# Work - Work This is the final application of integral that...

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Work This is the final application of integral that we’ll be looking at in this course. In this section we will be looking at the amount of work that is done by a force in moving an object. In a first course in Physics you typically look at the work that a constant force, F , does when moving an object over a distance of d . In these cases the work is, However, most forces are not constant and will depend upon where exactly the force is acting. So, let’s suppose that the force at any x is given by F(x) . Then the work done by the force in moving an object from to is given by, To see a justification of this formula see the Proof of Various Integral Properties section of the Extras chapter. Notice that if the force is *constant we get the correct formula for a constant force. where b-a is simply the distance moved, or d . So, let’s take a look at a couple of examples of non-constant forces. Example 1 A spring has a natural length of 20 cm. A 40 N force is required to stretch (and hold the spring) to a length of 30 cm. How much work is done in stretching the spring from 35 cm to 38 cm?

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Solution This example will require Hooke’s Law to determine the force. Hooke’s Law tells us that the
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Work - Work This is the final application of integral that...

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