1
Work
Another use of calculus is to calculate the amount of work done completing a task. For basic things, we have
the formula
Work = Force
×
Distance
Example 1.1.
Do an example in metric and Imperial.
But just like with our formulas for velocity and such, this only works if the force and the distance are
both constants. But in real life, they aren’t always. Often, the force can change as work is done. Let’s say
that at a given point
x
the force is
f
(
x
). How do we calculate the work done to move it from point
a
to
point
b
? Well, we do this like we’ve done everything else so far. We approximate.
First, we notice that even though the force can change over the interval, if we break it up into smaller
intervals, it might change as much. So first we break the interval down into subintervals [
x
i
, x
i
+1
] and look
at the work down over the smaller interval. The force will still change, but the formula
W
=
Fd
will be a
better approximation. The distance of each interval is Δ
x
. For the work done, pick any point in the interval,
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 Spring '08
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 Calculus, Formulas, Work, Continuous function, Inverse function, Inverses

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