Work is the way of transferring energy from one object to another. Work is said to be done when a body covers a certain distance in the direction of the applied force. It is represented by the symbol W and its SI unit is Joule.

Work (W) = Force (F) × displacement (s)

The energy stored in an object because of its position in the gravitational field is called gravitational potential energy. It is directly proportional to the mass of the object, acceleration of freefall as well as change in height.

ΔE_P = mgΔh
Here,

ΔE_P is the change in gravitational potential energy

m is the mass of the object

g is the acceleration of free fall

Δh is the change in height of the object

Proof:

Here,

Force applied on the block (F) = Weight of block (W) = mg

Displacement covered by the block (s) = Δh

Now, the work done on the block, w = F × s

= mg × Δh

= mgΔh

This work done on the block is stored on the block itself in the form of gravitational potential energy. Thus,

Gravitational potential energy (G.P.E.) = mgΔh

The energy possessed by an object in motion is its kinetic energy. It is directly proportional to the mass as well as to the square of the velocity of the object.

ΔE_K = $\frac{1}{2}$m(Δv)²

Here,

ΔE_K is the change in kinetic energy

m is the mass of the object

Δv is the change in velocity of the object

Proof:

Here,

Force applied on the block, F = ma

To find the displacement covered, let’s use the kinematic equation as shown below:
v² = u² + 2as
=> 2as = v² – u²
=> 2as = Δv²

where Δv is the change in velocity of the block.

s = $\frac{\Delta v^{2}}{2a}$

Now, the work done in moving the block, w = F × s

= ma × $\frac{\Delta v^{2}}{2a}$

= $\frac{1}{2}$mΔv²

This work done on the block in moving it is translated in the form of kinetic energy. Hence,

Kinetic energy, K.E. = $\frac{1}{2}$mΔv²

5.01 - Work, GPE and KE

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