# 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,
$$F = kd.$$