Practice Questions of Work, Energy, and Power

　　1. How much work does a person do in pushing a box with a force of 10 N over a distance of 4.0 m in the direction of the force?

　　(A)0.4 J

　　(B)4.0 J

　　(C)40 J

　　(D)400 J

　　(E)4000 J

　　2. A person pushes a 10 kg box at a constant velocity over a distance of 4 m. The coefficient of kinetic friction between the box and the floor is 0.3. How much work does the person do in pushing the box?

　　(A)12 J

　　(B)40 J

　　(C)75 J

　　(D)120 J

　　(E)400 J

　　3. How much work does the force of gravity do in pulling a 10 kg box down a 30 o inclined plane of length 8.0 m? Note that sin 30 = cos 60 = 0.500 and cos 30 = sin 60 = 0.866.

　　(A)40 J

　　(B)69 J

　　(C)400 J

　　(D)690 J

　　(E)800 J

　　4. How much work does a person do in pushing a box with a force of 20 N over a distance of 8.0 m in the direction of the force?

　　(A)1.6 J

　　(B)16 J

　　(C)160 J

　　(D)1600 J

　　(E)16000 J

　　5. The figure below is a force vs. displacement graph, showing the amount of force applied to an object by three different people. Al applies force to the object for the first 4 m of its displacement, Betty applies force from the 4 m point to the 6 m point, and Chuck applies force from the 6 m point to the 8 m point. Which of the three does the most work on the object?

　　(A)Al

　　(B)Betty

　　(C)Chuck

　　(D)Al and Chuck do the same amount of work

　　(E)Betty and Chuck do the same amount of work

　　6. When a car’s speed doubles, what happens to its kinetic energy?

　　(A)It is quartered

　　(B)It is halved

　　(C)It is unchanged

　　(D)It is doubled

　　(E)It is quadrupled

　　7. A worker does 500 J of work on a 10 kg box. If the box transfers 375 J of heat to the floor through the friction between the box and the floor, what is the velocity of the box after the work has been done on it?

　　(A)5 m/s

　　(B)10 m/s

　　(C)12.5 m/s

　　(D)50 m/s

　　(E)100 m/s

　　8. A person on the street wants to throw an 8 kg book up to a person leaning out of a window 5 m above street level. With what velocity must the person throw the book so that it reaches the person in the window?

　　(A)5 m/s

　　(B)8 m/s

　　(C)10 m/s

　　(D)40 m/s

　　(E)50 m/s

　　Questions 9 and 10 refer to a forklift lifting a crate of mass 100 kg at a constant velocity to a height of 8 m over a time of 4 s. The forklift then holds the crate in place for 20 s.

　　9. How much power does the forklift exert in lifting the crate?

　　(A)0 W

　　(B)2.0　103 W

　　(C)3.2　103 W

　　(D)2.0　104 W

　　(E)3.2　104 W

　　10. How much power does the forklift exert in holding the crate in place?

　　(A)0 W

　　(B)400 W

　　(C)1.6　103 W

　　(D)4.0　103 W

　　(E)1.6　104 W

　　Explanations

　　1.　　　C

　　When the force is exerted in the direction of motion, work is simply the product of force and displacement. The work done is (10 N)(4.0 m) = 40 J.

　　2.　　　D

　　The work done on the box is the force exerted multiplied by the box’s displacement. Since the box travels at a constant velocity, we know that the net force acting on the box is zero. That means that the force of the person’s push is equal and opposite to the force of friction. The force of friction is given by , where　is the coefficient of kinetic friction and N is the normal force. The normal force is equal to the weight of the box, which is mg = (10 kg )(10 m/s2) = 100 N. With all this in mind, we can solve for the work done on the box:

　　3.　　　C

　　The work done by the force of gravity is the dot product of the displacement of the box and the force of gravity acting on the box. That means that we need to calculate the component of the force of gravity that is parallel to the incline. This is mg sin 30 = (10 kg)(10 m/s2) sin 30. Thus, the work done is

　　4.　　　C

　　This is the same question as question 1. We were hoping that with different numbers and line spacing you wouldn’t notice. The test writers do that too sometimes.

　　5.　　　C

　　On a force vs. displacement graph, the amount of work done is the area between the graph and the x-axis. The work Al does is the area of the　right triangle:

　　The amount of work Betty does is equal to the area of a triangle of length 2 and height 4:

　　The amount of work done by Chuck is equal to the area of a rectangle of length 2 and height 4:　J. We can conclude that Chuck did the most work.

　　Don’t be fooled by D: the force exerted by Al is in the opposite direction of the object’s displacement, so he does negative work on the object.

　　6.　　　E

　　The formula for kinetic energy is KE =　mv2. Since the car’s kinetic energy is directly proportional to the square of its velocity, doubling the velocity would mean quadrupling its kinetic energy.

　　7.　　　A

　　The work-energy theorem tells us that the amount of work done on an object is equal to the amount of kinetic energy it gains, and the amount of work done by an object is equal to the amount of kinetic energy it loses. The box gains 500 J of kinetic energy from the worker’s push, and loses 375 J of kinetic energy to friction, for a net gain of 125 J. Kinetic energy is related to velocity by the formula KE =　mv2, so we can get the answer by plugging numbers into this formula and solving for v:

　　8.　　　C

　　When the book reaches the person in the window, it will have a gravitational potential energy of U = mgh. In order for the book to reach the window, then, it must leave the hands of the person at street level with at least that much kinetic energy. Kinetic energy is given by the formula KE = 1/2 mv2, so we can solve for v by making KE = U:

　　9.　　　B

　　Power is a measure of work divided by time. In turn, work is a measure of force multiplied by displacement. Since the crate is lifted with a constant velocity, we know that the net force acting on it is zero, and so the force exerted by the forklift must be equal and opposite to the weight of the crate, which is (100 kg)(10 m/s2) = 103 N. From this, we can calculate the power exerted by the forklift:

　　10.　　　A

　　Power is measured as work divided by time, and work is the dot product of force and displacement. While the crate is being held in the air, it is not displaced, so the displacement is zero. That means the forklift does no work, and thus exerts no power.