Work

Work done by the force acting on a body is defined as the product of force and displacement of the body in the direction of the force. It is a scalar quantity. Force acting on the body must produce a displacement for the work is to be done by the force. Thus for the work to be done, the following two conditions must be fulfilled:

• A force must be applied, and
• The applied force must produce a displacement in any direction except perpendicular to the direction of the force.

Mathematically,

Work= Force × Displacement (in the direction of the force)

i.e. W= F.d ................(i)

The SI unit of force is newton (N) and that of displacement is a metre (m). So, the unit of work is Newton metre (Nm), which is Joule (J).

Thus, one joule of work is said to be done when one Newton force displaces a body through one metre in its own direction.

Work against friction

Force is to be applied to move, roll, or drag a body over a surface of another body. Example: If an object is dragged to a certain distance (d).

Activity: To demonstrate work against friction.

At first, placed the brick over the surface of the table. Now, pulled the brick from initial position to final position as shown in the figure.It moves by a displacement's'. Here, force is applied against the frictional force between the surface of the brick and the table to set the brick in motion. Here, the work is done against friction.

Work against gravity

Force is applied to lift a body against the force of gravity. Example: If an object is lifted to a certain height (h).

Activity: To demonstrate the work against gravity.

Take a body of mass 'm' and a spring balance to lift the body. Then lift the body of mass 'm' upto the certain height 'h'. The pointer of the spring balance gives the force applied 'F' against the gravity. Here, the work is done against the gravity and it is given by the product of the force 'F' and height 'H'.

Measurement of work

On the basis of the direction of motion of a body and the direction of force applied, the way of calculation of work done is determined.

1. When a body moves in the direction of force applied:
   In the above conditions (work against friction and work against gravity) the direction of motion of the body and the direction are the same.
   Work done (W) = Force (F) × Displacement (d)
2. When a body moves oblique to the direction of force applied:
   Consider a body is pulled on an inclined plane AC. The direction of force applied on it is in AC direction but the motion direction is AB.
   In This condition,
   cosθ = \(\frac{Base}{Hypotenuse}\) = \(\frac{AB}{AC}\)
   AB = AC Cosθ
   ∴W= F Cosθ× D