Deck 6: Work and Kinetic Energy

Question 1

Energy conservation with nonconservative forces: A ball drops some distance and gains 30 J of kinetic energy. Do NOT ignore air resistance. How much gravitational potential energy did the ball lose?

A) more than 30 J
B) exactly 30 J
C) less than 30 J

Answer 1

more than 30 J

Question 2

Work-energy theorem: Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. When they hit the ground

A) both of them will have the same kinetic energy.
B) the heavier one will have twice the kinetic energy of the lighter one.
C) the heavier one will have four times the kinetic energy of the lighter one.
D) the heavier one will have times the kinetic energy of the lighter one.

Answer 2

the heavier one will have twice the kinetic energy of the lighter one.

Question 3

Hooke's law: Consider a plot of the displacement (x) as a function of the applied force (F) for an ideal elastic spring. The slope of the curve would be

A) the spring constant.
B) the reciprocal of the spring constant.
C) the acceleration due to gravity.
D) the reciprocal of the acceleration of gravity.
E) the mass of the object attached to the spring.

Answer 3

the reciprocal of the spring constant.

Question 4

Hooke's law: Which of the graphs in the figure represents a spring that gets less stiff the more it is stretched?

A) Graph a
B) Graph b
C) Graph c
D) Graph d

Question 5

Energy conservation with nonconservative forces: Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. If the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline?

A) We must know the actual masses of the blocks to answer.
B) Both blocks have the same speed at the bottom.
C) Block 1 is faster.
D) Block 2 is faster.
E) There is not enough information to answer the question because we do not know the value of the coefficient of kinetic friction.

Question 6

Energy conservation with conservative forces: A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment but instead compress the spring a distance of 2x

A) the box will go up the incline twice as high as before.
B) just as it moves free of the spring, the box will be traveling twice as fast as before.
C) just as it moves free of the spring, the box will be traveling four times as fast as before.
D) just as it moves free of the spring, the box will have twice as much kinetic energy as before.
E) just before it is released, the box has twice as much elastic potential energy as before.

Question 7

Energy conservation with conservative forces: Two stones, one of mass m and the other of mass 2m, are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance. Which statement about these stones is true?

A) The heavier stone will go twice as high as the lighter one because it initially had twice as much kinetic energy.
B) Both stones will reach the same height because they initially had the same amount of kinetic energy.
C) At their highest point, both stones will have the same gravitational potential energy because they reach the same height.
D) At its highest point, the heavier stone will have twice as much gravitational potential energy as the lighter one because it is twice as heavy.
E) The lighter stone will reach its maximum height sooner than the heavier one.

Question 8

Work-energy theorem: A 4.0-kg object is moving with speed 2.0 m/s. A 1.0-kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping?

A) the 4.0-kg object
B) the 1.0-kg object
C) Both objects travel the same distance.
D) It is impossible to know without knowing how long each force acts.

Question 9

Energy conservation with conservative forces: A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment with a box of mass 2m

A) the lighter box will go twice as high up the incline as the heavier box.
B) just as it moves free of the spring, the lighter box will be moving twice as fast as the heavier box.
C) both boxes will have the same speed just as they move free of the spring.
D) both boxes will reach the same maximum height on the incline.
E) just as it moves free of the spring, the heavier box will have twice as much kinetic energy as the lighter box.

Question 10

Energy conservation with conservative forces: Two identical balls are thrown directly upward, ball A at speed v and ball B at speed 2v, and they feel no air resistance. Which statement about these balls is correct?

A) Ball B will go twice as high as ball A because it had twice the initial speed.
B) Ball B will go four times as high as ball A because it had four times the initial kinetic energy.
C) The balls will reach the same height because they have the same mass and the same acceleration.
D) At its highest point, ball B will have twice as much gravitational potential energy as ball A because it started out moving twice as fast.
E) At their highest point, the acceleration of each ball is instantaneously equal to zero because they stop for an instant.

Question 11

Gravitational potential energy: Is it possible for a system to have negative potential energy?

A) Yes, as long as the kinetic energy is positive.
B) Yes, as long as the total energy is positive.
C) Yes, since the choice of the zero of potential energy is arbitrary.
D) No, because the kinetic energy of a system must equal its potential energy.
E) No, because this would have no physical meaning.

Question 12

Hooke's law: Which of the graphs in the figure illustrates Hooke's Law?

A) Graph a
B) Graph b
C) Graph c
D) graph d

Question 13

Work-energy theorem: If a force always acts perpendicular to an object's direction of motion, that force cannot change the object's kinetic energy.

Question 14

Work: A stock person at the local grocery store has a job consisting of the following five segments: (1) picking up boxes of tomatoes from the stockroom floor
(2) accelerating to a comfortable speed
(3) carrying the boxes to the tomato display at constant speed
(4) decelerating to a stop
(5) lowering the boxes slowly to the floor.
During which of the five segments of the job does the stock person do positive work on the boxes?

A) (1) and (5)
B) (1) only
C) (1), (2), (4), and (5)
D) (1) and (2)
E) (2) and (3

Question 15

Energy conservation with conservative forces: A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment but instead use a spring having force constant 2k

A) the box will go up the incline twice as high as before.
B) just as it moves free of the spring, the kinetic energy of the box will be twice as great as before.
C) just as it moves free of the spring, the speed of the box will be times as great as before.
D) All of the above choices are correct.
E) None of the above choices is correct.

Question 16

Energy conservation with nonconservative forces: A ball drops some distance and loses 30 J of gravitational potential energy. Do NOT ignore air resistance. How much kinetic energy did the ball gain?

A) more than 30 J
B) exactly 30 J
C) less than 30 J

Question 17

Energy conservation with conservative forces: 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 end of slide 1 compares with v₂, the speed of a swimmer reaching the end of slide 2?

A) v₁ > v₂
B) v₁ < v₂
C) v₁ = v₂
D) No simple relationship exists between v₁ and v₂ because we do not know the curvature of slide 2.

Question 18

Work: A 3.00-kg ball swings rapidly in a complete vertical circle of radius 2.00 m by a light string that is fixed at one end. The ball moves so fast that the string is always taut and perpendicular to the velocity of the ball. As the ball swings from its lowest point to its highest point

A) the work done on it by gravity and the work done on it by the tension in the string are both equal to -118 J.
B) the work done on it by gravity is -118 J and the work done on it by the tension in the string is +118 J.
C) the work done on it by gravity is +118 J and the work done on it by the tension in the string is -118 J.
D) the work done on it by gravity is -118 J and the work done on it by the tension in the string is zero.
E) the work done on it by gravity and the work done on it by the tension in the string are both equal to zero.

Question 19

Work: Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do

A) Both men do positive work, but Joel does 75% more work than Jerry.
B) Both men do positive work, but Joel does 50% more work than Jerry.
C) Both men do positive work, but Jerry does 50% more work than Joel.
D) Both men do positive work, but Joel does 25% more work than Jerry.
E) Neither of them does any work.

Question 20

Energy conservation with nonconservative forces: When an object is solely under the influence of conservative forces, the sum of its kinetic and potential energies does not change.

Question 21

Work: You carry a 7.0 kg bag of groceries above the level floor at a constant velocity of 75 cm/s across a room that is across. How much work do you do on the bag in the process?

A) 0.0 J
B) 82 J
C) 158 J
D) 134 J

Question 22

Work: An object is acted upon by a force that represented by the force vs. position graph in the figure. What is the work done as the object moves
(a) from 4 m to 6 m?
(b) from 6 m to 12 m?

Question 23

Work: A crane lifts a 425 kg steel beam vertically a distance of How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s²? Neglect frictional forces.

A) 5.8 × 10⁵ J
B) 3.4 × 10⁵ J
C) 4.0 × 10⁵ J
D) 4.9 × 10^{5 J}

Question 24

Work: A student slides her 80.0-kg desk across the level floor of her dormitory room a distance 4.00 m at constant speed. If the coefficient of kinetic friction between the desk and the floor is 0.400, how much work did she do?

A) 128 J
B) 3.14 kJ
C) 26.7 J
D) 1.26 kJ
E) 24.0 J

Question 25

Work: Find the net work done by friction on the body of a snake slithering in a complete circle of radius. The coefficient of friction between the ground and the snake is 0.25, and the snake's weight is

A) - 330 J
B) 0 J
C) - 3300 J
D) - 670 J

Question 26

Energy conservation with nonconservative forces: 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, and air resistance is negligible. 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?

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

Question 27

Hooke's law: A spring stretches by when a object is attached. What is the weight of a fish that would stretch the spring by

A) 199 N
B) 91.0 N
C) 145 N
D) 279 N

Question 28

Force and potential energy: The plot in the figure shows the potential energy of a particle, due to the force exerted on it by another particle, as a function of distance. At which of the three points labeled in the figure is the magnitude of the force on the particle greatest?

A) point X
B) point Y
C) point Z

Question 29

Hooke's law: An object attached to an ideal massless spring is pulled across a frictionless surface. If the spring constant is 45 N/m and the spring is stretched by 0.88 m when the object is accelerating at what is the mass of the object?

A) 20 kg
B) 17 kg
C) 22 kg
D) 26 kg

Question 30

Force and potential energy: A potential energy function for system 1 is given by U₁(x) = Cx² + Bx³. The potential energy function for system 2 is given by U₂(x) = A + Cx² + Bx³, where A is a positive quantity. How does the force on system 1 relate to the force on system 2 at a given position?

A) The force on the two systems will be in opposite directions.
B) The force is identical on the two systems.
C) The force on the second system will be with less than the force on the first system.
D) There is no relationship between the forces on the two systems.
E) The force on the second system will be with greater than the force on the first system.

Question 31

Work: In the figure, a 700-kg crate is on a rough surface inclined at 30°. A constant external force P = 5600 N is applied horizontally to the crate. As the force pushes the crate a distance of 3.00 m up the incline, the speed changes from 1.40 m/s to 2.50 m/s. How much work does gravity do on the crate during this process?

A) -10,300 J
B) -3400 J
C) +10,300 J
D) +3400 J
E) zero

Question 32

Hooke's law: In the figure, two identical ideal massless springs have unstretched lengths of 0.25 m and spring constants of 700 N/m. The springs are attached to a small cube and stretched to a length L of 0.30 m as in Figure A. An external force P pulls the cube a distance D = 0.020 m to the right and holds it there. (See Figure B.) The external force P, that holds the cube in place in Figure B, is closest to

A) 28 N.
B) 25 N.
C) 21 N.
D) 18 N.
E) 14 N.

Question 33

Work: A graph of the force on an object as a function of its position is shown in the figure. Determine the amount of work done by this force on the object during a displacement from x = -2.00 m to x = 2.00 m. (Assume an accuracy of 3 significant figures for the numbers on the graph.)

A) -12.0 J
B) -3.00 J
C) -1.00 J
D) 12.0 J
E) 3.00 J

Question 34

Work: A force = 12 N - 10 N acts on an object. How much work does this force do as the object moves from the origin to the point

A) 46 J
B) 266 J
C) 37 J
D) 62 J

Question 35

Work: A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap?

A) 75 N
B) 61 N
C) 85 N
D) 92 N

Question 36

Work: In the figure, a constant external force P = 160 N is applied to a 20.0-kg box, which is on a rough horizontal surface. While the force pushes the box a distance of 8.00 m, the speed changes from 0.500 m/s to 2.60 m/s. The work done by friction during this process is closest to

A) -1040 J
B) +1110 J
C) +1170 J
D) +1040 J
E) -1170 J

Question 37

Work: Three forces: F₁ = 20.0 N, F₂ = 40.0 N, and F₃ = 10.0 N act on an object with a mass of 2.00 kg which can move along a frictionless inclined plane as shown in the figure. The questions refer to the instant when the object has moved through a distance of 0.600 m along the surface of the inclined plane in the upward direction. Calculate the amount of work done by
(a) F₁
(b) F₂
(c) F₃

Question 38

Work: An airplane flies 120 km at a constant altitude in a direction 30.0° north of east. A wind is blowing that results in a net horizontal force on the plane due to the air of 2.40 kN in a direction 10.0° south of west. How much work is done on the plane by the air?

A) -2.71 × 10⁸ J
B) -0.985 × 10⁸ J
C) -221 × 10⁸ J
D) 221 × 10⁸ J
E) 0.821 × 10⁸ J

Question 39

Energy conservation with nonconservative forces: Which, if any, of the following statements concerning the work done by a conservative force is NOT true?

A) It can always be expressed as the difference between the initial and final values of a potential energy function.
B) It is independent of the path of the body and depends only on the starting and ending points.
C) When the starting and ending points are the same, the total work is zero.
D) All of the above statements are true.
E) None of the above statements are true.

Question 40

Work: A graph of the force on an object as a function of its position is shown in the figure. Determine the amount of work done by this force on an object that moves from x = 1.0 m to x = 6.0 m. (Assume an accuracy of 2 significant figures for the numbers on the graph.)

A) 26 J
B) 29 J
C) 22 J
D) 35 J
E) 27 J

Question 41

Work-energy theorem: A ball is thrown upward at an angle with a speed and direction such that it reaches a maximum height of 16.0 m above the point it was released, with no appreciable air resistance. At its maximum height it has a speed of 18.0 m/s. With what speed was the ball released?

A) 25.3 m/s
B) 22.2 m/s
C) 33.0 m/s
D) 29.2 m/s
E) 36.9 m/s

Question 42

Work-energy theorem: A worker lifts a 20.0-kg bucket of concrete from the ground up to the top of a 20.0-m tall building. The bucket is initially at rest, but is traveling at 4.0 m/s when it reaches the top of the building. What is the minimum amount of work that the worker did in lifting the bucket?

A) 3.92 kJ
B) 400 J
C) 560 J
D) 4.08 kJ
E) 160 J

Question 43

Work done by variable forces: A person pushes horizontally on a heavy box and slides it across the level floor at constant velocity. The person pushes with a 60.0 N force for the first at which time he begins to tire. The force he exerts then starts to decrease linearly from 60.0 N to 0.00 N across the remaining How much total work did the person do on the box?

A) 619 J
B) 826 J
C) 495 J
D) 925 J

Question 44

Kinetic energy: How much energy is needed to change the speed of a 1600 kg sport utility vehicle from 15.0 m/s to 40.0 m/s?

A) 1.10 MJ
B) 10.0 kJ
C) 20.0 kJ
D) 40.0 kJ
E) 0.960 MJ

Question 45

Work-energy theorem: A 5.00-kg box slides 4.00 m across the floor before coming to rest. What is the coefficient of kinetic friction between the floor and the box if the box had an initial speed of 3.00 m/s?

A) 1.13
B) 0.587
C) 0.115
D) 0.229
E) 0.267

Question 46

Kinetic energy: The coefficient of the restitution of an object is defined as the ratio of its outgoing to incoming speed when the object collides with a rigid surface. For an object with a coefficient of 0.78, what fraction of the object's kinetic energy is lost during a single collision?

A) 39%
B) 16%
C) 47%
D) 61%

Question 47

Work done by variable forces: A force on a particle depends on position such that F(x) = (3.00 N/ ) + ( 6.00 N/m)x for a particle constrained to move along the x-axis. What work is done by this force on a particle that moves from x = 0.00 m to x = 2.00 m?

A) 10.0 J
B) 20.0 J
C) - 48.0 J
D) 24.0 J
E) 48.0 J

Question 48

Hooke's law: Block A (0.40 kg) and block B (0.30 kg) are on a frictionless table (see figure). Spring 1 connects block A to a frictionless peg at 0 and spring 2 connects block A and block B. When the blocks are in uniform circular motion about 0, the springs have lengths of 0.60 m and 0.40 m, as shown. The springs are ideal and massless, and the linear speed of block B is 2.0 m/s. If the spring constant of spring 1 is equal to 30 N/m, the unstretched length of spring 1 is closest to

A) 0.51 m.
B) 0.52 m.
C) 0.53 m.
D) 0.54 m.
E) 0.55 m.

Question 49

Work done by variable forces: In the figure, two identical springs have unstretched lengths of 0.25 m and spring constants of 300 N/m. The springs are attached to a small cube and stretched to a length L of 0.36 m as in Figure A. An external force P pulls the cube a distance D = 0.020 m to the right and holds it there. (See Figure B.) The work done by the external force P in pulling the cube 0.020 m is closest to

A) 0.12 J.
B) 0.060 J.
C) 6.0 J.
D) 12 J.
E) 0.80 J.

Question 50

Work done by variable forces: A force F = bx³ acts in the x direction, where the value of b is 3.7 N/m³. How much work is done by this force in moving an object from to

A) 42 J
B) 13 J
C) 50 J
D) 57 J

Question 51

Work-energy theorem: A constant horizontal pull acts on a sled on a horizontal frictionless ice pond. The sled starts from rest. When the pull acts over a distance x, the sled acquires a speed v and a kinetic energy K. If the same pull instead acts over twice this distance:

A) The sled's speed will be 2v and its kinetic energy will be 2K.
B) The sled's speed will be 2v and its kinetic energy will be K .
C) The sled's speed will be v and its kinetic energy will be 2K.
D) The sled's speed will be v and its kinetic energy will be K
.
E) The sled's speed will be 4v and its kinetic energy will be 2K.

Question 52

Work-energy theorem: You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. If you had been traveling twice as fast, what distance would the car have skidded, under identical conditions?

A) It would have skidded 4 times farther.
B) It would have skidded 2 times farther.
C) It would have skidded times farther.
D) It would have skidded 1/ times farther.
E) It would have skidded 1/2 as far.

Question 53

Work-energy theorem: An unusual spring has a restoring force of magnitude F = (2.00 N/m)x + (1.00 N/m²)x², where x is the stretch of the spring from its equilibrium length. A 3.00-kg object is attached to this spring and released from rest after stretching the spring 1.50 m. If the object slides over a frictionless horizontal surface, how fast is it moving when the spring returns to its equilibrium length?

A) 2.06 m/s
B) 4.33 m/s
C) 3.27 m/s
D) 5.48 m/s
E) 1.50 m/s

Question 54

Work done by variable forces: It requires 49 J of work to stretch an ideal very light spring from a length of 1.4 m to a length of 2.9 m. What is the value of the spring constant of this spring?

A) 15 N/m
B) 44 N/m
C) 29 N/m
D) 22 N/m

Question 55

Work-energy theorem: In the figure, a 900-kg crate is on a rough surface inclined at 30°. A constant external force is applied horizontally to the crate. While this force pushes the crate a distance of 3.0 m up the incline, its velocity changes from 1.2 m/s to 2.3 m/s. How much work does friction do during this process?

A) - 3700 J
B) - 7200 J
C) + 3700 J
D) + 7200 J
E) zero

Question 56

Work-energy theorem: In the figure, two boxes, each of mass 24 kg, are at rest and connected as shown. The coefficient of kinetic friction between the inclined surface and the box is 0.31. Find the speed of the boxes just after they have moved 1.6 m.

Question 57

Work-energy theorem: A 4.00-kg mass is attached to a very light ideal spring hanging vertically and hangs at rest in the equilibrium position. The spring constant of the spring is 1.00 N/cm. The mass is pulled downward 2.00 cm and released. What is the speed of the mass when it is 1.00 cm above the point from which it was released?

A) 0.0443 m/s
B) 0.0744 m/s
C) 0.0201 m/s
D) 0.0866 m/s
E) The mass will not reach the height specified.

Question 58

Kinetic energy: A 1000.0 kg car is moving at If a truck has 18 times the kinetic energy of the car, how fast is the truck moving?

A) 45 km/h
B) 63 km/h
C) 54 km/h
D) 36 km/h

Question 59

Work-energy theorem: A 1000 kg car experiences a net force of 9500 N while decelerating from 30.0 m/s to 23.4 m/s. How far does it travel while slowing down?

A) 18.5 m
B) 17.4 m
C) 20.2 m
D) 21.9 m

Question 60

Hooke's law: Block A (0.40 kg) and block B (0.30 kg) are on a frictionless table (see figure). Spring 1 connects block A to a frictionless peg at 0 and spring 2 connects block A and block B. When the blocks are in uniform circular motion about 0, the springs have lengths of 0.60 m and 0.40 m, as shown. The springs are ideal and massless, and the linear speed of block B is 2.0 m/s. If the distance that spring 2 stretches is 0.060 m, the spring constant of spring 2 is closest to

A) 18 N/m.
B) 20 N/m.
C) 22 N/m.
D) 24 N/m.
E) 26 N/m.

Question 61

Work-energy theorem: A 7.0-kg rock is subject to a variable force given by the equation
F(x) = 6.0 N - (2.0 N/m)x + (6.0 N/m²)x²
If the rock initially is at rest at the origin, find its speed when it has moved 9.0 m.

Question 62

Power: Calculate the minimum average power output necessary for a person to run up a 12.0 m long hillside, which is inclined at 25.0° above the horizontal, in 3.00 s. You can neglect the person's kinetic energy. Express your answer in horsepower. (1 hp = 746 W)

A) 1.24 hp
B) 2.93 hp
C) 1.86 hp
D) 0.740 hp

Question 63

Energy conservation with conservative forces: A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position A as shown in the figure. The vertical height above ground level at position A is 200 m. Neglect friction. (a) What is the total mechanical energy of the roller coaster at point A?
(b) What is the total mechanical energy of the roller coaster at point B?
(c) What is the speed of the roller coaster at point B?
(d) What is the speed of the roller coaster at point C?

Question 64

Energy conservation with conservative forces: It requires 6.0 J of work is needed to push a 2.0-kg object from point A to point B of the frictionless ramp as shown in the figure. What is the length s of the ramp from A to B?

Question 65

Energy conservation with conservative forces: An 8.0-m massless rod is loosely pinned to a frictionless pivot at 0, as shown in the figure. A very small 4.0-kg ball is attached to the other end of the rod. The ball is held at A, where the rod makes a 30° angle above the horizontal, and is released. The ball-rod assembly then swings freely with negligible friction in a vertical circle between A and B. The tension in the rod when the ball passes through the lowest point at D is closest to

A) 160 N.
B) 200 N.
C) 120 N.
D) 80 N.
E) 40 N.

Question 66

Energy conservation with conservative forces: A 2.0 g bead slides along a frictionless wire, as shown in the figure. At point A, the bead is moving to the right but with negligible speed. (a) What is the potential energy of the bead at point A?
(b) What is the kinetic energy of the bead at point B?
(c) What is the speed of the bead at point B?
(d) What is the speed of the bead at point C?

Question 67

Power: A child pulls on a wagon with a horizontal force of If the wagon moves horizontally a total of in what is the average power generated by the child?

A) 18 W
B) 22 W
C) 24 W
D) 27 W

Question 68

Energy conservation with conservative forces: A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released from rest, the mass acquires a maximum speed v and a maximum kinetic energy K. If instead the mass initially compresses the spring twice as far:

A) Its maximum speed will be 2v and its maximum kinetic energy will be 2K.
B) Its maximum speed will be 2v and its maximum kinetic energy will be K.
C) Its maximum speed will be v and its maximum kinetic energy will be 2K.
D) Its maximum speed will be 2v and its maximum kinetic energy will be 4K.
E) Its maximum speed will be 4v and its maximum kinetic energy will be 2K.

Question 69

Energy conservation with conservative forces: In the figure, a 4.0-kg ball is on the end of a 1.6-m rope that is fixed at 0. The ball is held at point A, with the rope horizontal, and is given an initial downward velocity. The ball moves through three quarters of a circle with no friction and arrives at B, with the rope barely under tension. The initial velocity of the ball, at point A, is closest to

A) 4.0 m/s
B) 5.6 m/s
C) 6.3 m/s
D) 6.9 m/s
E) 7.9 m/s

Question 70

Power: A 1500-kg car accelerates from 0 to 25 m/s in 7.0 s with negligible friction and air resistance. What is the average power delivered by the engine? (1 hp = 746 W)

A) 50 hp
B) 60 hp
C) 70 hp
D) 80 hp
E) 90 hp

Question 71

Elastic potential energy: An athlete stretches a spring an extra 40.0 cm beyond its initial length. How much energy has he transferred to the spring, if the spring constant is 52.9 N/cm?

A) 423 J
B) 4230 kJ
C) 423 kJ
D) 4230 J

Question 72

Energy conservation with conservative forces: A tennis ball bounces on the floor three times. If each time it loses 22.0% of its energy due to heating, how high does it rise after the third bounce, provided we released it from the floor?

A) 110 cm
B) 11 cm
C) 110 mm
D) 140 cm

Question 73

Energy conservation with conservative forces: A 2.0 kg mass is moving along the x-axis. The potential energy curve as a function of position is shown in the figure. The kinetic energy of the object at the origin is 12 J. The system is conservative, and there is no friction. (a) What will be the kinetic energy at 2.0 m along the +x-axis?
(b) What will be the speed of the object at 6.0 m along the +x-axis?

Question 74

Power: If electricity costs 6.00¢/kWh (kilowatt-hour), how much would it cost you to run a 120 W stereo system 4.0 hours per day for 4.0 weeks?

A) $ 0.81
B) $ 0.12
C) $ 1.38
D) $ 2.27

Question 75

Power: The work performed as a function of time for a process is given by where What is the instantaneous power output at

A) 99 W
B) 69 W
C) 139 W
D) 208 W

Question 76

Gravitational potential energy: You do 174 J of work while pulling your sister back on a swing, whose chain is 5.10 m long. You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest. What is your sister's mass, assuming negligible friction?

A) 22.9 kg
B) 19.5 kg
C) 26.3 kg
D) 28.4 kg

Question 77

Power: How long will it take a 7.08 hp motor to lift a 250 kg beam directly upward at constant velocity from the ground to a height of 45.0 m? Assume frictional forces are negligible. (1 hp = 746 W)

A) 20.9 s
B) 1.56 × 10⁴ s
C) 2.18 × 10⁴ s
D) 39.7 s

Question 78

Work-energy theorem: The force on a 3.00-kg object as a function of position is shown in the figure. If an object is moving at 2.50 m/s when it is located at x = 2.00 m, what will its speed be when it reaches x = 8.00 m? (Assume that the numbers on the graph are accurate to 3 significant figures.)

A) 3.25 m/s
B) 3.70 m/s
C) 4.10 m/s
D) 2.90 m/s
E) 4.50 m/s

Question 79

Gravitational potential energy: An 8.0-kg block is released from rest, with v₁ = 0.00 m/s, on a rough incline, as shown in the figure. The block moves a distance of 1.6-m down the incline, in a time interval of 0.80 s, and acquires a velocity of v₂ = 4.0 m/s. How much work does gravity do on the block during this process?

A) +81 J
B) +100 J
C) +120 J
D) -81 J
E) -100 J

Question 80

Power: A car needs to generate in order to maintain a constant velocity of on a flat road. What is the magnitude of the total resistive force acting on the car (due to friction, air resistance, etc.)? (1 hp = 746 W)

A) 2.05 × 10³ N
B) 2.75 N
C) 1.03 × 10³ N
D) 2.87 × 10³ N