# 1) What Is the Correct Unit of Work Expressed in SI Units?

Chapter 6 HW Packet

**Conceptual Questions**

1) What is the correct unit of work expressed in SI units?

A) kg2 m/s2

B) kg m/s2

C) kg m2/s

D) kg m2/s2

**The easiest way to remember this so it becomes intuitive is that every time you think of work equaling force times distance you also think of the units—N times m, and then N = kgm/s2, and if you can’t remember that, think of it as F x d = ma x d = (kg)(m/s2)(m)= kgm2/s2. If you keep doing this eventually you won’t even have to think about it—you’ll just know that its kgm2/s2. Answer D (5-10 seconds)**

2) Can work be done on a system if there is no motion?

A) Yes, since motion is only relative.

B) No, because of the way work is defined.

C) Yes, if an outside force is provided.

D) No, since a system which is not moving has no energy. **Work is defined as ****—if there is no displacement, there is no work. Answer B (10-15 seconds)**

3) If you push twice as hard against a stationary brick wall, the amount of work you do

A) remains constant at zero.

B) doubles.

C) remains constant but non-zero.

D) is cut in half.**Work is defined as ****--if there is no displacement there is no work. If the wall is stationary, there is no work no matter how hard you push against it. Answer A (10-15 seconds)**

4) A 50-N object was lifted 2.0 m vertically and is being held there. How much work is being done in holding the box in this position?

A) 100 J

B) more than 100 J

C) less than 100 J, but more than 0 J

D) 0 J

**Work is defined as ****--if there is no displacement there is no work. As long as the box is being held in position, no work is being done. Answer D**

5) If you walk 5.0 m horizontally forward at a constant velocity carrying a 10-N object, the amount of work you do is (12/17)

A) less than 50 J, but more than 0 J.

B) equal to 50 J.

C) more than 50 J.

D) zero.

**Work is defined as ****--therefore, the force must be in the direction of the motion. If you are carrying an object the force on the object is directed upward (at 900) compared to the motion of the object. cos (900) = 0, so ****=0, so no work is done. Answer D (10-15 seconds).**

6) A container of water is lifted vertically 3.0 m then returned to its original position. If the total weight is 30 N, how much work was done? (17/17)

A) No work was done.

B) 45 J

C) 90 J

D) 180 J

**In lifting the container, a force equal to the weight of the container is applied over a distance of 3.0 m, and the force is in the direction of the container. So, in lifting the container, (30 N)(3.0 m)(cos(00)=90 J of work is performed on the container. In lowering the container, a force of 30 N must still be applied to the container, and the direction of this force is still in the upward direction. However, now the force is opposite the direction of the container, so ****. The net work is the sum of the work in both directions, and so = 0J. Answer A (15-30 seconds)**

7) Does the centripetal force acting on an object do work on the object? (16/17)

A) Yes, since a force acts and the object moves, and work is force times distance.

B) Yes, since it takes energy to turn an object.

C) No, because the object has constant speed.

D) No, because the force and the displacement of the object are perpendicular. **Remember that the force causing the displacement has to be in the direction of the displacement. The centripetal force, which would be the force causing an object to travel in a circular path, is perpendicular to the motion of the object traveling in the circle therefore, the angle between the force and the motion would be 900 and the cos of 900 is 0, so ****=0. Answer D (15-30 seconds)**

8) You throw a ball straight up. Compare the sign of the work done by gravity while the ball goes up with the sign of the work done by gravity while it goes down. (13/17)

A) Work is - on the way up and + on the way down.

B) Work is - on the way up and - on the way down.

C) Work is + on the way up and + on the way down.

D) Work is + on the way up and - on the way down. **Remember that force due to gravity is always acting in a downward direction. When the ball is traveling upward, this means that the angle between the motion and the direction of force is 1800. As cos 1800 is **

-1, **will have a negative value. On the way down, the ball is traveling in the same direction as the force so the angle between the direction of the force and the motion is 00, for which cos is 1. Therefore, **will have a positive value. Answer A (15 to 30 seconds)

9) The area under the curve, on a Force versus position (F vs. x) graph, represents (17/17)

A) work.

B) kinetic energy.

C) power.

D) potential energy.

Finding the area under the curve on a F vs d graph is the same thing as multiplying Fd. Therefore, the area under the curve of this type of graph represents work. Answer A (10 to 15 seconds)

10) On a plot of Force versus position (F vs. x), what represents the work done by the force F? ((17/17)

A) the slope of the curve

B) the length of the curve

C) the area under the curve

D) the product of the maximum force times the maximum x

See explanation for question 9. Answer C (10-15 seconds)

11) The quantity 1/2 mv2 is (15/17)

A) the kinetic energy of the object.

B) the potential energy of the object.

C) the work done on the object by the force.

D) the power supplied to the object by the force.

½ mv2 is the definition for kinetic energy. Be able to derive this from W = F x d. Answer A (10-15 seconds)

12) If the net work done on an object is positive, then the object's kinetic energy (17/17)

A) decreases.

B) remains the same.

C) increases.

D) is zero.

According to the work energy theorem, the change in kinetic energy equals the amount of work performed on the object. If the net work is positive, this means the final kinetic energy is greater than the initial kinetic energy , which means the kinetic energy must have increased. Answer C (10-15 seconds)

13) If the net work done on an object is negative, then the object's kinetic energy (17/17)

A) decreases.

B) remains the same.

C) increases.

D) is zero.

According to the work energy theorem, the change in kinetic energy equals the amount of work performed on the object. If the net work is negative, this means the final kinetic energy is less than the initial kinetic energy , which means the kinetic energy must have decreased. Answer A (10-15 seconds)

14) If the net work done on an object is zero, then the object's kinetic energy (13/17)/

A) decreases.

B) remains the same.

C) increases.

D) is zero.

According to the work energy theorem, the change in kinetic energy equals the amount of work performed on the object. If the net work is 0, this means the final kinetic energy equals the initial kinetic energy , which means the kinetic energy must have remained the same. Answer B (10-15 seconds)

15) A truck weighs twice as much as a car, and is moving at twice the speed of the car. Which statement is true about the truck's kinetic energy compared to that of the car? (16/17)

A) All that can be said is that the truck has more kinetic energy.

B) The truck has twice the kinetic energy of the car.

C) The truck has 4 times the kinetic energy of the car.

D) The truck has 8 times the kinetic energy of the car.

As with so many other questions like this the best way to solve this is write out the equation, isolate the variable you are comparing, and see how changing the other variable must affect it. As

you can see that if you double the mass (which would account for double the weight) and double the speed, the KE must be multiplied by 8 times. Write the formula out if necessary to visualize Answer D (30-45 seconds)

16) Car J moves twice as fast as car K, and car J has half the mass of car K. The kinetic energy of car J, compared to car K is (15/17)\]

A) the same.

B) 2 to 1.

C) 4 to 1.

D) 1 to 2.

Write out the equation, isolate the variable you are comparing, and see how changing the other variable(s) must affect it. Answer B (30-45 seconds)

17) An object hits a wall and bounces back with half of its original speed. What is the ratio of the final kinetic energy to the initial kinetic energy? (15/17)

A) 1/2

B) 1/4

C) 2

D) 4

This problem may be intuitive enough for you at this point that you can readily see the answer should be ¼ of the original KE because KE depends on the square of the velocity. However, it never hurts to write out the equation, isolate the variable you are comparing, and see how changing the other variable(s) must affect it. Answer B (30-45 seconds)

18) A brick is moving at a speed of 3 m/s and a pebble is moving at a speed of 5 m/s. If both objects have the same kinetic energy, what is the ratio of the brick's mass to the rock's mass? (16/17)

A) 25 to 9

B) 5 to 3

C) 12.5 to 4.5

D) 3 to 5

In this case write out the formula for KE for both objects, isolate the masses, create the ratio of the masses, then see what applying the velocities does to this ratio. Answer A (60-90 seconds)

19) A 4.0-kg mass is moving with speed 2.0 m/s. A 1.0-kg mass 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? (16/17)

A) the 4.0-kg mass

B) the 1.0-kg mass

C) Both travel the same distance.

D) cannot be determined from the information given

Because the same force is used to stop both objects, and , the stopping distance will depend only on the change in kinetic energy—which ever object has the greatest kinetic energy will take the longest to stop. You can quickly determine the first object has a kinetic energy of 8 J, and the second object also has a kinetic energy of 8J. Therefore, both will take the same distance to stop. Answer C (45-60 seconds)

20) 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 the same conditions?

A) It would have skidded 4 times farther.

B) It would have skidded twice as far.

C) It would have skidded 1.4 times farther.

D) It is impossible to tell from the information given.

This problem may be intuitive enough for you at this point that you can readily see that as the KE is proportional to the square of the velocity, if you double the velocity you will have four times the KE, and because this would equal the amount of work done stopping the car and W = Fd, this would mean four times the stopping distance. However, it never hurts to write out the equation, isolate the variable you are comparing, and see how changing the other variable(s) must affect it. Answer A (10-15 seconds)

21) A planet of constant mass orbits the Sun in an elliptical orbit. Neglecting any friction effects, what happens to the planet's kinetic energy?

A) It remains constant.

B) It increases continually.

C) It decreases continually.

D) It increases when the planet approaches the Sun, and decreases when it moves farther away.

As the distance from the sun decreases as the planet approaches the sun, the gravitational force will increase and the velocity of the planet will increase, therefore the KE will increase. As the distance from the sun increases as the planet moves away from the sun, the gravitational force will decrease and the velocity of the planet will decrease, therefore, KE will decrease. Answer D (10-15 seconds)

22) State the work-energy principle. The net work done on an object is equal to the change in the objects kinetic energy.

23) The quantity mgy is

A) the kinetic energy of the object.

B) the gravitational potential energy of the object.

C) the work done on the object by the force.

D) the power supplied to the object by the force.

We can determine the formula for the gravitational potential energy by recognizing that in increasing an objects gravitational potential, we are doing work against gravity, and . If there is no acceleration as we are raising the object, the force applied to the object must equal the force due to gravity, but the force is in the opposite direction of gravity so ==-1. If y equals the distance raised, PE=W becomes PE = -m(-g)y=mgy. Answer B (10-15 seconds)

24) The quantity 1/2 kx2 is

A) the kinetic energy of the object.

B) the elastic potential energy of the object.

C) the work done on the object by the force.

D) the power supplied to the object by the force.

Remember, the force required to stretch a spring a certain distance is given by , where k is the spring constant (Hooke’s law). To find the work required to stretch the spring, and so, the amount of PE stored in the spring by that amount of work, we cannot just multiply this force times the distance, because the force changes depending on the degree of stretching of the spring. We would therefore need to use the average force, which could be given by

The expression for PE stored in a spring then becomes

Answer B

25) Is it possible for a system to have negative potential energy?

A) Yes, as long as the total energy is positive.

B) Yes, since the choice of the zero of potential energy is arbitrary.

C) No, because the kinetic energy of a system must equal its potential energy.

D) No, because this would have no physical meaning.

As with all conservative forces, the calculation of potential energy depends on the position of an object with reference to a position representing 0 J of potential energy. If the position of the object is at a position that is negative to this reference, then the calculated potential energy will have a negative value. Answer B (15-30 seconds)

26) An object is released from rest a height h above the ground. A second object with four times the mass of the first if released from the same height. The potential energy of the second object compared to the first is

A) one-fourth as much.

B) one-half as much.

C) twice as much.

D) four times as much.

Write out the equation, isolate the variable you are comparing, and see how changing the other variable(s) must affect it. Answer D (30-45 seconds)

27) A 0.200-kg mass attached to the end of a spring causes it to stretch 5.0 cm. If another 0.200-kg mass is added to the spring, the potential energy of the spring will be

A) the same.

B) twice as much.

C) 3 times as much.

D) 4 times as much.

Remember that the F required to stretch a spring equals the spring constant times the distance stretched (). The work required to stretch the spring therefore is --except, F is not constant. As the spring stretches, the force changes so we need to use the average force (force at the beginning and end of the stretch divided by 2= ½ F). This makes the work required to stretch the spring:. This will also be the amount of PE we add to the spring. Adding another .200 kg of mass to the spring will stretch the spring an additional 5.0 cm. As the potential energy added is multiplied by the square of the distance, the PE will be four times as much. Answer D (45-60 seconds—or less)

28) The total mechanical energy of a system

A) is equally divided between kinetic energy and potential energy.

B) is either all kinetic energy or all potential energy, at any one instant.

C) can never be negative.

D) is constant, only if conservative forces act.

By definition, the total mechanical energy of a system is defined as KE + PE. If no non-conservative forces are present to modify these energies, the total mechanical energy of a system remains constant.

29) An acorn falls from a tree. Compare its kinetic energy K, to its potential energy U.

A) K increases and U decreases.

B) K decreases and U decreases.

C) K increases and U increases.

D) K decreases and U increases.

As any object falls under the influence of gravity, potential energy is exchanged for kinetic energy—K increases and U decreases—Answer A (10-15 seconds)

30) Describe the energy of a car driving up a hill.

A) entirely kinetic

B) entirely potential

C) both kinetic and potential

D) gravitational

As the car has motion it has kinetic energy. As it is traveling up a hill, it is also increasing in potential energy. Answer C (10-15 seconds)

31) A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill. Which rises to a greater height?

A) The heavy object, because it has greater kinetic energy.

B) The lightweight object, because it weighs less.

C) They both slide to the same height.

D) cannot be determined from the information given

Although they are both traveling at the same speed, the heavier object will have more KE. However, as they both convert their kinetic energy to potential energy, as mass is in both formulas, it will cancel out and amount of potential energy obtained will only be related to the speed, which is the same for both. So, they will climb to the same height. Answer C (15-30 seconds)

32) Consider two masses m1 and m2 at the top of two frictionless inclined planes. Both masses start from rest at the same height. However, the plane on which m1 sits is at an angle of 30° with the horizontal, while the plane on which m2 sits is at 60°. If the masses are released, which is going faster at the bottom of its plane?

A) m1

B) m2

C) They both are going the same speed.

D) cannot be determined without knowing the masses

Because the only thing that matters in the conversion of PE to KE in the absence of non-conservative forces is the difference in height, both objects will traveling a the same speed at the end of the incline.

Answer C (10-15 seconds)

33) State the principle of conservation of mechanical energy for conservative forces. If only conservative forces do work, the total mechanical energy of a system neither increases nor decreases in any process. It stays constant—it is conserved.

34) A ball falls from the top of a building, through the air (air friction is present), to the ground below. How does the kinetic energy (K) just before striking the ground compare to the potential energy (U) at the top of the building?

A) K is equal to U.

B) K is greater than U.

C) K is less than U.

D) It is impossible to tell.

If friction was not present, all of the potential energy, U, would be converted to kinetic energy, K, during the fall. However, as air-resistance, a dissipative force, is present, some of the PE will be used to overcome this, and the amount of K present at the ground will be reduced by this amount. Answer C (10-15 seconds)