# Quiz 8: Systems of Particles and Conservation of Linear Momentum

Physics & Astronomy

Q 1Q 1

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 10

^{4}kg · m/s at 48º S of E B) 1.26 10^{4}kg · m/s at 48º S of W C) 1.26 10^{4}kg · m/s at 48º N of W D) 1.78 10^{4}kg · m/s at 48º N of W E) 910 kg · m/s at 48º S of EFree

Multiple Choice

B

Free

Multiple Choice

E

Q 3Q 3

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.

Free

Multiple Choice

E

Q 4Q 4

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)

Free

Multiple Choice

Q 5Q 5

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)

Free

Multiple Choice

Q 6Q 6

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 10

^{3}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/sFree

Multiple Choice

Q 7Q 7

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.

Free

Multiple Choice

Q 8Q 8

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.

Free

Multiple Choice

Q 9Q 9

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

Free

Multiple Choice

Q 10Q 10

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) Mv

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Multiple Choice

Q 11Q 11

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

Free

Multiple Choice

Q 12Q 12

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.

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Multiple Choice

Q 13Q 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.

Free

Multiple Choice

Q 14Q 14

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.

Free

Multiple Choice

Q 15Q 15

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.

Free

Multiple Choice

Q 16Q 16

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.

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Multiple Choice

Q 17Q 17

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)

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Multiple Choice

Q 18Q 18

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

^{2}B) mv^{2}C) mv^{2}D) 2mv^{2}E) 4mv^{2}Free

Multiple Choice

Q 19Q 19

A superball of mass m is dropped vertically from a height, h. If the impact time with the floor is 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

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Multiple Choice

Q 20Q 20

Calculate the impulse by the force, as shown in the figure below.
A) 1.0 mNs
B) 2.0 mNs
C) 4.0 mNs
D) 10.0 mNs
E) 40.0 mNs

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Multiple Choice

Q 21Q 21

A force acting on an object is approximated as F = 4 sin (100t) N from t = 0 to t = 10 ms. Calculate the impulse on the object.
A) 1/(25) Ns
B) 2/(25) Ns
C) 1/(200) Ns
D) 1/(400) Ns
E) 1/(800) Ns

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Multiple Choice

Q 22Q 22

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/m

^{3}. A) 5 N B) 40 N C) 80 N D) 100 N E) 200 NFree

Multiple Choice

Q 23Q 23

An object of mass M

_{1}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, M_{1}and M_{2}stick together and move with a speed of A) v B) M_{1}v C) (M_{1}+ M_{2})v/M_{1 }D) M_{1}v/(M_{1}+ M_{2}) E) M_{1}v/M_{2 }Free

Multiple Choice

Q 24Q 24

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.

Free

Multiple Choice

Q 25Q 25

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

Free

Multiple Choice

Q 26Q 26

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.

Free

Multiple Choice

Q 27Q 27

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.

Free

Multiple Choice

Q 28Q 28

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

Free

Multiple Choice

Q 29Q 29

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

Free

Multiple Choice

Q 30Q 30

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.

Free

Multiple Choice

Q 31Q 31

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

Free

Multiple Choice

Q 32Q 32

A railway car having a total mass of 5.8 10

^{5}kg, moving with a speed of 9.1 km/h, strikes another car that has a mass of 8.7 10^{5}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/hFree

Multiple Choice

Q 33Q 33

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.

Free

Multiple Choice

Q 34Q 34

A mass m

_{1}= 2.5 kg is connected to another mass m_{2}= 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 m_{1}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/sFree

Multiple Choice

Q 35Q 35

The balls shown in the figure are strung on a taut wire and slide without friction. If the balls are of equal mass, the diagram that best represents an elastic collision is
A) 1
B) 2
C) 3
D) 4
E) 5

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Multiple Choice

Q 36Q 36

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.

Free

Multiple Choice

Q 37Q 37

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.

Free

Multiple Choice

Q 38Q 38

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.

Free

Multiple Choice

Q 39Q 39

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)

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Multiple Choice

Q 40Q 40

Consider an inelastic collision between balls of mass m

_{1}and m_{2}. 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 }Free

Multiple Choice

Q 41Q 41

The momentum vectors

_{1}and_{1}of two bodies are shown before collision. After the collision, body A is at rest. The vector that correctly represents the momentum of body B after the collision is A) B) C) D) E)Free

Multiple Choice

Q 42Q 42

Vectors and are the momentum vectors of two equal masses, m

_{1}and m_{2}. A third equal mass, m_{3}, has a momentum such that when the three masses collide and stick together the combined mass has zero velocity. The vector that best represents the momentum of mass m_{3}is A) B) C) D) E)Free

Multiple Choice

Q 43Q 43

Two objects, one of mass m

_{1}= 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. m_{1}is observed to recoil with velocity v_{1}= 2 m/s , and m_{2}shots forward with velocity v_{2}= 4 m/s . What is the mass of m_{2}? A) 0.5 kg B) 1 kg C) 2 kg D) 4 kg E) cannot be determinedFree

Multiple Choice

Q 44Q 44

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

Free

Multiple Choice

Q 45Q 45

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

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Multiple Choice

Q 46Q 46

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.

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Multiple Choice

Q 47Q 47

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/sFree

Multiple Choice

Q 48Q 48

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

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Multiple Choice

Q 49Q 49

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

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Multiple Choice

Q 50Q 50

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.

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Multiple Choice

Q 51Q 51

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

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Multiple Choice

Q 52Q 52

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

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Multiple Choice

Q 53Q 53

Two identical masses are hung on strings of the same length. One mass is released from a height h above its free-hanging position and strikes the second mass; the two stick together and move off. They rise to a height H given by
A) 3h/4
B) h/4
C) h/2
D) h
E) None of these is correct.

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Multiple Choice

Q 54Q 54

A particle with speed v

_{1}= 2.64 10^{6}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 v_{1}. The speed of the struck particle after the collision is approximately A) 3.4 10^{6}m/s B) 1.3 10^{6}m/s C) 0.53 10^{6}m/s D) 1.9 10^{6}m/s E) 6.4 10^{6}m/sFree

Multiple Choice

Q 55Q 55

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

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Multiple Choice

Q 56Q 56

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.

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Multiple Choice

Q 57Q 57

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

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Multiple Choice

Q 58Q 58

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

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Multiple Choice

Q 59Q 59

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

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Multiple Choice

Q 60Q 60

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 10

^{5}N B) 80.0 N C) 1.80 10^{2}N D) zero E) 2.20 10^{4}NFree

Multiple Choice

Q 61Q 61

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/s

^{2}toward the tree. B) zero with respect to the tree. C) 80 m/s^{2}away from the tree. D) 1.8 10^{2}m/s^{2}with respect to the car. E) 37 m/s^{2}away from the tree.Free

Multiple Choice

Q 62Q 62

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

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Multiple Choice

Q 63Q 63

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

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Multiple Choice

Q 64Q 64

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.

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Multiple Choice

Q 65Q 65

A ball of mass m and velocity

_{1}collides with and sticks to a ball of mass M and velocity_{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) zeroFree

Multiple Choice

Q 66Q 66

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

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Multiple Choice

Q 67Q 67

The force exerted on a 10-kg mass is given by
F = 10 + 2t
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

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Multiple Choice

Q 68Q 68

The force exerted on a body of mass 10 kg varies with time according to
F = 20t + 10
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

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Multiple Choice

Q 69Q 69

What is the physical significance of the area under the curve shown in the figure?
A) work
B) impulse
C) velocity
D) acceleration
E) mass

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Multiple Choice

Q 70Q 70

Using a mallet, you strike a ball of mass 0.50 kg that is initially at rest. The force F on the ball as a function of time is plotted in the figure. At t = 2.0 ms, the speed of the ball is
A) 10 m/s
B) 8.0 m/s
C) 6.0 m/s
D) 4.0 m/s
E) 2.0 m/s

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Multiple Choice

Q 71Q 71

A 4.0-kg block, initially at rest, experiences a force that varies with time as shown in the figure. When t = 6.0 ms, the speed of the block is
A) 3.0 m/s
B) 5.0 m/s
C) 6.0 m/s
D) 12 m/s
E) 6.0 km/s

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Multiple Choice

Q 72Q 72

A body is acted on by an impulsive force from time t = 0 to time t = 10 ms. During this time, the force decreases uniformly from 10

^{3}N to zero as shown in the graph. The change in momentum of the body during this interval is A) 10 kg · m/s B) 5.0 kg · m/s C) 0.16 kg · m/s D) 10^{5}kg · m/s E) a value that cannot be determined from this graph.Free

Multiple Choice

Q 73Q 73

The graph shows the momentum of a body as a function of time. The time at which the force acting on the body is greatest is
A) 0.5 s
B) 2.5 s
C) 4.0 s
D) 1.5 s
E) 5.0 s

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Multiple Choice

Q 74Q 74

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.Free

Multiple Choice

Q 75Q 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

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Multiple Choice

Q 76Q 76

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.

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Multiple Choice

Q 77Q 77

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

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Multiple Choice

Q 78Q 78

A 20-g bullet with an initial velocity of 3.0 10

^{4}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 10^{4}N B) 2.3 10^{3}N C) 9.8 10^{-3}N D) 2.0 10^{2}N E) 4.7 10^{-2}NFree

Multiple Choice

Q 79Q 79

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%

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Multiple Choice

Q 80Q 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

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Multiple Choice

Q 81Q 81

Two billiard balls are traveling to the right with speeds v

_{1}= +0.5 m/s and v_{2}= +0.3 m/s. If m_{1}= 2.5m_{2}, calculate the velocity of m_{1}after it catches up to and impacts m_{2}. The speed of m_{2}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/sFree

Multiple Choice

Q 82Q 82

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

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Multiple Choice

Q 83Q 83

A bullet (mass = m

_{1}) is fired at speed V into a block of mass m_{2}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) m_{1}V/ 3m_{2 }B) 2m_{1}V/ 3m_{2 }C) m_{2}V/ 3m_{1 }D) 2m_{2}V/ 3m_{1 }E) 4m_{2}V/ 9m_{1 }Free

Multiple Choice

Q 84Q 84

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}/mFree

Multiple Choice

Q 85Q 85

An object of mass M is moving with velocity V . Three smaller objects each of mass m are initially at rest. After the collision the small masses have velocities given by v( + ), v(2 ), and v(2 2 ). If m = M/6 and v = V/3, then the final vector velocity of the mass M is
A) 15V /18 + V /9
B) 23V /18 + V /9
C) 13V /6 + V /3
D) 13V /18 + V /9
E) 23V /18 + V /3

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Multiple Choice

Q 86Q 86

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/m

^{3 }) A) 27 N B) 190 N C) 47 N D) 60 N E) 94 NFree

Multiple Choice

Q 87Q 87

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

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Multiple Choice

Q 88Q 88

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

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Multiple Choice

Q 89Q 89

A block of mass 5 kg slides down a frictionless track from a height of 1.5 m. It collides with a second mass of 8 kg. The two blocks stick together and after the impact they begin to slide on a rough surface with a coefficient of kinetic friction of 0.65 until coming to rest. Calculate how far, d, the blocks slide on the rough surface.
A) 3.4 m
B) 0.22 m
C) 2.3 m
D) 0.34 m
E) 0.16 m

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Multiple Choice

Q 90Q 90

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/2mFree

Multiple Choice

Q 91Q 91

Two masses, m

_{1}and m_{2}, 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)Free

Multiple Choice

Q 92Q 92

Use the picture to the right to answer the next questions.
A puck of m

_{1}and moving with velocity v_{1}collides elastically with a second puck of mass m_{2}, which is initially at rest. After the collision, m_{1}moves with velocity v_{1}' at an angle below the x axis and m_{2}moves with velocity v_{2}' 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.Free

Multiple Choice

Q 93Q 93

Use the picture to the right to answer the next questions.
A puck of m

_{1}and moving with velocity v_{1}collides elastically with a second puck of mass m_{2}, which is initially at rest. After the collision, m_{1}moves with velocity v_{1}' at an angle below the x axis and m_{2}moves with velocity v_{2}' at an angle above the x axis. -The conservation of momentum along the x direction can be written as A) m_{1}v_{1}= m_{1}v_{1}' cos + m_{2}v_{2}' cos B) 0 = m_{1}v_{1}' cos + m_{2}v_{2}' cos C) m_{1}v_{1}= m_{1}v_{1}' sin + m_{2}v_{2}' sin D) 0 = m_{1}v_{1}' sin + m_{2}v_{2}' sin E) none of the aboveFree

Multiple Choice

Q 94Q 94

Use the scenario below for the next questions.
You were traveling north at speed v

_{c}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}Free

Multiple Choice

Q 95Q 95

Use the scenario below for the next questions.
You were traveling north at speed v

_{c}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 10^{5}J B) 5.3 10^{5}J C) 8.0 10^{5}J D) 1.3 10^{6}J E) 1.6 10^{6}JFree

Multiple Choice

Q 96Q 96

Two particles, m

_{1}and m_{2}, each with mass m, is moving with velocity and respectively. The momentum of m_{1}relative to the center-of-mass is A) B) C) D) E)Free

Multiple Choice

Q 97Q 97

A man in a spacecraft that is moving with a velocity V

_{0}in free space runs forward and then stops. The center of mass of the system (that is, the ship and the man) A) slows while the man is running, then speeds up when he stops. B) slows while the man is running, then resumes its original velocity when he stops. C) moves faster while the man is running, then slows when he stops. D) moves faster while the man is running, then resumes its original velocity when he stops. E) continues all the while at its original velocity.Free

Multiple Choice

Q 98Q 98

In a coordinate system whose center of mass moves with a velocity

_{c}, the total momentum in the center-of-mass coordinate system after collision of the two masses m_{1}and m_{2}is A) (m_{1}+ m_{2})_{c }B) [m_{1}m_{2 }/(m_{1}+ m_{2})]_{c }C) [m_{1}/(m_{1}+ m_{2})]_{c }D) [m_{2}/(m_{1}+ m_{2})]_{c }E) zeroFree

Multiple Choice

Q 99Q 99

A woman on a spaceship traveling at a velocity

_{0}in free space runs forward and then suddenly stops. When she stops, the center of mass of the system (that is, the ship and the woman) A) moves in the same direction as_{0}with a slight increase in speed. B) moves in the same direction as_{0}with a slight decrease in speed. C) comes to rest if the woman can run fast enough. D) continues unchanged at a velocity_{0}. E) moves in the direction that the woman runs until she stops.Free

Multiple Choice

Q 100Q 100

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.

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Multiple Choice

Q 101Q 101

In a center-of-mass reference frame,
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.

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Multiple Choice

Q 102Q 102

Cyrano de Bergerac, in the play by Edmond Rostand, claims to have invented six methods of reaching the moon. Five of these are listed below. Select the one that has a physically sound basis.
A) "Adorn my form with crystal vials filled with morning dew, and so be drawn aloft as the sun rises."
B) "Sealing up the air in a cedar chest, rarefy it by means of mirrors placed in an icosahedron."
C) "Construct the form of a huge locust, driven upward by leaps and bounds by impulses due to pellets of saltpeter ejected from the rear."
D) "Smoke, having a natural tendency to rise, blow in a globe enough to raise me."
E) "Seated on an iron plate, I hurl a magnet in the air-the iron follows-I catch the magnet-throw again-and so proceed indefinitely."

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Multiple Choice

Q 103Q 103

A Saturn V rocket with an initial mass m

_{0}of 3 10^{6}kg has a payload that accounts for 27% of this mass, a burn rate of 15 10^{3}kg/s, and a thrust F_{th}of 35 10^{6}N. The exhaust speed is A) 1.46 km/s B) 1.85 km/s C) 2.09 km/s D) 2.33 km/s E) 2.54 km/sFree

Multiple Choice

Q 104Q 104

A Saturn V rocket with an initial mass m

_{0}of 3 10^{6}kg has a payload that accounts for 27% of this mass, a burn rate of 15 10^{3}kg/s, and a thrust F_{th}of 35 10^{6}N. The burn time t_{b}is A) 135 s B) 185 s C) 209 s D) 233 s E) 146 sFree

Multiple Choice

Q 105Q 105

A Saturn V rocket with an initial mass m

_{0}of 3 10^{6}kg has a payload that accounts for 27% of this mass, a burn rate of 15 10^{3}kg/s, and a thrust F_{th}of 35 10^{6}N. The acceleration at lift-off is A) 1.86 m/s^{2 }B) 2.89 m/s^{2 }C) 3.46 m/s^{2 }D) 3.51 m/s^{2 }E) 3.67 m/s^{2 }Free

Multiple Choice

Q 106Q 106

A Saturn V rocket with an initial mass m

_{0}of 3 10^{6}kg has a payload that accounts for 27% of this mass, a burn rate of 15 10^{3}kg/s, and a thrust F_{th}of 35 10^{6}N. The acceleration at burnout is A) 27.8 m/s^{2 }B) 33.4 m/s^{2 }C) 34.7 m/s^{2 }D) 35.9 m/s^{2 }E) 37.7 m/s^{2 }Free

Multiple Choice

Q 107Q 107

A Saturn V rocket with an initial mass m

_{0}of 3 10^{6}kg has a payload that accounts for 27% of this mass, a burn rate of 15 10^{3}kg/s, and a thrust F_{th}of 35 10^{6}N. The final speed of the rocket is A) 1.45 km/s B) 1.57 km/s C) 1.62 km/s D) 1.72 km/s E) 1.83 km/sFree

Multiple Choice