Constant and Varying Force

In Physics, the word "work" takes on a different meaning from the one commonly used. Work is defined as a force applied through a distance. Work done on an object by a constant force is the product of the object's displacement and the force acting parallel to the displacement. In mathematical terms

W = F x d ------------ ( 1 )

The SI unit for work is the joule (J). One joule is the product of one Newton and one meter, or a joule is a one-Newton force applied through one meter, J = Nm.

While Equation 1 is valid for forces applied parallel to the direction of travel of an object, non-parallel forces present a problem. To calculate the work done by a force applied in a direction that is not parallel to an object's displacement, we must calculate the component of the force applied in the parallel direction. To do this, we can use Equation 2:

W = F x s x cos θ -----------( 2 )

where is the angle between the directions of the force and the net displacement. The net work done on an object is the algebraic sum of the work done by each acting force. Work Done By a Varying Force As work is the product of force and displacement, it can be represented as the area under a graph of force as a function of displacement. In Figure 3.1, the shaded region represents the work done on an object that undergoes a constant force. Thus, the work done (area of the shaded region) can be calculated by multiplying displacement (base) by force (height).

This graphical method of calculating work is also useful in estimating the work that results from a varying force. The force applied to the object in Figure 3.2 changes over time.