Deck 8: Systems of Particles and Conservation of Linear Momentum

Question 1

Two students,sitting on frictionless carts,push against each other.Both are initially at rest and the mass of student 1 and the cart is M,and that of student 2 and the cart is 1.5M.If student 1 pushes student 2 so that she recoils with velocity ,what is the change in momentum of the two students?

A)
B)
C)0
D)
E)

Answer 1

0

Question 2

An automobile of mass 1300 kg has an initial velocity of 7.20 m/s toward the north and a final velocity of 6.50 m/s toward the west.The magnitude and direction of the change in momentum of the car are

A)1.26 $\times$ 10⁴ kg · m/s at 48º S of E
B)1.26 $\times$ 10⁴ kg · m/s at 48º S of W
C)1.26 $\times$ 10⁴ kg · m/s at 48º N of W
D)1.78 $\times$ 10⁴ kg · m/s at 48º N of W
E)910 kg · m/s at 48º S of E

Answer 2

1.26 $\times$ 10⁴ kg · m/s at 48º S of W

Question 3

If the momentum of a mass M is doubled,its kinetic energy will be multiplied by a factor of

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

Answer 3

4

Question 4

Calculate the impulse by the force,as 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 5

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 6

If you take the derivative of the kinetic energy of a particle with respect to its velocity,you get

A)force.
B)momentum.
C)acceleration.
D)mass.
E)potential energy.

Question 7

The SI units of momentum are

A)kg · m · s
B)m²/s
C)kg · s/m
D)kg/J
E)kg · m/s

Question 8

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 9

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

Question 10

A superball of mass m is dropped vertically from a height,h.If the impact time with the floor is $\Delta$ t,what is the average force on the ball? (Assume that the superball bounces back to the same height.)

A)
B)
C)
D)
E)none of the above

Question 11

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 12

Two students,sitting on frictionless carts,push against each other.Both are initially at rest and the mass of student 1 and the cart is M,and that of student 2 and the cart is 1.5M.If student 1 pushes student 2 so that she recoils with velocity ,what is the velocity of student 2.

A)
B)
C)
D)
E)

Question 13

In any and all collisions of short duration and for which it is true that no external forces act on the collision participants,

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 14

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 15

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 16

Momentum is conserved in which of the following?

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

Question 17

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 18

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 19

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 20

A force acting on an object is approximated as F = 4 sin (100 $\pi$ t)N from t = 0 to t = 10 ms.Calculate the impulse on the object.

A)1/(25 $\pi$ )N.s
B)2/(25 $\pi$ )N.s
C)1/(200 $\pi$ )N.s
D)1/(400 $\pi$ )N.s
E)1/(800 $\pi$ )N.s

Question 21

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 22

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 23

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 24

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 25

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 26

A railway car having a total mass of 5.8 $\times$ 10⁵ kg,moving with a speed of 9.1 km/h,strikes another car that has a mass of 8.7 $\times$ 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 27

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.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 28

A 5.0-kg ball and a 10.0-kg ball approach each other with equal speeds of 20 m/s.If they collide 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

Question 29

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 30

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.
E)any type of collision in which the coefficient of restitution is zero.

Question 31

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 32

In riot control,the riot squad uses a water hose that shoots water at a rate of 5 m/s and volume of 40 L/s.What is the average force exerted on a person 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 33

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 34

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 35

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 36

A 40 kg boy,on a stunt,jumps from one ice sled to another sled placed next to the first one,and then quickly jumps back to the first one.The horizontal speed relative to the ice for each jump is 2 m/s and the mass of each sled is 20 kg.What is the speed of the second sled after the second jump? Assume that there is no friction between the sled and the ice.

A)1 m/s
B)2 m/s
C)3 m/s
D)4 m/s
E)8 m/s

Question 37

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 38

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 39

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<sub>1

1</sub> = m<sub>2

2</sub> + m<sub>2

2</sub>
B) ₂ - ₁ > ₁ - ₂
C) ₂ - ₁ = ₁ - ₂
D) ₂ - ₁ < ₁ - ₂
E) m₁( ₁)² + m₂( ₂)² = m₁( ₁)² + m₂( ₂)²

Question 40

An object of mass M₁ is moving with a speed v on a straight,level,frictionless track when it collides with another mass M₂ 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/M₁
D)M₁v/(M₁ + M₂)
E)M₁v/M₂

Question 41

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 42

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 $\times$ 10²m/s² with respect to the car.
E)37 m/s² away from the tree.

Question 43

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 44

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 45

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 motion of the other part just 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 46

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 $\times$ 10⁵ N
B)80.0 N
C)1.80 $\times$ 10² N
D)zero
E)2.20 $\times$ 10⁴ N

Question 47

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 48

Two identical cars approach an intersection.One is traveling east at 18 m/s.The second is traveling north at 24 m/s.They collide violently,sticking together.Immediately after the crash they are moving

A)30 m/s,37º N of E
B)30 m/s,37º E of N
C)15 m/s,37º N of E
D)15 m/s,37º E of N
E)42 m/s,37º N of E

Question 49

The force exerted on a body of mass 10 kg varies with time according to where the units are SI.If the velocity of the body was zero at t = 0,its velocity at t = 5 s is

A)11 m/s
B)16 m/s
C)23 m/s
D)30 m/s
E)0.11 km/s

Question 50

Two balls of equal mass are thrown against a massive wall with equal velocities.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 51

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 52

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 53

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 45º to the x axis and 2m moves off at 60º 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 54

You shoot an arrow with a mass of 0.54 kg at 45º 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 55

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

Question 56

A particle with speed v₁ = 2.64 $\times$ 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 45º to v₁.The speed of the struck particle after the collision is approximately

A)3.4 $\times$ 10⁶ m/s
B)1.3 $\times$ 10⁶ m/s
C)0.53 $\times$ 10⁶ m/s
D)1.9 $\times$ 10⁶ m/s
E)6.4 $\times$ 10⁶ m/s

Question 57

The force exerted on a 10-kg mass is given by where the units are SI.If the mass starts from rest,its velocity after 2 s is

A)14 m/s
B)2.0 m/s
C)2.4 m/s
D)0.20 m/s
E)0.24 km/s

Question 58

A projectile with a mass 6M is fired at a speed of 400 m/s at an angle of 60º 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 59

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 60

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 61

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 62

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 63

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

Question 64

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 $\times$ (M+m))^1/2 $\times$ d/M
B)(k $\times$ (M))^1/2 $\times$ d/m
C)(k $\times$ (M+m))^1/2 $\times$ d/m
D)(k $\times$ (M-m))^1/2 $\times$ d/m
E)(k $\times$ (M+m))^1/2 $\times$ d/2m

Question 65

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 $\times$ 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 66

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 67

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 68

A 20-g bullet with an initial velocity of 3.0 $\times$ 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 $\times$ 10⁴ N
B)2.3 $\times$ 10³ N
C)9.8 $\times$ 10^-3 N
D)2.0 $\times$ 10² N
E)4.7 $\times$ 10^-2 N

Question 69

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 70

Use the scenario below for the next question.
You were traveling north at speed vc in your car of mass m_c = 2000 kg through an intersection when you were struck by a light truck of mass m_t = 4000 kg traveling West. After the collision the two vehicles are stuck together and travel a distance of 20 m in the direction 30° N of W.
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 71

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 72

Use the picture to the right to answer the next question. A puck of m₁ and moving with 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 α below the x axis and m₂ moves with velocity v₂’ at an angle θ above the x axis.


-The conservation of momentum along the x direction can be written as

A)m₁ v₁ = m₁v₁' cos $\alpha$ + m₂v₂' cos $\theta$
B)0 = m₁v₁' cos $\alpha$ + m₂v₂' cos $\theta$
C)m₁ v₁ = m₁v₁' sin $\alpha$ + m₂v₂' sin $\theta$
D)0 = m₁v₁' sin $\alpha$ + m₂v₂' sin $\theta$
E)none of the above

Question 73

Use the picture to the right to answer the next question. A puck of m₁ and moving with 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 α below the x axis and m₂ moves with velocity v₂’ at an angle θ 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 74

A bullet is fired at 100 m/s horizontally into a 2-kg block suspended by a light string of length 1.2 m.If the block and bullet system swing up by 20 degrees to the vertical,the mass of the bullet is given by:

A)79 g
B)24 g
C)28 g
D)15 g
E)123 g

Question 75

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 76

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 $\times$ (1gL/3)^1/2/m
B)M $\times$ (2gL/3)^1/2/m
C)M $\times$ (3gL/4)^1/2/m
D)m $\times$ (4gL/3)^1/2/M
E)M $\times$ (4gL/3)^1/2/m

Question 77

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

Question 78

Use the scenario below for the next question.
You were traveling north at speed vc in your car of mass m_c = 2000 kg through an intersection when you were struck by a light truck of mass m_t = 4000 kg traveling West. After the collision the two vehicles are stuck together and travel a distance of 20 m in the direction 30° N of W.

-If your speed is 72 km/h,what is the work done by friction in bringing the two vehicles to rest after the collision?

A) -4.0 $\times$ 10⁵ J
B) -5.3 $\times$ 10⁵ J
C) - 8.0 $\times$ 10⁵ J
D) -1.3 $\times$ 10⁶ J
E) -1.6 $\times$ 10⁶ J

Question 79

A bullet (mass = m₁)is fired at speed V into a block of mass m₂ at rest.If the bullet escapes from the block with only a third of its original speed then the recoil speed of the block is given by

A)m₁V/ 3m₂
B)2m₁V/ 3m₂
C)m₂V/ 3m₁
D)2m₂V/ 3m₁
E)4m₂V/ 9m₁

Question 80

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