7.5 | Work


Definition of Work Done by a Constant Force
If an object is moved a distance \(D\) in the direction of an applied constant force \(F\), then the work \(W\) done by the force is defined as \(W = FD\).
Definition of Work Done by a Variable Force
If an object is moved along a striaght line by a continuously varying force \(F(x)\), then the work \(W\) done by the force as the object is moved from \(x = a\) to \(x = b\) is given by
$$
\begin{aligned}
W &= \lim_{||\Delta|| \rightarrow 0} \sum_{j = 1}^n \Delta W_i
& = \int_a^b F(x) \; dx.
\end{aligned}
$$
Hooke’s Law
The force \(F\) required to compress or stretch a spring (within its elastic limit) is proportional to the distance \(d\) that the spring is compressed or stretched from its original length. That is,
$$
F = kd.
$$

E 7.5 Exercises