the triangle?

A) 0.24 m
B) 0.55 m
C) 0.47 m
D) 0.71 m
E) 0.35 m

Question 68

A 3 kg mass is positioned at (0, 8), and a 1 kg mass is positioned at (12, 0). What are the coordinates of a 4 kg mass which will result in the center of mass of the system of three masses being located at the origin (0, 0)?

A) (-3, -6)
B) (-6, -3)
C) (-12, -8)
D) (3, 6)

Question 69

Two astronauts, of masses 60. kg and 80. kg, are initially at rest in outer space. They push each other apart. What is their separation after the heavier astronaut has moved 12. m?

A) 9. m
B) 24. m
C) 16. m
D) 21. m
E) 28. m

Question 70

Two astronauts, with masses 60. and 80. kg, are initially at rest in outer space. They push each other apart. How far has the heavier astronaut moved when the lighter astronaut has moved 12. m?

A) 7.0 m
B) 21. m
C) 16. m
D) 12. m
E) 9.0 m

Question 71

Astronaut Jennifer's lifeline to her spaceship comes loose and she finds herself stranded, "floating" 100. m from the mothership. She throws her 2.00 kg wrench at 20.0 m/s in a direction away from the ship. If she and her spacesuit have a combined mass of 200. kg how long does it take her to coast back to her spaceship?

A) 500. s
B) 250. s
C) 2.50 minutes
D) 750. s
E) 1000. s