Deck 7: Rotational Motion and the Law of Gravity: Part A

Question 1

Alex throws a 0.15-kg rubber ball down onto the floor.The ball's speed just before impact is 6.5 m/s and just after is 3.5 m/s.If the ball is in contact with the floor for 0.050 s,what is the magnitude of the average force applied by the floor on the ball?

A) 60 N
B) 133 N
C) 30 N
D) 3.5 N

Answer 1

30 N

Question 2

A rock is moving with speed v.If the mass of the rock were tripled and the speed were reduced to v/3,which of the following statements would be true?

A) The kinetic energy of the rock is smaller than in the first case,but the momentum is larger.
B) The kinetic energy of the rock is smaller than in the first case,but the momenta of both are the same.
C) The kinetic energies of the rocks are the same in both cases.
D) The kinetic energy of the rock is 1/9 its previous value.

Answer 2

The kinetic energy of the rock is smaller than in the first case,but the momenta of both are the same.

Question 3

Ann the Astronaut weighs 60 kg.She is space-walking outside the space shuttle and pushes a 270-kg satellite away from the shuttle at 0.90 m/s.What speed does this give Ann as she moves toward the shuttle?

A) 4.0 m/s
B) 5.3 m/s
C) 8.5 m/s
D) 9.0 m/s

Answer 3

4.0 m/s

Question 4

A billiard ball is moving in the x direction at 40.0 cm/s and strikes another billiard ball moving in the y direction at 30.0 cm/s.As a result of the collision,the first ball moves at 50.0 cm/s,and the second ball stops.What is the change in kinetic energy of the system as a result of the collision?

A) 0
B) some positive value
C) some negative value
D) No answer above is correct.

Question 5

Lonnie pitches a baseball of mass 0.15 kg.The ball arrives at home plate with a speed of 40 m/s and is batted straight back to Lonnie with a return speed of 60 m/s.If the bat is in contact with the ball for 0.050 s,what is the impulse experienced by the ball?

A) 360 N·s
B) 20 N·s
C) 400 N·s
D) 15 N·s

Question 6

Two masses m₁ and m₂,with m₁ > m₂,have momenta with equal magnitudes.How do their kinetic energies compare?

A) KE₁ < KE₂
B) KE₁ = KE₂
C) KE₁ > KE₂
D) More information is needed.

Question 7

A soccer ball (mass = 0.43 kg)is moving at a speed of 20 m/s when it is kicked with a force of 300 N resulting in it going in the opposite direction with the same speed as before.What is the magnitude of the impulse delivered to the ball?

A) 0,because the before and after momenta cancel each other.
B) 8.6 kg·m/s
C) 17 kg·m/s
D) 2 600 kg·m/s

Question 8

An unfueled 1000-kg experimental rocket sled at rest on level frictionless rails is loaded with 50 kg of propellant.It exhausts the propellant in a 20 s "burn." The rocket moves at 160 m/s after the burn.What average force is experienced by the rocket during the burn?

A) 0.80 × 10⁴ N
B) 0.75 × 10⁴ N
C) 0.60 × 10⁴ N
D) 0.35 × 10⁴ N

Question 9

Jerome pitches a baseball of mass 0.15 kg.The ball arrives at home plate with a speed of 40 m/s and is batted straight back to Jerome with a return speed of 60 m/s.What is the magnitude of change in the ball's momentum?

A) 4.0 kg
m/s
B) 8.0 kg
m/s
C) 15 kg
m/s
D) 20 kg
m/s

Question 10

A 0.12-kg ball is moving at 6.0 m/s when it is hit by a bat,causing it to reverse direction and have a speed of 8.0 m/s.What is the magnitude of the change in the momentum of the ball?

A) 0.39 kg
m/s
B) 0.42 kg
m/s
C) 1.7 kg
m/s
D) 2.4 kg
m/s

Question 11

A 7.0-kg bowling ball strikes a 2.0-kg pin.The pin flies forward with a velocity of 6.0 m/s;the ball continues forward at 5.0 m/s.What was the original velocity of the ball?

A) 4.0 m/s
B) 5.7 m/s
C) 6.7 m/s
D) 3.3 m/s

Question 12

A 2500-kg truck moving at 10.00 m/s strikes a car waiting at a traffic light,hooking bumpers.The two continue to move together at 6.00 m/s.What was the mass of the struck car?

A) 1730 kg
B) 1670 kg
C) 1200 kg
D) 1070 kg

Question 13

A car wash nozzle directs a steady stream of water at 1.5 kg/s,with a speed of 20 m/s,against a car window.What force does the water exert on the glass? Assume the water does not splash back.

A) 30 N
B) 45 N
C) 300 N
D) 440 N

Question 14

A 75-kg swimmer dives horizontally off a 250-kg raft initially at rest.If the diver's speed immediately after leaving the raft is 2 m/s,what is the corresponding raft speed?

A) 0.2 m/s
B) 0.3 m/s
C) 0.6 m/s
D) 4.0 m/s

Question 15

A crane drops a 0.40-kg steel ball onto a steel plate.The ball's speeds just before impact and after are 4.5 m/s and 4.2 m/s,respectively.If the ball is in contact with the plate for 0.030 s,what is the magnitude of the average force that the ball exerts on the plate during impact?

A) 87 N
B) 116 N
C) 3.0 N
D) 3.5 N

Question 16

Alex throws a 0.43-kg rubber ball down onto the floor.The ball's speed just before impact is 6.5 m/s,and just after is 5.5 m/s.What is the magnitude of the change in the ball's momentum?

A) 0.09 kg
m/s
B) 1.0 kg
m/s
C) 4.3 kg
m/s
D) 5.2 kg
m/s

Question 17

A 0.10-kg object moving initially with a velocity of +0.20 m/s makes an elastic head-on collision with a 0.15-kg object initially at rest.What percentage of the original kinetic energy is gained by the 0.15-kg object?

A) 4%
B) −4%
C) 50%
D) 96%

Question 18

An unfueled 1 000-kg experimental rocket sled on level frictionless rails is loaded with 50 kg of propellant.It exhausts the propellant in a 20 s "burn." If the rocket,initially at rest,moves at 160 m/s after the burn,what impulse is experienced by the rocket sled?

A) 1.1 × 10⁵ kg·m/s
B) 1.6 × 10⁵ kg·m/s
C) 1.5 × 10⁵ kg·m/s
D) 1.9 × 10⁵ kg·m/s

Question 19

A 75-kg swimmer dives horizontally off a 500-kg raft.The diver's speed immediately after leaving the raft is 1.6 m/s.A micro-sensor system attached to the edge of the raft measures the time interval during which the diver applies an impulse to the raft just prior to leaving the raft surface.If the time interval is read as 0.20 s,what is the magnitude of the average horizontal force by diver on the raft?

A) 900 N
B) 450 N
C) 600 N
D) 1500 N

Question 20

A 30-kg object sitting at rest is struck elastically in a head-on collision with a 10-kg object initially moving at +3.0 m/s.Find the final velocity of the 30 kg object after the collision.

A) −1.0 m/s
B) +1.2 m/s
C) +1.5 m/s
D) +2.0 m/s

Question 21

A 90-kg halfback running north with a speed of 10 m/s is tackled by a 120-kg opponent running south at 5.0 m/s.The collision is perfectly inelastic.Compute the velocity of the two players just after the tackle.

A) 1.4 m/s south
B) 2.8 m/s south
C) 2.8 m/s north
D) 1.4 m/s north

Question 22

A 6-kg object is moving to the right at 4 m/s and collides with a 4-kg object moving to the left at 6 m/s.The objects collide and stick together.After the collision,the combined object:

A) has the same kinetic energy that the system had before the collision.
B) has more kinetic energy than the system had before the collision.
C) has no kinetic energy.
D) has less momentum than the system had before the collision.

Question 23

A 20-g bullet moving at 1000 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s.What is the change in the kinetic energy of the bullet-block system as a result of the collision assuming the block is free to move?

A) 0 J
B) −9.5 kJ
C) 9.5 kJ
D) −18 J

Question 24

A miniature spring-loaded,radio-controlled gun is mounted on an air puck.The gun's bullet has a mass of 5.00 g,and the gun and puck have a combined mass of 130g.With the system initially at rest,the radio controlled trigger releases the bullet causing the puck and empty gun to move with a speed of 0.500 m/s.What is the bullet's speed?

A) 4.80 m/s
B) 13.0 m/s
C) 48.0 m/s
D) 12.5 m/s

Question 25

A railroad freight car,mass 15,000 kg,is allowed to coast along a level track at a speed of 2.0 m/s.It collides and couples with a 60,000-kg loaded second car,initially at rest and with brakes released.What percentage of the initial kinetic energy of the 15,000-kg car is preserved in the two-coupled cars after collision?

A) 20%
B) 23%
C) 86%
D) 100%

Question 26

A machine gun is attached to a railroad flatcar that rolls with negligible friction.If the railroad car has a mass of 6.25 × 10⁴ kg,how many bullets of mass 25 g would have to be fired at 250 m/s off the back to give the railroad car a forward velocity of 0.3 m/s?

A) 400
B) 2000
C) 3000
D) 5000

Question 27

A billiard ball (Ball #1)moving at 5.00 m/s strikes a stationary ball (Ball #2)of the same mass.After the elastic collision,Ball #1 moves at a speed of 3.50 m/s.Find the speed of Ball #2 after the collision.

A) 1.25 m/s
B) 1.50 m/s
C) 2.16 m/s
D) 3.57 m/s

Question 28

During a snowball fight,two balls with masses of 0.4 and 0.6 kg,respectively,are thrown in such a manner that they meet head-on and combine to form a single mass.The magnitude of initial velocity for each is 20 m/s.What is the speed of the 1.0-kg mass immediately after collision?

A) zero
B) 3 m/s
C) 4 m/s
D) 5 m/s

Question 29

Popeye,of mass 70 kg,has just downed a can of spinach.He accelerates quickly and stops Bluto,of mass 700 kg (Bluto is very dense),who is charging in at 5.0 m/s.What was Popeye's remarkable speed?

A) 10 m/s
B) 31 m/s
C) 50 m/s
D) 100 m/s

Question 30

A 1000-kg vehicle is moving in the positive y-direction along the y-axis at 10 m/s.A 2000-kg vehicle is moving in the positive x-direction at along the x-axis at 20 m/s.The vehicles collide and stick together.They move as a single object in a direction ​θ as measured counterclockwise from the x-axis immediately after the collision.What is the value of tan ​θ?

A) 2.0
B) 4.0
C) 0.50
D) 0.25

Question 31

A 1.00-kg duck is flying overhead at 1.50 m/s when a hunter fires straight up.The 0.0100-kg bullet is moving 200 m/s when it hits the duck and stays lodged in the duck's body.What is the speed of the duck and bullet immediately after the hit?

A) 1.49 m/s
B) 1.80 m/s
C) 2.48 m/s
D) 2.50 m/s

Question 32

A 20-g bullet moving at 1000 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s.If the block had been originally at rest and is free to move,what is its resulting speed?

A) 800 m/s
B) 80 m/s
C) 16 m/s
D) 8 m/s

Question 33

In an inelastic collision between two objects with unequal masses:

A) the velocity of one will increase by the amount that the velocity of the other decreases.
B) the momentum of one will increase by the amount that the momentum of the other decreases.
C) the energy of one increases by the amount that the energy of the other decreases.
D) the total momentum of the system will decrease.

Question 34

Three masses are moving along the x-axis.Their masses and velocities are ​m​₁ = ​m​ with ​v_​1 = ​v​,​m_​2 = 2​m with v₂ = 2v,and m₃ = 3m with v₃ = -3v ​(the minus sign indicating this velocity is in the negative x-direction).The three masses collide and stick together in a completely inelastic collision.What is the resultant velocity of the combined mass?

A) 0,since their combined momentum is zero.
B) -2v/3
C) 14v/3
D) -v

Question 35

A cannon of mass 1500 kg fires a 10-kg shell with a velocity of 200 m/s at an angle of 30° above the horizontal.Find the recoil velocity of the cannon across the level ground.

A) 1.15 m/s
B) 0.94 m/s
C) 2.41 m/s
D) 1.94 m/s

Question 36

A 70-kg man is standing in a 20-kg boat.Thinking he is stepping out onto the dock,the man steps to the right.However,the following will actually happen (ignore the friction of the water or air on the boat or the man):

A) The man only moves a short distance to the right while the boat moves a larger distance to the left.
B) The man actually stays still while the boat moves toward the left.
C) The boat doesn't move and the man moves to the right.
D) None of the above.

Question 37

A miniature,spring-loaded,radio-controlled gun is mounted on an air puck.The gun's bullet has a mass of 5.00 g,and the gun and puck have a combined mass of 130g.With the system initially at rest,the radio-controlled trigger releases the bullet,causing the puck and empty gun to move with a speed of 0.500 m/s.Of the total kinetic energy of the gun-puck-bullet system,what percentage is in the bullet?

A) 50%
B) 96%
C) 3.4%
D) 100%

Question 38

A baseball infielder,mass 75.0 kg,jumps up with velocity 2.00 m/s and catches a 0.150-kg baseball moving horizontally at 50.0 m/s.Of the following,which is closest to the final momentum of the system,infielder and baseball?

A) 158 kg
m/s
B) 155 kg
m/s
C) 152 kg
m/s
D) 150 kg
m/s

Question 39

A 20-g bullet moving at 1000 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s.What is the kinetic energy of the block that results from the collision if the block had not been moving prior to the collision and was free to move?

A) 10 kJ
B) 9.8 kJ
C) 0.16 kJ
D) 0.13 kJ

Question 40

Two skaters,both of mass 75 kg,are initially at rest on skates on a frictionless ice pond.One skater throws a 0.3-kg ball at 10 m/s to his friend,who catches it and throws it back at 10 m/s.When the first skater has caught the returned ball,what is the velocity of each of the two skaters?

A) 0.08 m/s,moving apart
B) 0.04 m/s,moving apart
C) 0.08 m/s,moving towards each other
D) 0.04 m/s,moving towards each other

Question 41

A 4.0 ft by 8.0 ft sheet of plywood of uniform density and thickness lies in the 1^st quadrant with its long side along the x axis,one corner at the origin,and the diagonally opposite corner at position (x,y)= (8.0 ft,4.0 ft).The lower right 2.0 ft by 4.0 ft quarter of the sheet is removed from the sheet.What are the coordinates of the center of mass of the remaining portion of the sheet?

A) (2.0 ft,4.0 ft)
B) (1.0 ft,2.0 ft)
C) (3.3 ft,1.7 ft)
D) (3.3 ft,2.3 ft)

Question 42

Mitch throws a 100-g lump of clay at a 200-g target,which is at rest on a horizontal surface.After impact,the target,including the attached clay,slides 2.1 m before stopping.If the coefficient of friction is µ = 0.50,find the speed of the clay before impact.

A) 4.5 m/s
B) 14 m/s
C) 27 m/s
D) 36 m/s

Question 43

A model car is propelled by a cylinder of carbon dioxide gas.The cylinder emits gas at a rate of 4.5 g/s with an exit speed of 80.0 m/s.The car has a mass of 200 g,including the CO₂ cylinder.Starting from rest,what is the car's initial acceleration?

A) 0.90 m/s²
B) 1.8 m/s²
C) 9.0 m/s²
D) 36 m/s²

Question 44

Three masses are positioned along the x-axis.Their masses and positions are m₁ = m with x₁ = 1 m,m₂ = 2m with x₂ = 2 m,and m₃ = 4m with x₃ = 3 m.What is the x-coordinate of the center of mass of this system,to the nearest tenth?

A) 4.7 m
B) 2.4 m
C) 2.0 m
D) 1.1 m
E) Not enough information

Question 45

A helicopter stays aloft by pushing large quantities of air downward every second.What mass of air must be pushed downward at 30.0 m/s every second to keep a 1000 kg helicopter aloft?

A) 120 kg
B) 245 kg
C) 327 kg
D) 490 kg

Question 46

At liftoff,the engines of the Saturn V rocket consumed 14,000 kg/s of fuel and exhausted the combustion products at 2900 m/s.What was the total upward force (thrust)provided by the engines?

A) 3.77 × 10⁷ N
B) 7.54 × 10⁷ N
C) 1.47 × 10⁸ N
D) 4.06 × 10⁷ N

Question 47

A system of 3 masses is located as follows: m₁ = m₀ at (0,L),m₂ = 2m₀ at the origin,and m₃ = 3m₀ at (3L,0).Where is the center of mass of these masses?

A)

B)

C)

D)

Question 48

A "double satellite" is launched into space.It consists of a satellite of mass m and another satellite of mass 5m.The connecting mechanism of these satellites is an explosive bolt and a compressed spring,both of negligible mass.The bolt is exploded and the satellites drift apart having been pushed by the spring.When the less massive satellite has moved a distance of 2.5 m from the center of mass of the double satellite,how far away from it is the satellite of greater mass?

A) 3.0 m
B) 2.0 m
C) 0.5 m
D) 4.5 m