Work done by a constant force F on a body is given by an expression as the following
, where‘d’ is the displacement of the body and
is the angle between the force and displacement.
But in practical situations, a body may be acted upon by a force which may not be constant and is a variable force
A variable force
is a force whose magnitude or direction or both vary during the displacement of a body on which it acts.
As the spring oscillates between the extreme positions O and A the restoring force on it keeps changing with the displacement from the mean position. This is a variable force on the spring.
Work done by variable forces:
Let us suppose that a body moves along the direction of variable force acting on it.
We then plot a graph of force (F) versus displacement (x), which helps calculate the varying force with the displacement as shown.
The work done by the variable force can be found by calculating the area under the graph by dividing the total displacements into ‘n’ is