Question 1

Which, if any, of the following statements concerning the work done by a conservative force is NOT true?

Accepted Answer

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. 
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 2

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

Accepted Answer

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. 
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 3

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

Accepted Answer

A) True 
 B)False

Question 4

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?

Accepted Answer

A)  2.13 m/s 
B)  3.00 m/s 
C)  4.68 m/s 
D)  3.67 m/s 
A)  2.13 m/s 
B)  3.00 m/s 
C)  4.68 m/s 
D)  3.67 m/s

Question 5

A particle experiences a force given by F(x) = α - βx3. Find the potential field U(x) the particle is in. (Assume that the zero of potential energy is located at x = 0.)

Accepted Answer

A)  U(x) = -αx +   x4 
B)  U(x) = αx -   x4 
C)  U(x) = 3βx2 
D)  U(x) = -3βx2 
A)  U(x) = -αx +   x4 
B)  U(x) = αx -   x4 
C)  U(x) = 3βx2 
D)  U(x) = -3βx2

Question 6

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?

Accepted Answer

A)  0.71 m/s 
B)  4.0 m/s 
C)  1.4 m/s 
D)  2.8 m/s 
A)  0.71 m/s 
B)  4.0 m/s 
C)  1.4 m/s 
D)  2.8 m/s

Question 7

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

Accepted Answer

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

Question 8

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?

Accepted Answer

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

Question 9

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.

Accepted Answer

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. 
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 10

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?

Accepted Answer

(a) 24 J

Question 11

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  
.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 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?

Accepted Answer

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. 
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 13

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?

Accepted Answer

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

Question 14

The potential energy for a certain mass moving in one dimension is given by U(x) = (2.0 J/m3)x3 - (15 J/m2)x2 + (36 J/m)x - 23 J. Find the location(s) where the force on the mass is zero.

Accepted Answer

A)  4.0 m, 5.0 m 
B)  1.0 m 
C)  2.0 m, 3.0 m 
D)  3.0 m, 5.0 m 
A)  4.0 m, 5.0 m 
B)  1.0 m 
C)  2.0 m, 3.0 m 
D)  3.0 m, 5.0 m

Question 15

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?

Accepted Answer

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

Question 16

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:

Accepted Answer

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. 
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 17

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

Accepted Answer

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. 
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 18

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?

Accepted Answer

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

Question 19

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.)

Accepted Answer

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

Question 20

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?

Accepted Answer

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. 
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.

Exam 11: Work

Which, if any, of the following statements concerning the work done by a conservative force is NOT true?

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

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

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 particle experiences a force given by F(x) = α - βx3. Find the potential field U(x) the particle is in. (Assume that the zero of potential energy is located at x = 0.)

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 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?

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.

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 .

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 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?

The potential energy for a certain mass moving in one dimension is given by U(x) = (2.0 J/m3)x3 - (15 J/m2)x2 + (36 J/m)x - 23 J. Find the location(s) where the force on the mass is zero.

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 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 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 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 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?

Concepts of Motion

Kinematics in One Dimension

Vectors and Coordinate Systems

Kinematics in Two Dimensions

Force and Motion

Dynamics I: Motion Along a Line

Newtons Third Law

Dynamics Ii: Motion in a Plane

Impulse and Momentum

Energy

Rotation of a Rigid Body

Newtons Theory of Gravity

Oscillations

Fluids and Elasticity

A Macroscopic Description of Matter

Work, Heat, and the First Law of Thermodynamics

The Micromacro Connection

Heat Engines and Refrigerators

Traveling Waves

Superpositions

Wave Optics

Ray Optics

Optical Instruments

Electric Charges and Forces

The Electric Field

Gausss Law

The Electric Potential

Potential and Field

Current and Resistance

Fundamentals of Circuits

The Magnetic Field

Electromagnetic Induction

Electromagnetic Fields and Waves

Ac Circuits

Relativity

The Foundations of Modern Physics

Quantization

Wave Functions and Uncertainty

One-Dimensional Quantum Mechanics

Atomic Physics

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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 particle experiences a force given by F(x) = α - βx³. Find the potential field U(x) the particle is in. (Assume that the zero of potential energy is located at x = 0.)

The potential energy for a certain mass moving in one dimension is given by U(x) = (2.0 J/m³)x³- (15 J/m²)x²+ (36 J/m)x - 23 J. Find the location(s) where the force on the mass is zero.

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?