Deck 7: Momentum, Collisions, and the Center of Mass

Question 1

A 5.0-kg ball and a 10.0-kg ball approach each other with equal speeds of 20 m/s. If they collide perfectly inelastically, the speed of the balls just after the collision is approximately

A) 1.0 m/s.
B) 20 m/s.
C) 6.7 m/s.
D) 1.5 m/s.
E) zero.

Answer 1

6.7 m/s.

Question 2

An object of mass M₁ is moving with a speed v on a straight, level, frictionless track when it collides with another mass, M_2, that is at rest on the track. After the collision, M₁ and M₂ stick together and move with a speed of

A) v.
B) M₁v.
C) M₁ + M₂)v/M_1.
D) M₁v/M₁ + M₂).
E) M₁v/M_2.

Answer 2

M₁v/M₁ + M₂).

Question 3

A puck of mass m₁ and initial velocity v₁ collides elastically with a second puck of mass m₂, which is initially at rest. After the collision, m₁ moves with velocity v₁' at an angle below the x axis) and m₂ moves with velocity v₂' at an angle above the x axis). The conservation of momentum along the x direction can be written as

A) m₁ v₁ = m₁v₁' cos + m₂v₂' cos).
B) 0 = m₁v₁' cos + m₂v₂' cos).
C) m₁ v₁ = m₁v₁' sin + m₂v₂' sin).
D) 0 = m₁v₁' sin + m₂v₂' sin).
E) none of the above

Answer 3

m₁ v₁ = m₁v₁' cos + m₂v₂' cos).

Question 4

If a body moves in such a way that its linear momentum is constant, then

A) its kinetic energy is zero.
B) the sum of all the forces acting on it must be zero.
C) its acceleration is greater than zero and is constant.
D) its center of mass remains at rest.
E) the sum of all the forces acting on the body is constant and nonzero.

Question 5

A bullet with a mass of 20 g and a speed of 960 m/s strikes a block of wood of mass 4.5 kg resting on a horizontal surface. The bullet gets embedded in the block. The speed of the block immediately after the collision

A) cannot be found because we don't know whether the surface is frictionless.
B) is 0.21 km/s.
C) is 65 m/s.
D) is 9.3 m/s.
E) None of these is correct.

Question 6

A 40-kg girl, standing at rest on the ice, gives a 60-kg boy, who is also standing at rest on the ice, a shove. After the shove, the boy is moving backward at 2.0 m/s. Ignore friction. The girl's speed is

A) zero.
B) 1.3 m/s.
C) 2.0 m/s.
D) 3.0 m/s.
E) 6.0 m/s.

Question 7

Two masses M and 5M rest on a horizontal frictionless table with a compressed spring of negligible mass between them. When the spring is released, the energy of the spring is shared between the two masses in such a way that

A) M gets 3/5 of the energy.
B) M gets 1/6 of the energy.
C) M gets 1/5 of the energy.
D) M gets 4/5 of the energy.
E) none of these will occur.

Question 8

A boy and girl on ice skates face each other. The girl has a mass of 20 kg and the boy has a mass of 30 kg. The boy pushes the girl backward at a speed of 3.0 m/s. As a result of the push, the speed of the boy is

A) zero.
B) 2.0 m/s.
C) 3.0 m/s.
D) 4.5 m/s.
E) 9.0 m/s.

Question 9

Two masses, m₁ and m₂, are moving with velocities and when they collide. After the collision, the final velocities are and . Which of the following expressions is true? The subscripts x and y represent the components along x and y respectively.)

A)
B)
C)
D)
E) A and B

Question 10

Momentum is conserved in which of the following?

A) elastic collisions
B) inelastic collisions
C) explosions
D) All of these are correct.

Question 11

In a real collision,

A) kinetic energy is conserved.
B) linear momentum is conserved in the absence of external forces.
C) both momentum and kinetic energy are conserved.
D) neither momentum nor kinetic energy is conserved.
E) the extent to which momentum and kinetic energy are conserved depends on the coefficient of restitution.

Question 12

The condition necessary for the conservation of linear momentum in a given system is that

A) energy is conserved.
B) one body is at rest.
C) the net external force is zero.
D) internal forces equal external forces.
E) none of these is correct.

Question 13

A car of mass 1850 kg is traveling at 22.5 m/s in a straight line. A truck of mass 3170 kg has the same momentum as the car. The speed of the truck is

A) 38 m/s.
B) 13 m/s.
C) 10 m/s.
D) 40 m/s.
E) 27 m/s.

Question 14

A puck of mass m₁ and initial velocity v₁ collides elastically with a second puck of mass m₂, which is initially at rest. After the collision, m₁ moves with velocity v₁' at an angle below the x axis) and m₂ moves with velocity v₂' at an angle above the x axis). Which of the following statements is true?

A) Momentum is conserved in the x direction.
B) Momentum is conserved in the y direction.
C) The total momentum before equals the total momentum after the collision.
D) The kinetic energies are conserved.
E) All of the above statements are true.

Question 15

Two identical bodies of mass M move with equal speeds v. The direction of their velocities is illustrated above. The magnitude of the linear momentum of the system is

A) 2Mv.
B) Mv.
C) 4Mv.
D) Mv.
E) 411ec81b3_1997_07ad_8138_b1a53b0bacf9_TB7291_11Mv.

Question 16

A toy car of mass 2.0 kg moving to the right with a speed of 8.0 m/s collides perfectly inelastically with another toy car of mass 3.0 kg that is moving to the left with a speed of 2.0 m/s. Immediately after the collision the velocity of the system is

A) 4.4 m/s to the right.
B) 2.0 m/s to the right.
C) 0 m/s.
D) -2.0 m/s to the right.
E) 10 m/s to the right.

Question 17

Two identical air-hockey pucks are moving on an air-hockey track with an x-y axis drawn upon it. Puck A has a velocity of 5 m/s at an angle of 35 degrees above the x-axis. Puck B has a velocity of 6 m/s at an angle of 70 degrees above the horizontal. Which puck has a larger momentum in the x-direction?

A) Puck A
B) Puck B
C) Their momentums are equal.
D) There is not enough information given.

Question 18

For brief collisions between objects with no external forces applied to them,

A) kinetic energy is conserved.
B) both momentum and kinetic energy are conserved.
C) neither momentum nor kinetic energy is conserved.
D) the relative velocities before and after impact are equal and oppositely directed.
E) momentum is conserved.

Question 19

For this question, assume that all velocities are horizontal and that there is no friction. Two skaters A and B are on an ice surface. A and B have the same mass M = 90.5 kg. Skater A is initially motionless, and then throws a ball with mass m = 200 g toward B with a speed v = 21.5 m/s relative to the ice. B catches the ball and throws it back to A with the same speed. After A catches the ball, his speed with respect to the ice is

A) 4.3  10³ m/s.
B) 4.3 m/s.
C) 4.8  10^-2 m/s.
D) 9.5  10^-2 m/s.
E) 0.34 m/s.

Question 20

A golf ball and a Ping-Pong ball are dropped in a vacuum chamber. When they have fallen halfway to the floor, they have the same

A) speed.
B) potential energy.
C) kinetic energy.
D) momentum.
E) speed, potential energy, kinetic energy, and momentum.

Question 21

A particle of mass 2m is moving to the right in projectile motion. At the top of its trajectory, an explosion breaks the particle into two equal parts. After the explosion, one part falls straight down with no horizontal motion. What is the direction of the velocity of the other part in the instant after the explosion?

A) up and to the left
B) stops moving
C) up and to the right
D) straight up
E) down and to the right

Question 22

A 7000-kg coal car of a train coasts at 7.0 m/s on a frictionless track when a 3000-kg load of coal is dropped vertically onto the car. The coal car's speed after the coal is added is

A) 2.1 m/s.
B) 3.0 m/s.
C) 4.9 m/s.
D) 7.0 m/s.
E) 16 m/s.

Question 23

Instead of a ballistic pendulum, we could use a system where the bullet mass = m) is fired into a block mass = M) that is coupled to an uncompressed spring with spring constant k). The speed of the bullet, v, can be found by measuring the maximum distance, d, of compression of the spring. In this situation the initial speed of the bullet is given by

A) k  M+m))^1/2  d/M.
B) k  M))^1/2  d/m.
C) k  M+m))^1/2  d/m.
D) k  M-m))^1/2  d/m.
E) k  M+m))^1/2  d/2m.

Question 24

A block that has a mass M = 4.25 kg is hanging at rest on a light string. A projectile with a mass m = 250 g moving horizontally strikes M and sticks to it. The block and its projectile swing up, and the center of mass rises a distance h = 12.0 cm. The speed of the projectile is approximately

A) 28 m/s.
B) 42 m/s.
C) 0.28 km/s.
D) 26 m/s.
E) 14 m/s.

Question 25

Five billiard balls are in contact and at rest on a wire that passes through their centers. Two billiard balls are slammed into one end of the row of five at a velocity . If the balls are free to slide but not roll and if the collision is elastic, which of the following is most likely to take place?

A) One ball at each end goes off with a speed v.
B) One ball on the side opposite the striking balls goes off with a speed of 2v.
C) The five balls move off together with a speed of 2v/5.
D) Two balls on the side opposite the striking balls go off with a speed of v.
E) None of these will occur.

Question 26

An 1810-kg truck traveling eastward at 64.4 km/h collides at an intersection with a 905-kg automobile traveling northward at 96.5 km/h. The vehicles lock together and immediately after the collision are headed in which direction?

A) 30^o N of E
B) 37^o N of E
C) 45^o N of E
D) 53^o N of E
E) 67^o N of E

Question 27

The figure shows a ballistic pendulum in three states. The system considered to be the ball and the pendulum) will move in such a way that

A) the kinetic energy is conserved during the collision.
B) the linear momentum is conserved after the collision.
C) the linear momentum is not conserved during the collision.
D) the total mechanical energy is conserved during the collision.
E) the total mechanical energy is conserved after the collision.

Question 28

For a system consisting of two particles that undergo an elastic collision,

A) momentum is conserved but the total energy is not conserved.
B) neither the kinetic energy nor the momentum is conserved.
C) neither the total energy nor the momentum is necessarily conserved.
D) the mechanical energy is conserved but momentum is not conserved.
E) both kinetic energy and momentum are conserved.

Question 29

A 20-g bullet is fired into a 2.0-kg block of wood placed on a horizontal surface. The bullet stops in the block. The impact moves the block + bullet) a distance of 5 m before it comes to rest. If the coefficient of kinetic friction between the block and surface is 0.25, calculate the speed of the block + bullet) system immediately after impact.

A) 20 m/s
B) 3.5 m/s
C) 25 m/s
D) 5.0 m/s
E) 2.2 m/s

Question 30

A block of wood with a mass M = 4.65 kg is resting on a horizontal surface when a bullet with a mass m = 18 g and moving with a speed v = 725 m/s strikes it. The coefficient of friction between the block and the surface is µ = 0.35. The distance the block moves across the surface is

A) 1.1 m.
B) 3.3 m.
C) 0.41 m.
D) 11 m.
E) None of these is correct.

Question 31

A projectile with a mass 6M is fired at a speed of 400 m/s at an angle of 60^o above the horizontal. At the highest point of its trajectory, the projectile is broken into two equal pieces by an internal explosion. Just after the explosion, one of the two pieces is known to be traveling vertically downward at a speed of 300 m/s. The magnitude of the velocity of the other half of the projectile is

A) 500 m/s.
B) 1.50 km/s.
C) 400 m/s.
D) 710 m/s.
E) 123 m/s.

Question 32

A bullet of mass m and velocity strikes and becomes imbedded in a wooden block of mass M, which is initially at rest on a frictionless surface. The ratio of the velocity of the system after collision to the initial velocity of the bullet is

A) M + m)/m.
B) M + m)/M.
C) M/m + M).
D) m/m + M).
E) M/m - M).

Question 33

A bullet, m = 0.500 kg, traveling with a velocity of 100 m/s strikes and embeds itself in the bob of a ballistic pendulum, M = 9.50 kg. The combined masses rise to a height h = 1.28 m. The speed V_f of the combined masses immediately following impact is

A) 5.00 m/s.
B) 5.26 m/s.
C) 9.10 m/s.
D) 10.0 m/s.
E) 22.3 m/s.

Question 34

Consider an inelastic collision between balls of mass m₁ and m₂. The velocities before the collision are ₁ and ₂, respectively, and the velocities after the collision are ₁ and ₂, respectively. Which of the following statements concerning this collision is true?

A) m_{1 1} + m_1
1 = m_2
2 + m_2
2
B) ₂ -
₁ >
₁ -
₂
C) ₂ -
₁ =
₁ -
₂
D) ₂ -
₁ <
₁ -
₂
E) m_1
1)² +
M_2
2)² =
M_1
1)² +
M_2
2)²

Question 35

Two equal masses travel in opposite directions with equal speeds. They collide in a collision that is between elastic and inelastic. Just after the collision, their velocities are

A) zero.
B) equal to their original velocities.
C) equal in magnitude but opposite in direction to their original velocities.
D) less in magnitude and in the same direction as their original velocities.
E) less in magnitude and opposite in direction to their original velocities.

Question 36

What is the truck speed in terms of v_c?

A) 0.5v_c
B) 0.75v_c
C) 0.87v_c
D) v_c
E) 1.15v_c

Question 37

A railway car having a total mass of 5.8  10⁵ kg, moving with a speed of 9.1 km/h, strikes another car that has a mass of 8.7  10⁵ kg and is initially at rest. The speed of the coupled cars after the collision is

A) 9.1 km/h.
B) 7.2 km/h.
C) 3.6 km/h.
D) 1.8 km/h.
E) 4.2 km/h.

Question 38

A bullet mass = m) is fired at speed V into a block of mass M with M > m) which is hanging vertically from a light string of length L. The bullet stops in the block. If the recoiling block + bullet system reaches a height of 2/3L, then the initial speed of the bullet is given by

A) M  1gL/3)^1/2/m.
B) M  2gL/3)^1/2/m.
C) M  3gL/4)^1/2/m.
D) m  4gL/3)^1/2/M.
E) M  4gL/3)^1/2/m.

Question 39

Two cars of equal mass travel in opposite directions at equal speeds. They collide in a perfectly inelastic collision. Just after the collision, their velocities are

A) zero.
B) equal to their original velocities.
C) equal in magnitude but opposite in direction to their original velocities.
D) less in magnitude and in the same direction as their original velocities.
E) less in magnitude and opposite in direction to their original velocities.

Question 40

A moving particle is stopped by a single head-on collision with a second, stationary particle if the moving particle undergoes

A) an elastic collision with a second particle of much smaller mass.
B) an elastic collision with a second particle of much greater mass.
C) an elastic collision with a second particle of equal mass.
D) an inelastic collision with a second particle of any mass.

Question 41

Two billiard balls are traveling to the right with speeds v₁ = +0.5 m/s and v₂ = +0.3 m/s. If m₁ = 2.5m₂, calculate the velocity of m₁ after it catches up to and impacts m₂. The speed of m₂ after the collision is +0.55 m/s.

A) +0.45 m/s
B) +0.25 m/s
C) +0.75 m/s
D) +0.35 m/s
E) +0.40 m/s

Question 42

A superball of mass m is dropped vertically from a height, h. If the impact time with the floor is Δt, what is the average force on the ball? Assume that the superball bounces back to the same height it started at.)

A)
B)
C)
D)
E) None of the above.

Question 43

A helium atom mass = 4m) moving with speed collides elastically with a deuterium hydrogen 2) atom mass = 2m) at rest. Calculate the percentage change in the kinetic energy of the helium atom after the collision.

A) 11%
B) 36%
C) 50%
D) 64%
E) 89%

Question 44

While in horizontal flight at a speed of 20 m/s, a baseball of mass 0.11 kg is struck by a bat. After leaving the bat, the baseball has a speed of 29 m/s in a direction opposite to its original direction. The magnitude of the impulse given the ball is

A) 0.99 kg · m/s.
B) 5.4 kg · m/s.
C) 2.2 kg · m/s.
D) 3.2 kg · m/s.
E) 0.55 kg · m/s.

Question 45

Glider A, traveling at 10 m/s on an air track, collides elastically with glider B traveling at 8.0 m/s in the same direction. The gliders are of equal mass. The final speed of glider B is

A) 8.4 m/s.
B) 10 m/s.
C) 8.0 m/s.
D) 4.0 m/s.
E) 12 m/s.

Question 46

Two bodies A and B move toward each other with speeds of 80 cm/s and 20 cm/s, respectively. The mass of A is 140 g and that of B is 60 g. After a head-on, perfectly elastic collision, the speed of B is

A) 8.0 cm/s.
B) 20 cm/s.
C) 92 cm/s.
D) 1.2 m/s.
E) 1.3 m/s.

Question 47

A helium atom mass = 4m) moving with speed V collides elastically with a tritium hydrogen 3) atom mass = 3m) at rest. Calculate the speed of the tritium atom after the collision.

A) 0.86 V
B) 1.33 V
C) 1.14 V
D) 1.25 V
E) 1.00 V

Question 48

A car having a total mass of 2250 kg and traveling at 72 km/h smashes into a tree. The car is stopped in 0.25 s. The driver of the car is not held in place by a seat belt or any other restraining device. Just after the impact but before the driver hits any part of the car, the acceleration of the driver is

A) 80 m/s² toward the tree.
B) zero with respect to the tree.
C) 80 m/s² away from the tree.
D) 1.8  102m/s² with respect to the car.
E) 37 m/s² away from the tree.

Question 49

In an elastic collision of two objects,

A) momentum is not conserved.
B) momentum is conserved, and the kinetic energy after the collision is less than its value before the collision.
C) momentum is conserved, and the kinetic energy after the collision is the same as the kinetic energy before the collision.
D) momentum is not conserved, and the kinetic energy of the system after the collision differs from the kinetic energy of the system before the collision.
E) the kinetic energy of the system after the collision depends on the masses of the objects.

Question 50

A particle of mass m moving at 5.0 m/s in the positive x direction makes a glancing elastic collision with a particle of mass 2m that is at rest before the collision. After the collision, m moves off at an angle of 45^o to the x axis and 2m moves off at 60^o to the x axis. The speed of m after the collision is

A) 4.5 m/s.
B) 2.5 m/s.
C) 3.3 m/s.
D) 1.8 m/s.
E) 1.1 m/s.

Question 51

A particle with speed v₁ = 2.64  10⁶ m/s makes a glancing elastic collision with another particle that is at rest. Both particles have the same mass. After the collision, the struck particle moves off at 45^o to v₁. The speed of the struck particle after the collision is approximately

A) 3.4  106 m/s.
B) 1.3  106 m/s.
C) 0.53  106 m/s.
D) 1.9  106 m/s.
E) 6.4  106 m/s.

Question 52

You shoot an arrow with a mass of 0.54 kg from a bow. The bow exerts a force of 125 N for 0.65 s. The speed of the arrow as it leaves the bow is

A) 0.23 km/s.
B) 0.10 km/s.
C) 0.15 km/s.
D) 0.30 km/s.
E) 0.27 km/s.

Question 53

You shoot an arrow with a mass of 0.54 kg at 45^o above the horizontal. The bow exerts a force of 125 N for 0.65 s. With no air resistance, the maximum height the arrow reaches is

A) 1.2 km.
B) 5.4 m.
C) 0.57 km.
D) 0.29 km.
E) 0.61 km.

Question 54

A car having a total mass of 2250 kg and traveling at 72.0 km/h smashes into a tree. The car is stopped in 0.250 s. The average force acting on the car during the collision is

A) 1.80  10⁵ N.
B) 80.0 N.
C) 1.80  10² N.
D) zero.
E) 2.20  10⁴ N.

Question 55

Two equal masses travel in opposite directions with equal speed. If they collide in a perfectly elastic collision, then, just after the collision, their velocities will be

A) zero.
B) equal to their original velocities.
C) equal in magnitude but opposite in direction to their original velocities.
D) less in magnitude and in the same direction as their original velocities.
E) less in magnitude and opposite in direction to their original velocities.

Question 56

A firefighter uses a hose that shoots water at a rate of 5 m/s and volume flow rate of 40 L/s. If the firefighter is spraying the wall of a house, what is the average force exerted on the wall, assuming that the water splashes sideways in all directions? The density of water is 1000 kg/m³.

A) 5 N
B) 40 N
C) 80 N
D) 100 N
E) 200 N

Question 57

Two identical teacups, A and B, are dropped from the same height. Teacup A is dropped onto cement and breaks, and Teacup B is dropped onto a trampoline and does not break. Which of the following variables is NOT equal for Teacups A and B?

A) Their mass
B) Their impulse from the collision
C) Their force from the collision
D) Their initial momentum
E) Their final momentum

Question 58

Calculate the impulse delivered by the force shown in the figure below.

A) 1.0 mN s
B) 2.0 mN s
C) 4.0 mN s
D) 10.0 mN s
E) 40.0 mN s

Question 59

Two objects, one of mass m₁ = 2 kg and the second of unknown mass, are connected by a compressed spring with negligible mass. The system is at rest on a frictionless table. Both objects are released simultaneously, and m₁ is observed to recoil with velocity v₁ = 2 m/s , and m₂ shots forward with velocity v₂ = 4 m/s . What is the mass of m₂?

A) 0.5 kg
B) 1 kg
C) 2 kg
D) 4 kg
E) Cannot be determined.

Question 60

A mass m₁ = 2.5 kg is connected to another mass m₂ = 4.0 kg by a compressed spring. Both masses are at rest on a frictionless surface. When the spring is released, the masses are pushed apart and a total energy of 16.8 J is given to the two masses. The speed of mass m₁ is

A) 3.2 m/s.
B) 2.9 m/s.
C) 1.8 m/s.
D) 8.3 m/s.
E) 5.4 m/s.

Question 61

A particle of unknown mass has a momentum of 73 kg · m/s. At a time 7.3 s later, the momentum of the particle is 38 kg · m/s. What is the magnitude of the force acting on the particle during the interval, assuming the motion is in a straight line?

A) It cannot be determined because the mass of the particle is not given.
B) 4.8 N
C) 10 N
D) 5.3 N
E) 9.4 N

Question 62

Water is fired horizontally out of a 7-cm diameter hose directly onto a wall at a speed of 7m/s. Assuming that the water after impact falls straight down the wall, the average force on the wall is density of water = 1000 kg/m³):

A) 27 N.
B) 190 N.
C) 47 N.
D) 60 N.
E) 94 N.

Question 63

A 20-g bullet with an initial velocity of 3.0  104 cm/s penetrates 6.0 cm into a stationary wall. The average force exerted on the bullet by the wall in bringing it to rest is approximately

A) 1.5  104 N.
B) 2.3 103 N.
C) 9.8  10-3 N.
D) 2.0  102 N.
E) 4.7  10-2 N.

Question 64

An automatic rifle fires 0.040-kg projectiles at a speed of 800 m/s. If the gunner holding the rifle in her hands can exert an average force of 160 N against the gun, the maximum number of projectiles she can fire in one minute is

A) 15.
B) 300.
C) 800.
D) 4000.
E) 48,000.

Question 65

A pitcher throws a baseball with a velocity of 27 m/s. After being struck by a bat the ball travels in the opposite direction with a velocity of 40 m/s. If the ball has a mass of 0.11 kg and is in contact with the bat for 3.0 ms, the average force exerted by the bat on the ball is

A) 0.99 kN.
B) 4.8 kN.
C) 1.5 kN.
D) 7.4 kN.
E) 2.5 kN.

Question 66

A uniform 12-inch ruler has a 5-g mass at the "1-inch" mark, and a 10-g mass at the "7-inch" mark. Where is the system's center of mass?

A) At the "0-inch" mark
B) Between the "1-inch" mark and the "6-inch" mark
C) Between the "6-inch" mark and the "10-inch" mark
D) At the "6-inch" mark
E) At the "12-inch" mark

Question 67

Two balls are dropped from a height of 6 m. Ball A bounces up to a height of 4 m whereas ball B bounces up to 2 m. Which ball experiences the larger impulse during its collision with the floor?

A) Ball A
B) Ball B
C) They both experience the same impulse.
D) It is impossible to tell without knowing the masses of the balls.
E) It is impossible to tell without knowing the durations of the collisions.

Question 68

Two balls of equal mass are thrown with equal velocities against a massive wall. The first rebounds with a speed equal to its striking speed, and the second sticks to the wall. The impulse that the first ball transmits to the wall, relative to the second, is

A) twice as great.
B) half as great.
C) the same.
D) four times as great.
E) one-fourth as great.

Question 69

A 200-g ball dropped from a height of 50 cm rebounds to a height of 35 cm after impact. The change in momentum of the ball is

A) 0.51 kgm/s.
B) 0.59 kgm/s.
C) 1.2 kgm/s.
D) 3.3 kgm/s.
E) 0.82 kgm/s.

Question 70

The center of mass of a system of particles is so defined that

A) it is always at rest.
B) it is always at rest or moving with constant velocity.
C) it always moves in a straight line even if the particles are rotating about it.
D) the kinetic energy of the system is a maximum about any axis through the center of mass.
E) its location depends only on the masses of the particles and their locations.

Question 71

₂. If the pair moves on with velocity , the impulse given the ball of mass m during the collision must have been

A) m -
₁).
B) m +
₁).
C) m + M) .
D) m + M) -
₂).
E) zero.

Question 72

In a center-of-mass reference frame for a system with no external forces applied to it,

A) the system's kinetic energy is zero.
B) momentum is not conserved.
C) the total momentum is zero.
D) all collisions are elastic.
E) None of these is correct.

Question 73

A ball with a mass of 50 g is dropped from a point 5.41 m above a sidewalk. The ball is in contact with the sidewalk for 8.1  10^-3 s. What is the magnitude of the average force exerted on the ball?

A) 0.12 kN
B) 89 N
C) 9.2 N
D) 0.49 N
E) It cannot be determined without knowing how high the ball bounces.

Question 74

Two particles, each of mass m, are moving with velocity and The kinetic energy at the center of mass is

A) mv².
B) mv².
C) mv².
D) 2mv².
E) 4mv².

Question 75

A ball of mass m strikes a wall that is perpendicular to its path at speed +v and rebounds in the opposite direction with a speed -v. The impulse imparted to the ball by the wall is

A) 2mv.
B) mv.
C) zero.
D) -mv.
E) -2mv.