Overview of Work & Work by Variable Force

Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After completing this lesson, you will be able to explain what work is, and how to calculate work using the equation, and a force-distance graph. A short quiz will follow.

What Is Work?

One day you're standing in a library when the librarian asks for your help. 'Can you hold these books for me?' she asks. Being the helpful person that you are, of course you say yes. The librarian puts a huge, heavy stack of books in your arms, and says she'll be right back. Ten minutes later she's still not back, and your arms are really aching.

When you're holding the books like that, are you doing work? It sure seems like it - you're getting tired and can hardly hold the books by the end of it. But did you know that in a physics sense, you're doing no work at all?

Work in physics is a force applied over a distance. To do work you have to apply a force, and cause an object to move a distance in the direction of that force. The equation for work is work equals force times the distance moved in the direction of that force:

Work Equation
Work Equation

So if you're just holding the books, you're not doing work in this sense - you're not doing work ON the books.

But work is also an energy transfer. Whenever energy is being transferred, work is being done somewhere. Since you're getting tired, using the energy in the food you ate, work must still be being done deep inside your body. It's just that strictly speaking your hands are not doing work on the books, because the books aren't moving a distance.

Force-Distance Graphs

Aside from using the equation, another way to figure out the work being done is to use a force-distance graph. Since work is force multiplied by distance, that means that the area under the force-distance graph gives you the work done.

If the force is constant, this means just finding the area of a rectangle.

Force-Distance Graph
Force-Distance Graph

Work Done by a Variable Force

But sometimes the force isn't constant. The truth is that the equation work equals force times distance only applies when the force is constant. When the force is variable you have to use the force-distance graph. Luckily, finding the area under a graph with a variable force is easy - you just have to find the area of a triangle.

Variable Force Graph
Variable Force Graph

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