Force, work, power and energy

Work Done by a Constant Force
A wooden block is kept on a table. When a force of magnitude F acts on the block, it gets displaced through a distance S in the direction of the applied force, as shown in the given figure.



The magnitude of work done is given by the product of force (F) and displacement (S).

Let W be the work done on the block.

\ Work = Force × Displacement




Work has magnitude only. It has no direction.

Unit of Work

To obtain the unit of work, we substitute the SI units of force, i.e. N, and distance, i.e. m, in the equation of work.

W = N × m

= Nm

Hence, the unit of work is Nm. In the honour of physicist James P. Joule, the SI unit of work is written as Joule (J).

Hence, 1 J = 1 Nm

1 Joule is defined as the amount of work done by a unit force such that it displaces an object by a distance of 1 m.

Work done against gravity

When force is applied on an object in order to lift it above the ground, it is said that work is done against the force of gravity.

Assume that a constant force of magnitude F is applied on a block of mass m to lift it to a height h above the ground.

In this case, the work done by the force against gravity is given by the product of the weight of the block and the height through which it is lifted above the ground.

Work done = Weight × Height

W = mg × h

W = mgh

Where, g is acceleration due to gravity.




Negative work

A soccer player moves backward while stopping a fast moving football. To move backward, he applies a force in the forward direction. Is the direction of displacement and the direction of applied force the same?

Here, the directions of displacement (S) and applied force (F) are exactly opposite to each other. Hence, we can say that the work done by the force is negative. This case can be described with the help of the following figures.





Hence, the work done by force F is given by

W = F × (−S) or W = (−F) × S

In both the cases, the work done will be negative.

Zero Work

When a body moves through a distance at right angle to the direction of force, the work done by the force on the body is zero.



A book kept on a table moves from point A to point B through a distance S. In this case, the work done on the book by gravitational force is zero because the force is acting at right angle to the displacement of the book.