Work Done by Applied Constant Force and Variable Force

Physical work is said to be done when applied force is able to produce displacement in the body. If the applied force is not sufficient to overcome the inertia and friction, work is not done.Physical work is different from the work that we use some times in daily life. For example, we can say that i have read a physics book for the entire day and done a lot of work.This is not the mechanical work rather a work with brain. Here in physics, we are actually talking about the physical work but not psychological work.

How much is work is done depends on the size of the force applied and the displacement caused in the body by that force.Suppose, we are applying lot of force on a heavy body but the body is not going any where, then as per physics, we have not done any work.

If the applied force produces some displacement in the body, then we shall see weather entire applied force is the cause of the displacement or a portion of it.We shall consider only the force or component of force which is the cause of the motion.

If we apply a large force on a vertical wall and it has not moved.Then the force applied by you has not produced any displacement and hence work done by us zero.

If we apply a horizontal force on the body and the body moves in the same direction of applied force, then work done is the product of applied force and the displacement of the body and here we are neglecting the frictional force role.

If the body is on a smooth horizontal surface and a force is applied making an angle with the horizontal, then body gets displaced in the horizontal direction. It is very clear that the entire force is not acting horizontally. We can resolve the force into components using vectors resolution.

We can understand that horizontal component of force is in the direction of the displacement of the body and some work is done in that case.

The vertical component of force is trying to lift the body in up ward direction but the body has no vertical displacement. Hence no work is done in vertical direction by the vertical component of force. Therefore work done in this case is only product of horizontal component of force and displacement. Here displacement is the shortest distance between initial and final positions in a specified direction.

We can define work done as the product of component of force along the direction of displacement and displacement.Both of them are vectors but when we multiply them we get a scalar. This kind of product of two vectors is called scalar product or dot product.

So we can define work done as the dot product of force and displacement.