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The Physics
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Opus in profectus
Work
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Discussion
what is work?
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 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 should have then 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 difficult to explain in a way that can be grasped quickly. I think this is mostly due to the fact that the word work has two meanings: the ordinary one of everyday life and the technical one of physics.
Technically, work is the force-displacement product (for those of you who prefer algebra)
W = F̅Δs cos θ
or the force-displacement path integral (for those of you who prefer calculus).
W = ⌠
⌡ F · ds
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 being 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 any significant external work.
