Deck 11: Work

Question 1

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)

Answer 1

(1) and (2)

Question 2

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

Answer 2

True

Question 3

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.

Answer 3

v₁ = v₂

Question 4

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

Question 5

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

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 7

If two nonzero vectors point in the same direction, their dot product must be zero.

Question 8

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.

Question 9

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 10

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 11

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 12

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 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.

Question 14

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

Question 15

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

Question 16

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 17

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 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

Question 19

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

Question 20

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 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.

Question 22

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

Question 23

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/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

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 25

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

Question 26

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

Question 27

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 28

If
= 3
-
+ 4
and
= x
+
- 5
, find x so
will be perpendicular to
.

Question 29

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.

Question 30

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)

Question 31

What is the angle between the vector = +3
- 2
- 3
And the +y-axis?

A) 115°
B) 65°
C) 25°
D) 155°
E) 90°

Question 32

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

Question 33

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°.

Question 34

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 35

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 36

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°

Question 37

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 38

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 39

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 40

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

Question 41

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

Question 42

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

Question 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

Question 44

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 45

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 46

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 47

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 48

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 49

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

Question 50

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 51

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 52

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 53

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 54

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 55

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 56

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 57

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 58

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 59

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 60

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 61

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?

Question 62

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 63

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∙m²)/x². 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/s

Question 64

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 65

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

Question 66

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 × 10⁵ N/m
B) 3.92 × 10⁵ N/m
C) 5.45 × 10⁴ N/m
D) 4.12 × 10⁵ N/m
E) 8.83 × 10⁴ N/m

Question 67

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 68

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

Question 69

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

Question 70

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

Question 71

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 72

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 73

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 74

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

Question 75

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

Question 76

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 77

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 78

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

Question 79

The work performed as a function of time for a process is given by W = at³ where a = 2.4 J/s³. What is the instantaneous power output at t = 3.7 s?

A) 99 W
B) 69 W
C) 138 W
D) 207 W

Question 80

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?