# Quiz 9: Work and Kinetic Energy

Physics & Astronomy

Q 1Q 1

If the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other.
A) True
B) False

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Multiple Choice

A

Q 2Q 2

If two nonzero vectors point in the same direction, their dot product must be zero.
A) True
B) False

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Multiple Choice

B

Q 3Q 3

The value of the dot product of two vectors depends on the particular coordinate system being used.
A) True
B) False

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Multiple Choice

B

Q 4Q 4

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.

Free

Multiple Choice

Q 5Q 5

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)

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Multiple Choice

Q 6Q 6

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.

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Multiple Choice

Q 7Q 7

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.

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Multiple Choice

Q 8Q 8

Which of the graphs in the figure illustrates Hooke's Law?
A) Graph a
B) Graph b
C) Graph c
D) graph d

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Multiple Choice

Q 9Q 9

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

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Multiple Choice

Q 10Q 10

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.

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Multiple Choice

Q 11Q 11

If a force always acts perpendicular to an object's direction of motion, that force cannot change the object's kinetic energy.
A) True
B) False

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Multiple Choice

Q 12Q 12

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.

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Multiple Choice

Q 13Q 13

Determine the scalar product of = 6.0 + 4.0 - 2.0 and = 5.0 - 6.0 - 3.0 .
A) 30 + 24 + 6
B) 30 - 24 + 6
C) 12
D) 60
E) undefined

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Multiple Choice

Q 14Q 14

Determine the angle between the directions of vector = 3.00 + 1.00 and vector = -3.00 + 3.00 .
A) 26.6°
B) 30.0°
C) 88.1°
D) 117°
E) 45.2°

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Multiple Choice

Q 15Q 15

The scalar product of vector = 3.00 + 2.00 and vector is 10.0. Which of the following vectors could be vector ?
A) 2.00 + 4.00
B) 4.00 + 6.00
C) 5.00 + 4.00
D) 12.0
E) 2.00 + 2.00

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Multiple Choice

Q 16Q 16

The angle between vector = 2.00 + 3.00 and vector is The scalar product of vectors and is 3.00. If the x component of vector is positive, what is vector .
A)
B)
C)
D)
E)

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Multiple Choice

Q 17Q 17

What is the angle between the vector = +3 - 2 - 3 and the +y-axis?
A) 115°
B) 65°
C) 25°
D) 155°
E) 90°

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Multiple Choice

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Short Answer

Q 19Q 19

Two boys searching for buried treasure are standing underneath the same tree. One boy walks east and then north. The other boy walks west and then north. Find the scalar product of their net displacements from the tree.

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Essay

Q 20Q 20

A rectangular box is positioned with its vertices at the following points: A = (0,0,0) C = (2,4,0) E = (0,0,3) G = (2,4,3)
B = (2,0,0) D = (0,4,0) F = (2,0,3) H = (0,4,3)
If the coordinates all have three significant figures, the angle between the line segments AG and AH is closest to:
A) 21.8°.
B) 22.5°.
C) 26.6°.
D) 36.9°.
E) 45.0°.

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Multiple Choice

Q 21Q 21

For the vectors shown in the figure, assume numbers are accurate to two significant figures. The scalar product × is closest to
A) zero.
B) 16.
C) 45.
D) -16.
E) -45.

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Multiple Choice

Q 22Q 22

Three forces, F

_{1}= 20.0 N, F_{2}= 40.0 N, and F_{3}= 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) F_{1}(b) F_{2}(c) F_{3}.Free

Short Answer

Q 23Q 23

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 room. 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

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Multiple Choice

Q 24Q 24

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

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Multiple Choice

Q 25Q 25

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

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Multiple Choice

Q 26Q 26

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/s

^{2}? Neglect frictional forces. A) 5.8 × 10^{5}J B) 3.4 × 10^{5 }J C) 4.0 × 10^{5}J D) 4.9 × 10^{5 J}Free

Multiple Choice

Q 27Q 27

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 × 10

^{8}J B) -0.985 × 10^{8}J C) -221 × 10^{8}J D) 221 × 10^{8}J E) 0.821 × 10^{8}JFree

Multiple Choice

Q 28Q 28

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

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Multiple Choice

Q 29Q 29

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?

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Short Answer

Q 30Q 30

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.

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Multiple Choice

Q 31Q 31

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

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Multiple Choice

Q 32Q 32

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

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Multiple Choice

Q 33Q 33

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

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Multiple Choice

Q 34Q 34

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

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Multiple Choice

Q 35Q 35

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

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Multiple Choice

Q 36Q 36

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

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Multiple Choice

Q 37Q 37

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.

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Multiple Choice

Q 38Q 38

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.

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Multiple Choice

Q 39Q 39

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.

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Multiple Choice

Q 40Q 40

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

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Multiple Choice

Q 41Q 41

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

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Multiple Choice

Q 42Q 42

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

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Multiple Choice

Q 43Q 43

A force F = bx

^{3}acts in the x direction, where the value of b is 3.7 N/m^{3}. 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 JFree

Multiple Choice

Q 44Q 44

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.

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Multiple Choice

Q 45Q 45

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

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Multiple Choice

Q 46Q 46

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

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Multiple Choice

Q 47Q 47

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%

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Multiple Choice

Q 48Q 48

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

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Multiple Choice

Q 49Q 49

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

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Multiple Choice

Q 50Q 50

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

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Multiple Choice

Q 51Q 51

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.

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Multiple Choice

Q 52Q 52

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

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Multiple Choice

Q 53Q 53

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

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Multiple Choice

Q 54Q 54

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.

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Multiple Choice

Q 55Q 55

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.

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Short Answer

Q 56Q 56

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.

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Multiple Choice

Q 57Q 57

An unusual spring has a restoring force of magnitude F = (2.00 N/m)x + (1.00 N/m

^{2})x^{2}, 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/sFree

Multiple Choice

Q 58Q 58

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

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Multiple Choice

Q 59Q 59

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/m

^{2})x^{2}If the rock initially is at rest at the origin, find its speed when it has moved 9.0 m.Free

Short Answer

Q 60Q 60

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

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Multiple Choice

Q 61Q 61

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

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Multiple Choice

Q 62Q 62

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 × 10

^{3}N B) 2.75 N C) 1.03 × 10^{3}N D) 2.87 × 10^{3}NFree

Multiple Choice

Q 63Q 63

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 × 10

^{4}s C) 2.18 × 10^{4}s D) 39.7 sFree

Multiple Choice

Q 64Q 64

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

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Multiple Choice

Q 65Q 65

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

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Multiple Choice

Q 66Q 66

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

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Multiple Choice