1. Work pg. 21
This is the second lesson on work and energy. It presents what physicists mean by “work”; how to calculate the work done in moving an object; and the meaning behind the SI unit for work and energy–the joule (abbreviated J).

2. Objectives Physics terms
Define the joule in terms of force and distance.
State the connection between work and energy.
Apply the work equation to calculate work, force, or distance.
joule (J)
work
For advanced students, it may be worth noting that there are other ways to express the joule in terms of more fundamental quantities:
mass, length (or distance), and time (just as a newton is a kg meter per squared second).
It also may bear noting that energy doesn’t HAVE to be stated in joules; kilowatt-hours and calories may be more familiar. But we need to stick with joules to use the SI unit system.

3. Equations
𝐹= 𝑊 𝑑
𝑑= 𝑊 𝐹
The work done on an object equals the force on the object multiplied by the distance the object moves in the direction of the force.
Reassure students that very soon we’ll understand why we need to say “in the direction of the force.”
Prompt them to think of situations in which they push on something, but it doesn’t move (or it moves, but not in the direction they pushed).

4. The meaning of work
Work is done by forces that change the motion of an object.
A force of 1 newton acting over 1 meter does one joule of physical work.
Discussion points: ask students to describe real-world situations that would require them to move something 1 meter with a force of 1 newton (roughly ¼ pound, or the approximate weight of a 100 g object). Allow some time for students to respond. (Possible example: lifting a stick of butter though a height of 1 m requires approximately 1 joule of work.)
Point out that the axis of motion doesn’t have to be horizontal, as shown here. Remind students that weight is a force!

5. Exploring the ideas Click this interactive calculator on page 257.
The interactive calculator that accompanies this lesson will help the students visualize how varying either force or distance affects work. Ask the students to find this interactive calculator button in their e-Book and click it.

6. Engaging with the concepts
The robot applies 100 N of force to the crate over a distance of 40 m.
How much work does it do?
Work
100 40
100 10
Tell the students to watch the behavior of the robot as well as the numbers in the boxes!

7. Engaging with the concepts
What if the force is reduced to 10 N, but the distance stays the same (40 m)?
How much work is done?
Work 10 40
100 10
Possible prompt: “This is one-tenth the previous force, but the same distance is involved. So what will happen to the number for work?” (The answer is 100 J, one-tenth the previous value for Work.)

8. Engaging with the concepts
Energy is needed to do work. Assume a robot has 2000 J of energy in its battery.
The robot pushes with a force of 25 N. How far can it push the crate?
Distance
2000 25
100 10
Remind students that work and energy are interchangeable in this context – the energy equals the amount of work that can be done (assuming none is wasted or lost to friction). Prompt students to identify the two givens and the one unknown implied by this question.

9. Many ways to do the same work
Discussion topic: “You’ve got to lift a heavy box and put it in the bed of your pickup truck. Which will be easier: lifting it straight up, or pushing it up a ramp?”
The work required to move the box from the ground to the truck is the same no matter what route is taken (neglecting friction!). Therefore we can trade a short distance for a long one and exert much smaller forces, reducing the odds of hurting our back or knees.
This idea—that there are many ways to perform the same work—is behind pulleys, wrenches, gears, and many other devices.

10. Calculating work
How much work do you do on a wall if you push on it with a force of 100 N?
Hint: “d” is the distance that the object moves in response to the force!

11. Calculating work
How much work do you do on a wall if you push on it with a force of 100 N?
Zero! The wall does not move.
The physics definition of work requires that the object moves some distance in the direction of the force.
No matter how hard you push the wall, you will do zero work—mechanically speaking—if the wall doesn’t move!
If the distance that the wall moves is d = 0 meters, then no work is done on the wall.

12. Zero work
But pushing with that much force is not easy! Why is the work zero?
Point out that in physics, work has a special definition. Work is not the same as effort.
One hundred newtons might also be the force that a waitress uses to hold up a huge tray of food …

13. Zero work
But pushing with that much force is not easy! Why is the work zero?
The physics concept of work is that it transfers energy that can potentially be regained. If the wall doesn’t move, it doesn’t gain or lose energy.
One hundred newtons might also be the force that a waitress uses to hold up a huge tray of food …
...and while it’s hard to believe it, she isn’t doing any work (in the vertical direction) on the tray unless she raises or lowers it while walking about!

14. Zero work
But pushing with that much force is not easy! Why is the work zero?
The physics concept of work is that it transfers energy that can potentially be regained. If the wall doesn’t move, it doesn’t gain or lose energy.
Work IS done by your muscles contracting. Your body uses energy to produce that force. You did work on yourself, but not on the wall.
That is, she isn’t doing any work ON THE TRAY while carrying it around at a fixed height (at a constant speed). That’s because she puts a force upward on the tray to keep it from falling, but the tray does not MOVE upward.

15. Which forces do work?
distance
This 10 kg crate is being pulled to the right with a rope, across a rough surface. Four forces act on it. What are they?
When multiple forces act on an object, it is important for students to be clear about WHICH force they are focusing on when they calculate work. Prompt the students to name these forces.

16. Which forces do work?
Normal force
Tension
distance
Friction
Weight
Any of these forces may or may not be doing work.
For each force acting on this crate, decide if it is doing work or not.
Prompt the students: “Two of these forces are doing zero work as the crate moves. Which ones do no work? Why?

17. Which forces do work?
Normal force
Tension
distance
Friction
Weight
The normal force and the weight do zero work on the crate because the crate does not move in the direction of these forces.
Prompt the students: “One of the forces does positive work and one does negative work. Why?”

18. Which forces do work?
Normal force
Tension
distance
Friction
Weight
The force of tension does positive work on the crate because the crate moves in the same direction of the force.
Prompt the students: “What about the force of friction? Do you think it does zero work, positive work, or negative work?”

19. Which forces do work?
Normal force
Tension
distance
Friction
Weight
The force of friction does negative work on the crate because the crate moves in the opposite direction of the force.
A force that does negative work acts against the motion.

20. Which forces do work?
Normal force
distance
Friction
Tension
Weight
From the force vectors, we see that the net force acts to the right.
So the net force does positive work on the crate.
The weight and normal force cancel out. The tension force shown is greater than friction in this example, so there IS a net force. Ask “what will this object do when positive net work is done on it?? Answer: it will speed up!

21. Test your knowledge
Two robots apply a combined horizontal force of 200 N to a 40 kg box, causing it to slide 5.0 meters. The force of friction between the floor and the box is 50 N.
How much work is done by each force acting on the box?
40 kg
Gravity:
Normal force:
Applied force:
Friction:
The answers appear on the next slide.

22. Test your knowledge
Two robots apply a combined horizontal force of 200 N to a 40 kg box, causing it to slide 5.0 meters. The force of friction between the floor and the box is 50 N.
How much work is done by each force acting on the box?
40 kg
Gravity: 0 joules
Normal force: 0 joules
Applied force: joules
Friction: joules

23. Why is work important?
All physical changes are due to changes in energy.

24. Why is work important?
When work is done, energy is transferred from one object to another, or transformed from one type of energy to another.
The amount of work done equals the amount of energy transformed.

25. Assessment
How is the joule composed of the units for force and distance?
What do each of the symbols mean in this equation: W = Fd?
joule = newton × meter
W = work (in joules)
F = force (in newtons)
d = distance (in meters)
A 75 N force acts on an object over a distance of 10 meters, in the same direction as the object moves. How much work is done?
Again, do all 75 newtons play a role in moving this object?
They do … so we can go ahead and plug the givens into the formula and calculate the unknown work.
W = Fd = 75 N × 10 m = 750 J

26. Assessment
What is the maximum distance through which a 30 N force can act while using 330 joules of energy?
A battery stores 9,000 J of energy. What is the largest force any device can exert continuously over 50 meters by using only the energy in the battery?
W = Fd d = W/F = 330 J / 30 N = 11 meters
W = Fd F = W/d = 9,000 J / 50 m = 180 N
Note that neither of these problems uses the term “work” – you have correctly equated work with a type of energy! This equivalence is at the heart of the work-energy theorem, which we’ll study in detail in a later lesson.

27. Assessment
Which of these statements correctly describes the relationship between work and energy?
Energy is the ability to do work.
Work must be done in order for energy to be transferred between objects.
Work must be done in order for energy to change from one form to another.
All of the above.
It takes energy to do work. Work must be done in order to transfer energy between objects or transform one type of energy into another.

28. Assessment
Which of these statements correctly describes the relationship between work and energy?
Energy is the ability to do work.
Work must be done in order for energy to be transferred between objects.
Work must be done in order for energy to change from one form to another.
All of the above.