# Work Done

## Work Done

When force is exerted on an object and object is displaced, work is said to be done. When we apply some force on a block then the body moves with some acceleration or speed increases or decreases depending on the direction of the force applied. As the speed increases or decreases, the kinetic energy of the system changes and we know that energy can neither be created nor be destroyed so the energy must be getting transformed into another form, here it is termed as work done. When the work done is negative, energy is decreases and when the work done is positive, energy is increases.

Derivation of Work Done:

We know that:

Work done (W) = Change in kinetic energy (Δ K.E)

W = ½ mv² – ½ mu²

W = ½ m (v² – u²)

W = ½ m (2as) [∵ v² – u² = 2as]

W = m x a x s

W = (ma) s

W = F s [∵ F = ma]

∴ Work Done (W) = Force (F) x Displacement (s).

The SI unit of work is joule and is denoted as ‘J’, The 1 joule of work done is equal to 1N x 1 m.

One joule = N.m.

Direction of Force Positive and Negative Work:

When force is applied in the direction of displacement, the work done is considered as positive.

i.e. Work Done (W) = F x s.

When force is applied in opposite direction of displacement, the work done is considered as negative.

i.e. Work Done (W) = – F x s.

For example, when an engine works to accelerate or move the vehicle, the work done is positive. But when brakes are applied to stop a moving vehicle, i.e. the work done against the direction of displacement of the vehicle, the work done is considered as negative.

Conditions:

1. If force (F) = 0.

∴ Work done (W) = 0 x s = 0.

2. If displacement (s) = 0.

∴ Work done (W) = F x 0 = 0.

Thus, there are two conditions for work is considered done.

• Force should act on the object.
• Object must be displaced.

In the absence of any one of the above two conditions, work done will be equal to zero, that is work is not considered as done.