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To really understand Work you need calculus

The equation W=Fxcos(theta) is ok if you have a constant force. But work is really one of those things that requires calculus to understand. If a force varies based on location, that affects how much work was done. So Newton figured out that by finding the area under the curve on a (x,F) graph, you can deal with such non-constant forces. This is called taking the integral of F with respect to x, and it is written mathematically as shown on the bottom left.

 

Getting areas under curves is hard. That's why Newton, Leibniz, (and apparently Archimedes in ancient Greece 1800 years ago, but we lost his book until recently) invented integral calculus to do it. In AP 1, you won't be able to get the area under the parabola shown at bottom center. But you will be able to get the area under the trapezoid shown at bottom right, simply by using geometry (I'd break it into 3 pieces to do it.) If you're given a non constant force, you'll know because there'll be a graph (or they ask you to plot one.) Get the area under the curve and you've got work. If they tell you its a constant force, feel free to use W=Fxcos(theta). Note that this COMES from the area under a horizontal curve.

 

Obviously in a calculus based physics class we could get the area under both curves.

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Uploaded on January 22, 2016
Taken on January 21, 2016