Deck 8: Potential Energy and Conservation of Energy

Question 1

A stone can slide down one of four different frictionless ramps,as shown in the figure.For which ramp will the speed of the ball be the greatest at the bottom?

A)Ramp X
B)Ramp Y
C)Ramp Z
D)The speed of the ball will be the same for all ramps.

Answer 1

The speed of the ball will be the same for all ramps.

Question 2

If the units of your answer are kg ∙ m²/s³,which of the following types of quantities could your answer be? (There could be more than one correct choice. )

A)kinetic energy
B)potential energy
C)force
D)power
E)work

Answer 2

power

Question 3

A heavy stone and a light stone are released from rest in such away that they both have the same amount of gravitational potential energy just as they are released.Air resistance is negligibly small.Which of the following statements about these stones are correct? (There could be more than one correct choice. )

A)The initial height of the light stone is greater than the initial height of the heavy stone.
B)The stones must have been released from the same height.
C)The stones both have the same speed just as they reach the ground.
D)Just as it reaches the ground,the light stone is traveling faster than the heavy stone.
E)The stones both have the same kinetic energy just as they reach the ground.

Answer 3

The initial height of the light stone is greater than the initial height of the heavy stone.
Just as it reaches the ground,the light stone is traveling faster than the heavy stone.
The stones both have the same kinetic energy just as they reach the ground.

Question 4

A 1-kg ball is released from a height of 6 m,and a 2-kg ball is released from a height of 3 m.Air resistance is negligible as they fall.Which of the following statements about these balls are correct? (There could be more than one correct choice. )

A)As they reach the ground,the 1-kg ball will have more kinetic energy than the 2-kg ball because it was dropped from a greater height.
B)As they reach the ground,the 1-kg ball will be moving faster than the 2-kg ball.
C)Both balls will reach the ground with the same speed.
D)Both balls will reach the ground with the same kinetic energy.
E)Both balls will take the same time to reach the ground.

Question 5

You and your friend,who weighs the same as you,want to go to the top of the Eiffel Tower.Your friend takes the elevator straight up.You decide to walk up the spiral stairway,taking longer to do so.Compare the gravitational potential energy of you and your friend,after you both reach the top.

A)It is impossible to tell,since the times you both took are unknown.
B)It is impossible to tell,since the distances you both traveled are unknown.
C)Your friend's gravitational potential energy is greater than yours,because he got to the top faster.
D)Both of you have the same amount of gravitational potential energy at the top.
E)Your gravitational potential energy is greater than that of your friend,because you traveled a greater distance in getting to the top.

Question 6

Two frisky otters slide down frictionless hillsides of the same height but different slopes.The slope of the hill of otter 1 is 30°,while the slope of the hill of otter 2 is 60°.If both start from rest,which otter is moving faster when she reaches the bottom of her hill?

A)Otter 1 is moving faster.
B)Otter 2 is moving faster.
C)The heavier otter is moving faster,no matter which hill she used.
D)Both otters have the same speed at the bottom.
E)The otter that took the shorter time is moving faster.

Question 7

Swimmers at a water park have a choice of two frictionless water slides,as shown in the figure.Although both slides drop over the same height h,slide 1 is straight while slide 2 is curved,dropping quickly at first and then leveling out.How does the speed v₁ of a swimmer reaching the bottom of slide 1 compare with v₂,the speed of a swimmer reaching the end of slide 2?

A)v₁ > v₂
B)v₁ < v₂
C)v₁ = v₂
D)The heavier swimmer will have a greater speed than the lighter swimmer,no matter which slide he uses.
E)No simple relationship exists between v₁ and v₂.

Question 8

A girl throws a stone from a bridge.Consider the following ways she might throw the stone.The speed of the stone as it leaves her hand is the same in each case.
Case A: Thrown straight up.
Case B: Thrown straight down.
Case C: Thrown out at an angle of 45° above horizontal.
Case D: Thrown straight out horizontally.
In which case will the speed of the stone be greatest when it hits the water below if there is no significant air resistance?

A)Case A
B)Case B
C)Case C
D)Case D
E)The speed will be the same in all cases.

Question 9

A heavy sled and a light sled,both moving horizontally with the same speed,suddenly slide onto a rough patch of snow and eventually come to a stop.The coefficient of kinetic friction between the sleds and the rough snow is the same for both of them.Which of the following statements about these sleds are correct? (There could be more than one correct choice. )

A)Both sleds will slide the same distance on the rough snow before stopping.
B)The heavy sled will slide farther on the rough snow than the light sled.
C)The light sled will slide farther on the rough snow than the heavy sled.
D)The friction from the snow will do more negative work on the heavy sled than on the light sled.
E)The friction from the snow will do the same amount of work on both sleds.

Question 10

You do 116 J of work while pulling your sister back on a frictionless swing,whose chain is
Long,until the swing makes an angle of 32.0° with the vertical.What is your sister's mass?

A)15.3 kg
B)13.0 kg
C)17.6 kg
D)19.0 kg

Question 11

Two identical grasshoppers jump into the air with the same initial speed and experience no air resistance.Grasshopper A goes straight up,but grasshopper B goes up at a 66° angle above the horizontal.Which of the following statements about these grasshoppers are correct? (There could be more than one correct choice. )

A)At their highest point,both of them have the same amount of gravitational potential energy.
B)At their highest point,both of them have the same amount of kinetic energy.
C)At their highest point,both of them have the same amount of mechanical energy.
D)At their highest point,grasshopper B is moving faster than grasshopper A.
E)At their highest point,grasshopper A has more gravitational potential energy than grasshopper B.

Question 12

A heavy dart and a light dart are launched vertically by identical ideal springs.Both springs were initially compressed by the same amount.There is no significant air resistance.Which of the following statements about these darts are correct? (There could be more than one correct choice. )

A)The heavy dart goes higher than the light dart.
B)The light dart goes higher than the heavy dart.
C)Both darts reach the same maximum height.
D)At the maximum height,both darts have the same gravitational potential energy.
E)Both darts began moving upward with the same initial speed.

Question 13

A heavy rock and a light rock are dropped from the same height and experience no significant air resistance as they fall.Which of the following statements about these rocks are correct? (There could be more than one correct choice. )

A)Both rocks have the same kinetic energy when they reach the ground.
B)Both rocks have the same speed when they reach the ground.
C)The heavier rock reaches the ground before the lighter rock.
D)Just as they were released,both rocks had the same amount of gravitational potential energy.
E)When they reach the ground,the heavier rock has more kinetic energy than the lighter rock.

Question 14

Joe and Bill throw identical balls vertically upward.Joe throws his ball with an initial speed twice as high as Bill.If there is no air resistance,the maximum height of Joe's ball will be

A)four times that of Bill's ball.
B)two times that of Bill's ball.
C)equal to that of Bill's ball.
D)eight times that of Bill's ball.
E)roughly 1.4 times that of Bill's ball.

Question 15

A person stands on the edge of a cliff.She throws three identical rocks with the same speed.Rock X is thrown vertically upward,rock Y is thrown horizontally,and rock Z is thrown vertically downward.If the ground at the base of the cliff is level,which rock hits the ground with the greatest speed if there is no air resistance?

A)Rock X
B)Rock Y
C)Rock Z
D)They all hit the ground with the same speed.

Question 16

If a stone is dropped with an initial gravitational potential energy of 100 J but reaches the ground with a kinetic energy of only 75 J,this is a violation of the principle of conservation of energy.

Question 17

A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface.They both slide up the same frictionless hill with no air resistance.Which object rises to a greater height?

A)The heavy object,because it has greater initial kinetic energy.
B)The light object,because gravity slows it down less.
C)The lightweight object,because the force of gravity on it is less.
D)The heavy object,because it has more mass to carry it up the hill.
E)They both slide to exactly the same height.

Question 18

A heavy dart and a light dart are launched horizontally on a frictionless table by identical ideal springs.Both springs were initially compressed by the same amount.Which of the following statements about these darts are correct? (There could be more than one correct choice. )

A)The darts both have the same kinetic energy just as they move free of the spring.
B)The lighter dart leaves the spring moving faster than the heavy dart.
C)The heavy dart had more initial elastic potential energy than the light dart.
D)Both darts move free of the spring with the same speed.
E)Both darts had the same initial elastic potential energy.

Question 19

A stone is held at a height h above the ground.A second stone with four times the mass of the first one is held at the same height.The gravitational potential energy of the second stone compared to that of the first stone is

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

Question 20

A heavy sled and a light sled,both moving horizontally with the same kinetic energy,suddenly slide onto a rough patch of snow and eventually come to a stop.The coefficient of kinetic friction between the sleds and the rough snow is the same for both of them.Which of the following statements about these sleds are correct? (There could be more than one correct choice. )

A)Both sleds will slide the same distance on the rough snow before stopping.
B)The heavy sled will slide farther on the rough snow than the light sled.
C)The light sled will slide farther on the rough snow than the heavy sled.
D)On the rough snow,the change in kinetic energy will be the same for both sleds.
E)The friction from the snow will do the same amount of work on both sleds.

Question 21

A tennis ball bounces on the floor three times,and each time it loses 23.0% of its energy due to heating.How high does it bounce after the third time,if we released it
From the floor?

A)180 cm
B)18 cm
C)180 mm
D)240 cm

Question 22

A spring-loaded dart gun is used to shoot a dart straight up into the air,and the dart reaches a maximum height of 24 meters.The same dart is shot up a second time from the same gun,but this time the spring is compressed only half as far (compared to the first shot).How far up does the dart go this time (neglect all friction and assume the spring is ideal)?

A)6.0 m
B)12 m
C)3.0 m
D)48 m

Question 23

A prankster drops a water balloon from the top of a building.If the balloon is traveling at 29.1 m/s when it strikes a window ledge that is 1.5 m above the ground,how tall is the building? Neglect air resistance.

A)45 m
B)43 m
C)46 m
D)47 m

Question 24

An ideal spring with a force constant (spring constant)of 15 N/m is initially compressed by 3.0 cm from its uncompressed position.How much work is required to compress the spring an additional 4.0 cm?

A)0.0068 J
B)0.012 J
C)0.024 J
D)0.030 J

Question 25

A 5.0-N projectile leaves the ground with a kinetic energy of 220 J.At the highest point in its trajectory,its kinetic energy is 120 J.To what vertical height,relative to its launch point,did it rise if there was no air resistance?

A)44 m
B)24 m
C)20 m
D)10 m
E)It is impossible to determine the height without knowing the angle of launch.

Question 26

An ideal spring has a spring constant (force constant)of 60 N/m.How much energy does it store when it is stretched by 1.0 cm?

A)0.0030 J
B)0.30 J
C)60 J
D)600 J

Question 27

A toy rocket that weighs 10 N blasts straight up from ground level with an initial kinetic energy of 40 J.At the exact top of its trajectory,its total mechanical energy is 140 J.To what vertical height above the ground does it rise,assuming no air resistance?

A)1.0 m
B)10 m
C)14 m
D)24 m

Question 28

A bead is moving with a speed of 20 m/s at position A on the track shown in the figure.This track is friction-free,and there is no appreciable air resistance.What is the speed of the bead at point C?

A)0 m/s
B)34 m/s
C)69 m/s
D)20 m/s
E)We cannot solve this problem without knowing the mass of the bead.

Question 29

An ideal spring with a spring constant (force constant)of
Is stretched from equilibrium to 2.9 m.How much work is done in the process?

A)93 J
B)186 J
C)47 J
D)121 J

Question 30

The figure shows a famous roller coaster ride.You can ignore friction.If the roller coaster leaves point Q from rest,what is its speed at the top of the 25-m peak (point S)?

A)10 m/s
B)22 m/s
C)44 m/s
D)62 m/s
E)120 m/s

Question 31

If the work done to stretch an ideal spring by 4.0 cm is 6.0 J,what is the spring constant (force constant)of this spring?

A)300 N/m
B)3000 N/m
C)3500 N/m
D)7500 N/m
E)6000 N/m

Question 32

How much work is required to stretch an ideal spring of spring constant (force constant)40 N/m from x = 0.20 m to x = 0.25 m if the unstretched position is at x = 0.00 m?

A)0.45 J
B)0.80 J
C)1.3 J
D)0.050 J

Question 33

A 60-kg skier pushes off the top of a frictionless hill with an initial speed of 4.0 m/s.How fast will she be moving after dropping 10 m in elevation? Air resistance is negligible.

A)0.20 km/s
B)15 m/s
C)10 m/s
D)0.15 km/s
E)49 m/s

Question 34

Assuming negligible friction,what spring constant (force constant)would be needed by the spring in a "B-B gun" to fire a 10-g pellet to a height of 100 m if the spring is initially compressed by 0.10 m?

A)20 N/cm
B)200 N/m
C)2000 N/cm
D)0.0020 N/m

Question 35

If 4.0 J of work are performed in stretching an ideal spring with a spring constant (force constant)of 2500 N/m,by what distance is the spring stretched?

A)3.2 cm
B)3.2 m
C)0.3 cm
D)5.7 m
E)5.7 cm

Question 36

What is the minimum energy needed to lift a 1.0-kg rocket to a height of 200 km and to give it a speed of 8.0 km/s at that height? (Neglect air resistance and the small decrease in g over that distance. )

A)34 TJ
B)34 kJ
C)34 MJ
D)34 GJ
E)34 J

Question 37

A rock falls from a vertical cliff that is 4.0 m tall and experiences no significant air resistance as it falls.At what speed will its gravitational potential energy (relative to the base of the cliff)be equal to its kinetic energy?

A)3.1 m/s
B)4.4 m/s
C)6.3 m/s
D)8.9 m/s
E)13 m/s

Question 38

If a spring-operated gun can shoot a pellet to a maximum height of 100 m on Earth,how high could the pellet rise if fired on the Moon,where g = 1.6 m/s²?

A)17 m
B)160 m
C)3.6 km
D)100 m
E)610 m

Question 39

A block slides down a frictionless inclined ramp and experiences no significant air resistance.If the ramp angle is 17.0° above the horizontal and the length of the surface of the ramp is
Find the speed of the block as it reaches the bottom of the ramp,assuming it started sliding from rest at the top.

A)10.7 m/s
B)114 m/s
C)7.57 m/s
D)19.6 m/s

Question 40

It takes 87 J of work to stretch an ideal spring from 1.4 m to 2.9 m from equilibrium.What is the value of the spring constant (force constant)of this spring?

A)27 N/m
B)77 N/m
C)52 N/m
D)39 N/m

Question 41

A 0.46-kg block is held in place against the spring by a 30-N horizontal external force.The external force is removed,and the block is projected with a velocity v1=1.2 m/s. Upon separation from the spring,as shown in the figure.The block descends a ramp and has a velocity v2=1.5 m/ s. At the bottom.The track is frictionless between points A and B.The block enters a rough section at point B,extending to E.The coefficient of kinetic friction between the block and the rough surface is 0.38.The velocity of the block is v3=1.4 m/ s. At point C.The block moves on to D,where it stops.What distance does the block travel between points B and D?

A)0.30 m
B)0.039 m
C)0.26 m
D)0.40 m
E)0.60 m

Question 42

A 1500-kg car accelerates from rest to 25 m/s in 7.0 s.What is the average power delivered by the engine? (1 hp = 746 W)

A)60 hp
B)70 hp
C)80 hp
D)90 hp

Question 43

An object with a mass of 10 kg is initially at rest at the top of a frictionless inclined plane that rises at 30° above the horizontal.At the top,the object is initially 8.0 m from the bottom of the incline,as shown in the figure.When the object is released from this position,it eventually stops at a distance d from the bottom of the inclined plane along a horizontal surface,as shown.The coefficient of kinetic friction between the horizontal surface and the object is 0.20,and air resistance is negligible.Find the distance d.

A)5.0 m
B)10 m
C)15 m
D)20 m
E)25 m

Question 44

A small 1.4-N stone slides down a frictionless bowl,starting from rest at the rim.The bowl itself is a hemisphere of radius 75 cm.Just as the stone reaches the bottom of the bowl,how hard is the bowl pushing on it?

A)0.70 N
B)1.4 N
C)2.8 N
D)4.2 N
E)5.6 N

Question 45

If electricity costs 7.06¢/kW∙h,how much would it cost you to run a
Stereo system
Per day for

A)$0.95
B)$0.14
C)$1.62
D)$2.66

Question 46

A 30-N stone is dropped from a height of 10 m and strikes the ground with a speed of 13 m/s.What average force of air friction acted on the stone as it fell?

A)4.1 N
B)2.9 N
C)0.13 kN
D)7.2 N
E)1.2 N

Question 47

At what minimum rate is a 60.0-kg boy using energy when,in 8.00 s,he runs up a flight of stairs that is 10.0-m high?

A)75.0 W
B)735 W
C)4.80 kW
D)48.0 W

Question 48

A small but dense 2.0-kg stone is attached to one end of a very light rod that is 1.2 m long.The other end of the rod is attached to a frictionless pivot.The rod is raised until it is vertical,with the stone above the pivot.The rod is released and the stone moves in a vertical circle with no air resistance.What is the tension in the rod as the stone moves through the bottom of the circle?

A)20 N
B)40 N
C)60 N
D)80 N
E)100 N

Question 49

A 1500-kg car moving at 25 m/s hits an initially uncompressed horizontal ideal spring with spring constant (force constant)of 2.0 × 10⁶ N/m.What is the maximum distance the spring compresses?

A)0.17 m
B)0.34 m
C)0.51 m
D)0.68 m

Question 50

A roller coaster starts from rest at a height h at the left side of a loop-the-loop,as shown in the figure.It is not attached to the track in anyway,and there is no friction from the track or from air resistance.If the radius of the loop is R = 6.0 m,what is the minimum height h for which the roller coaster will not fall off the track at the top of the loop?

A)21 m
B)18 m
C)15 m
D)12 m
E)8.5 m

Question 51

A 60-kg skier starts from rest from the top of a 50-m high slope.If the work done by friction is -6.0 kJ,what is the speed of the skier on reaching the bottom of the slope?

A)17 m/s
B)24 m/s
C)28 m/s
D)31 m/s

Question 52

How many joules of energy are used by a 1.0-hp motor that runs for 1.0 hour? (1 hp = 746 W)

A)3.6 kJ
B)2.7 MJ
C)45 kJ
D)4.8 J

Question 53

A stone is released from rest at a height h at the left side of a loop-the-loop,as shown in the figure.There is no appreciable friction from the track or from air resistance.If the radius of the loop is R,what is the minimum height h for which the stone will not fall off the track at the top of the loop?

A)3.5 R
B)2.5 R
C)2.0 R
D) R
E)3.0 R

Question 54

What is the net power needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s in 4.00 seconds?

A)100 kW
B)10.0 kW
C)140 kW
D)14.0 kW
E)275 kW

Question 55

As shown in the figure,a 1.45-kg block is held in place against the spring by a 21-N horizontal external force.The external force is removed,and the block is projected with a velocity
As it separates from the spring.The block descends a ramp and has a velocity
At the bottom.The track is frictionless between points A and B.The block enters a rough section at B,extending to E.The coefficient of kinetic friction between the block and the rough surface is 0.29.The velocity of the block is
At C.The block moves on to D,where it stops.How much work is done by friction between points B and C?

A)-1.8 J
B)-3.6 J
C)-14 J
D)-6.4 J
E)-7.0 J

Question 56

In a museum exhibit of a simple pendulum,a very small but dense 6.0-kg ball swings from a very light 2.5-m wire.The ball is released from rest when the pendulum wire makes a 65° angle with the vertical,and it swings in a circular arc with no appreciable friction or air resistance.What is the tension in the wire just as the ball swings through its lowest position?

A)11 N
B)59 N
C)68 N
D)130 N
E)0 N

Question 57

On a planet where g = 10.0 m/s² and air resistance is negligible,a sled is at rest on a rough inclined hill rising at 30° as shown in the figure.The object is allowed to move and it stops on a rough horizontal surface,at a distance of 4.0 m from the bottom of the hill.The coefficient of kinetic friction on the hill is 0.40.What is the coefficient of kinetic friction between the horizontal surface and the sled?

A)0.10
B)0.20
C)0.31
D)0.40
E)0.60

Question 58

In the figure,a ball hangs by a very light string.What is the minimum speed of the ball at the bottom of its swing (point B) in order for it to reach point A,which is 1.0 m above the bottom of the swing?

A)2.2 m/s
B)3.1 m/s
C)4.4 m/s
D)4.9 m/s

Question 59

A 1,321-kg car climbs a 5.0° slope at a constant speed of 80.0 km/h. Assuming that air resistance may be neglected,at what rate (in kW)must the engine deliver energy to the drive wheels of the car?

A)25 kW
B)287 kW
C)38 kW
D)48 kW

Question 60

A 0.12-kg block is held in place against the spring by a 35-N horizontal external force.The external force is removed,and the block is projected with a velocity v₁=1.2 m/s. When it separates from the spring,as shown in the figure.The block descends a ramp and has a velocity v2=1.4 m/s. At the bottom of the ramp.The track is frictionless between points A and B.The block enters a rough section at B,extending to E.The coefficient of kinetic friction between the block and the rough surface is 0.26.The block moves on to D,where it stops.By how many centimeters was the spring initially compressed?

A)0.49 cm
B)0.26 cm
C)0.18 cm
D)0.99 cm
E)0.67 cm

Question 61

A certain battery charger uses 12 W of power.At 6.0 cents per kilowatt-hour,how much does it cost to charge batteries for a full day?

A)28¢
B)1.4¢
C)75¢
D)1.7¢
E)2.3¢

Question 62

A sand mover at a quarry lifts 2,000 kg of sand per minute a vertical distance of 12 m.The sand is initially at rest and is discharged at the top of the sand mover with speed 5.0 m/s into a loading chute.What minimum power must be supplied to this machine?

A)520 W
B)3.9 kW
C)6.7 kW
D)4.3 kW
E)1.1 kW