Work

The Physics Hypertextbook™
© 1998-2008 by Glenn Elert -- A Work in Progress
All Rights Reserved -- Fair Use Encouraged

prev | up | next

Discussion

The target audience of this book is people with some amount of education. This isn't intended to be a children's book; and by children, I don't mean the opposite of adults. I consider adolescents (or teenagers, if you prefer) to be proto-adults. If this describes you, then you've had some formal science education (good, bad, or ugly). Somewhere along the line, you should have been introduced to the concept of energy. If you haven't, then stop reading this and go get yourself some education (or at least some life experience).

Those of you with a bit of formal education were probably given a lesson on energy at some point in your life. If so, then the chances are pretty good that you were given a definition of energy as "the ability to do work". If you were a good student or you just wanted to please your teacher, you probably heard this and said to yourself, "OK, energy is the ability to do work." If you were a bad student and you enjoyed ruining class time for as many people as you could, you ignored this and contemplated new ways to make your teacher's life more difficult than the average adult. But if you were a really good student with a desire to learn or a really bad student with a desire to point out your teacher's intellectual shortcomings, you asked the next logical question …

What is work?

Hopefully you were given the right answer, but chances are fifty-fifty you were shrugged off. Not because the right answer is so difficult to know, but rather because the right answer is so difficult to explain. Or at least, to explain in a way that can be grasped quickly. Primarily, I think, because the word work has an ordinary meaning outside of its technical meaning in physics.

Technically, work is the "force-displacement product" or the "force-displacement integral" for those of you who prefer calculus to faking it. I understand that for many of you this is a meaningless definition. So many words and so little said, no? Actually, quite the contrary. This definition is so compact it's like poetry. It says as much as it can in as few words as possible. It's so compact that explaining it in ordinary language makes the half dozen words of the technical definition expand to nearly a hundred words of so-called "natural language". Let me explain what work is though a series of mental images. Whenever an example is presented, remember that work is done whenever a force causes a displacement.

Imagine that a physics teacher is standing motionless before a class of students. Since he isn't exerting any forces that will displace anything outside of his body he isn't doing any work. Obviously. But doing this for any length of time will certainly drain him of energy just as if he had pushed papers across his desk all day (an example where a force does result in a displacement). Surely, you could now convince him that his definition of work must be wrong. Maybe a lesser teacher would cave under the pressure, but not a physics teacher.

Most certainly, a physics teacher or any other person standing is doing work, but the work done isn't easily visible. Inside the body the heart is pumping blood, the digestive system is grinding away on breakfast, receptors are driving molecules across cell membranes. We do work even as we sleep. Forces causing displacement are happening everywhere under our skins. The human body is a busy place.

If a system as a whole exerts a force on its surroundings and a displacement occurs, the work done is called external work. A physics teacher pushing papers across his desk is doing external work. A physics teacher standing motionless is not doing external work.

If a part of a system exerts a force on another part of the same system and a displacement occurs, the work done is called internal work. A physics teacher talking or marking papers or lying in a coma is doing internal work. A physics teacher doing anything -- or nothing for that matter -- is doing internal work. A physics teacher who is dead is not doing any work, internal or external. In mechanics, when we say work has been done we are usually referring to external work.

Now that we've decided that a teacher standing still isn't doing any work, let's imagine a teacher moving around and ask if work was done. Hmm, well anytime arms and legs get moving the situation is moderately complex. This makes it hard to identify what it is about the motion that involves work and what doesn't We need to simplify things just a little bit more. Give the teacher a book (How about a physics textbook?) and ask him to move the book around in a few simple ways. The question now is, "Did the teacher do any work on the book?" This is much narrower than asking if the teacher did any work, which means it's easier to answer and better suited to introducing the concept.

No work is done on a textbook when it is held at rest. Positive work is done on a textbook when it is raised vertically at a constant velocity. Positive work is also done on a textbook when it is raised diagonally at a constant velocity.
No work is done on a textbook when it is carried horizontally at a constant velocity. Negative work is done on a textbook when it is lowered diagonally at a constant velocity. Negative work is also done on a textbook when it is lowered vertically at a constant velocity.

 

Positive work is done when pushing a textbook to the right across a level tabletop at a constant velocity. Positive work is also done when pushing a textbook to the left across a level tabletop at a constant velocity

 

Equations for Work
using an average force W = F∥Δs
using a variable force W = ∫ F · dr

Thomas Young (1773-1829) was the first to use this formula. ← Is this right?

Units:

Sign conventions:

The work energy theorem

W = ΔE

Summary

Equations for Work
using an average force W = F∥Δs
using a variable force W = ∫ F · dr

Problems

practice

  1. Write something.
    • Answer it.
  2. The graph below shows applied force vs. distance for a light plane.
     
    graph
     
    1. How much work is done by the engine during each segment of the journey?
    2. How much total work was done during the flight?
    • Answer it.
  3. Write something different.
    • Answer it.
  4. Write something completely different.
    • Answer it.

numerical

  1. problems

Resources

prev | up | next

Another quality webpage by

Glenn Elert		 eglobe logo home | contact

bent | chaos | eworld | facts | physics