# Quiz 11: Work

Physics & Astronomy

Q 1Q 1

If the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other.

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True False

True

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True False

False

Q 3Q 3

The value of the dot product of two vectors depends on the particular coordinate system being used.

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True False

False

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.

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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

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 8Q 8

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

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True False

Q 9Q 9

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 10Q 10

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 v

_{1}of a swimmer reaching the end of slide 1 compares with v_{2}, the speed of a swimmer reaching the end of slide 2? A) v_{1}> v_{2}B) v_{1}< v_{2}C) v_{1}= v_{2}D) No simple relationship exists between v_{1}and v_{2}because we do not know the curvature of slide 2.Free

Multiple Choice

Q 11Q 11

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.

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Multiple Choice

Q 12Q 12

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.

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Multiple Choice

Q 13Q 13

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.

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Multiple Choice

Q 14Q 14

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.

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Multiple Choice

Q 15Q 15

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.

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Multiple Choice

Q 16Q 16

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

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True False

Q 17Q 17

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

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Multiple Choice

Q 18Q 18

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

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Multiple Choice

Q 19Q 19

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.

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Multiple Choice

Q 20Q 20

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.

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Multiple Choice

Q 21Q 21

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.

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Multiple Choice

Q 22Q 22

A potential energy function for system 1 is given by U

_{1}(x) = Cx^{2}+ Bx^{3}. The potential energy function for system 2 is given by U_{2}(x) = A + Cx^{2}+ Bx^{3}, 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.Free

Multiple Choice

Q 23Q 23

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

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Multiple Choice

Q 24Q 24

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 25Q 25

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 26Q 26

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 27Q 27

The angle between vector = 2.00
+ 3.00
And vector
Is 45.0°. 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 28Q 28

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 30Q 30

Two boys searching for buried treasure are standing underneath the same tree. One boy walks 18 m east and then 18 m north. The other boy walks 16 m west and then 11 m north. Find the scalar product of their net displacements from the tree.

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Short Answer

Q 31Q 31

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 32Q 32

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 33Q 33

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

Essay

Q 34Q 34

You carry a 7.0 kg bag of groceries 1.2 m above the level floor at a constant velocity of 75 cm/s across a room that is 2.3 m 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 35Q 35

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 36Q 36

Find the net work done by friction on the body of a snake slithering in a complete circle of 3.93 m 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 37Q 37

A crane lifts a 425 kg steel beam vertically a distance of 117 m. 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 38Q 38

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 39Q 39

A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If 908 J 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 40Q 40

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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Essay

Q 41Q 41

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 42Q 42

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 43Q 43

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 44Q 44

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 45Q 45

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 46Q 46

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 47Q 47

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 48Q 48

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 49Q 49

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 50Q 50

In the figure, a 900-kg crate is on a rough surface inclined at 30°. A constant external force
P = 7200 N 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 51Q 51

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 52Q 52

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 53Q 53

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 54Q 54

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 55Q 55

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 56Q 56

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 57Q 57

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 58Q 58

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 59Q 59

A child pulls on a wagon with a horizontal force of 75 N. If the wagon moves horizontally a total of 42 m in 3.0 min, 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 60Q 60

A car needs to generate 75.0 hp in order to maintain a constant velocity of 27.3 m/s 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 61Q 61

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 62Q 62

Calculate the minimum average power output necessary for a 55.8 kg 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 63Q 63

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 64Q 64

The work performed as a function of time for a process is given by W = at

^{3}where a = 2.4 J/s^{3}. What is the instantaneous power output at t = 3.7 s? A) 99 W B) 69 W C) 138 W D) 207 WFree

Multiple Choice

Q 65Q 65

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?

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Short Answer

Q 66Q 66

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?

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Essay

Q 67Q 67

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?

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Essay

Q 68Q 68

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.

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Multiple Choice

Q 69Q 69

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?

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Essay

Q 70Q 70

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.

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Multiple Choice

Q 71Q 71

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

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Multiple Choice

Q 72Q 72

In the figure, a very small toy race car of mass m is released from rest on the loop-the-loop track. If it is released at a height 2R above the floor, how high is it above the floor when it leaves the track, neglecting friction?
A) 1.67 R
B) 2.00 R
C) 1.50 R
D) 1.33 R
E) 1.25 R

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Multiple Choice

Q 73Q 73

In the figure, a 5.00-kg block is moving at 5.00 m/s along a horizontal frictionless surface toward an ideal massless spring that is attached to a wall. After the block collides with the spring, the spring is compressed a maximum distance of 0.68 m. What is the speed of the block when it has moved so that the spring is compressed to only one-half of the maximum distance?

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Short Answer

Q 74Q 74

A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass. The platform drops 6.00 cm before the person comes to rest. What is the spring constant of the spring?
A) 2.56 × 10

^{5}N/m B) 3.92 × 10^{5}N/m C) 5.45 × 10^{4}N/m D) 4.12 × 10^{5}N/m E) 8.83 × 10^{4}N/mFree

Multiple Choice

Q 75Q 75

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 above its point of release. 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 friction and assume the spring is ideal and massless.)
A) 6.0 m
B) 12 m
C) 3.0 m
D) 48 m

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Multiple Choice

Q 76Q 76

A block slides down a frictionless inclined ramp. If the ramp angle is 17.0° and its length 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) 13.1 m/s
B) 172 m/s
C) 9.26 m/s
D) 24.0 m/s

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Multiple Choice

Q 77Q 77

Consider the motion of a 1.00-kg particle that moves with potential energy given by
U(x) = (-2.00 J∙m)/x + (4.00 J∙m

^{2})/x^{2}. Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m? A) 2.13 m/s B) 3.00 m/s C) 4.68 m/s D) 3.67 m/sFree

Multiple Choice

Q 78Q 78

A car on a roller coaster starts at zero speed at an elevation above the ground of 26 m. It coasts down a slope, and then climbs a hill. The top of the hill is at an elevation of 16 m. What is the speed of the car at the top of the hill? Neglect any frictional effects.
A) 14 m/s
B) 18 m/s
C) 10 m/s
D) 9.0 m/s
E) 6.0 m/s

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Multiple Choice

Q 79Q 79

A projectile is fired from ground level at an angle of 40.0° above horizontal at a speed of 30.0 m/s. What is the speed of the projectile when it has reached a height equal to 50.0% of its maximum height?
A) 26.0 m/s
B) 27.4 m/s
C) 28.7 m/s
D) 26.7 m/s
E) 28.1 m/s

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Multiple Choice

Q 80Q 80

A very small 100-g object is attached to one end of a massless 10-cm rod that is pivoted without friction about the opposite end. The rod is held vertical, with the object at the top, and released, allowing the rod to swing. What is the speed of the object at the instant that the rod is horizontal?
A) 0.71 m/s
B) 4.0 m/s
C) 1.4 m/s
D) 2.8 m/s
E) 2.8 m/s

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Multiple Choice

Q 81Q 81

A 2.0-kg object is moving without friction along the x-axis. The potential energy curve as a function of position is shown in the figure, and the system is conservative. If the speed of the object at the origin is 4.0 m/s, what will be its speed at 7.0 m along the +x-axis?
A) 4.0 m/s
B) 4.2 m/s
C) 4.4 m/s
D) 4.6 m/s
E) 9.8 m/s

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Multiple Choice

Q 82Q 82

A small hockey puck slides without friction over the icy hill shown in the figure and lands 6.20 m from the foot of the cliff with no air resistance. What was its speed v

_{0}at the bottom of the hill? A) 20.8 m/s B) 17.4 m/s C) 14.4 m/s D) 13.7 m/s E) 4.71 m/sFree

Multiple Choice

Q 83Q 83

An object is attached to a hanging unstretched ideal and massless spring and slowly lowered to its equilibrium position, a distance of 6.4 cm below the starting point. If instead of having been lowered slowly the object was dropped from rest, how far then would it then stretch the spring at maximum elongation?
A) 13 cm
B) 9.1 cm
C) 6.4 cm
D) 18 cm
E) 26 cm

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Multiple Choice

Q 84Q 84

In the figure, a stunt car driver negotiates the frictionless track shown in such a way that the car is barely in contact with the track at the top of the loop. The radius of the track is 9.9 m and the mass of the car is 1800 kg. Find the magnitude of the force of the car on the track when the car is at point A. You can treat the car as a point mass.

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Short Answer

Q 85Q 85

A 50.0-kg skier starting from rest travels 200 m down a hill that has a 20.0° slope and a uniform surface. When the skier reaches the bottom of the hill, her speed is 30.0 m/s.
(a) How much work is done by friction as the skier comes down the hill?
(b) What is the magnitude of the friction force if the skier travels directly down the hill?

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Essay

Q 86Q 86

A 5.00-kg object moves clockwise around a 50.0 cm radius circular path. At one location, the speed of the object is 4.00 m/s. When the object next returns to this same location, the speed is 3.00 m/s.
(a) How much work was done by nonconservative (dissipative) forces as the object moved once around the circle?
(b) If the magnitude of the above nonconservative (dissipative) forces acting on the object is constant, what is the value of this magnitude?

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Essay

Q 87Q 87

In the figure, a block of mass m is moving along the horizontal frictionless surface with a speed of 5.70 m/s. If the slope is 11.0° and the coefficient of kinetic friction between the block and the incline is 0.260, how far does the block travel up the incline?

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Short Answer

Q 88Q 88

An object of mass 4.0 kg starts at rest from the top of a rough inclined plane of height 10 m as shown in the figure. If the speed of the object at the bottom of the inclined plane is 10 m/s, how much work does friction do on this object as it slides down the incline?

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Short Answer

Q 89Q 89

An 0.80-kg block is held in place against the spring by a 67-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v

_{1}= 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity v_{2}= 1.9 m/s 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 over this section is 0.39. The velocity of the block is v_{3}= 1.4 m/s at C. The block moves on to D, where it stops. The spring constant of the spring is closest to A) 3900 N/m. B) 2600 N/m. C) 2000 N/m. D) 1600 N/m. E) 1100 N/m.Free

Multiple Choice

Q 90Q 90

A 1.37-kg block is held in place against the spring by a 74-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v

_{1}= 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity v_{2}= 1.4 m/s 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 over this section is 0.24. The velocity of the block is v_{3}= 1.4 m/s at C. The block moves on to D, where it stops. The initial compression of the spring is closest to: A) 2.7 cm. B) 1.4 cm. C) 0.96 cm. D) 5.3 cm. E) 3.6 cm.Free

Multiple Choice

Q 91Q 91

A 1.86-kg block is held in place against the spring by a 81-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v

_{1}= 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity v_{2}= 1.9 m/s 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 over this section is 0.28. The velocity of the block is v_{3}= 1.4 m/s at C. The block moves on to D, where it stops. The height h of the ramp is closest to A) 11 B) 7.3 C) 15 D) 17 E) 18Free

Multiple Choice

Q 92Q 92

A 2.5-kg box, sliding on a rough horizontal surface, has a speed of 1.2 m/s when it makes contact with a spring (see the figure). The block comes to a momentary halt when the compression of the spring is 5.0 cm. The work done by the friction, from the instant the block makes contact with the spring until is comes to a momentary halt, is -0.50 J.
(a) What is the spring constant of the spring?
(b) What is the coefficient of kinetic friction between the box and the rough surface?

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Essay

Q 93Q 93

The only force acting on an object moving along the x-axis is the conservative force given by F(x) = (2.00 N/m)x + (1.00 N/m

^{3})x^{3}. (a) What is the change in potential energy when the object moves from x = 1.00 m to x = 2.00 m? (b) What is the change in kinetic energy when the object moves from x = 1.00 m to x = 2.00 m?Free

Essay

Q 94Q 94

A force on an object is given by F(x) = (2.00 N/m)x - (3.00 N/m

^{3})x^{3}. What is a potential energy function U(x) for this conservative force?Free

Essay

Q 95Q 95

A force on an object is given by F(x) = ( -4.00 N/m)x + ( 2.00 N/m

^{3})x^{3}. What is the change in potential energy in moving from x = 1.00 m to x = 2.00 m? A) 10.0 J B) -1.50 J C) -10.0 J D) 1.50 J E) 12.0 JFree

Multiple Choice

Q 96Q 96

A potential energy function is given by U(x) = (3.00 J)x + (1.00 J/m

^{2})x^{3}. What is the force function F(x) that is associated with this potential energy function?Free

Short Answer

Q 97Q 97

A potential energy function is given by U(x) = ( 3.00 N/m)x - ( 1.00 N/m

^{3})x^{3}. At what position or positions is the force equal to zero? A) m and - m B) 0.00 m, m and - m C) 1.00 m and -1.00 m D) 3.00 m and -3.00 m E) The force is not zero at any location.Free

Multiple Choice

Q 98Q 98

The potential energy for a certain mass moving in one dimension is given by U(x) = (2.0 J/m

^{3})x^{3 }- (15 J/m^{2})x^{2 }+ (36 J/m)x - 23 J. Find the location(s) where the force on the mass is zero. A) 4.0 m, 5.0 m B) 1.0 m C) 2.0 m, 3.0 m D) 3.0 m, 5.0 mFree

Multiple Choice

Q 99Q 99

A particle experiences a force given by F(x) = α - βx

^{3}. Find the potential field U(x) the particle is in. (Assume that the zero of potential energy is located at x = 0.) A) U(x) = -αx + x^{4}B) U(x) = αx - x^{4}C) U(x) = 3βx^{2}D) U(x) = -3βx^{2}Free

Multiple Choice

Q 100Q 100

When a particle is a distance r from the origin, its potential energy function is given by the equation U(r) = kr, where k is a constant and r =
(a) What are the SI units of k?
(b) Find a mathematical expression in terms of x, y, and z for the y component of the force on the particle.
(c) If U = 3.00 J when the particle is 2.00 m from the origin, find the numerical value of the y component of the force on this particle when it is at the point (-1.00 m, 2.00 m, 3.00 m).

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Essay