Class 9 > Unit # 08:Energy Sources & Transfer of Energy > Potential Energy

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Potential Energy: Definition and Derivation

Q.3 Define Potential Energy and derive its formula.

Definition

"Energy stored by a body due to its position in a gravitational field is known as 'Gravitational Potential Energy'."

Formula

$\text{P.E} = mgh$

Fig: A body of mass $m$ raised to height $h$ against gravitational force ($W = mg$).

Derivation

Consider a body of mass $m$ placed at a height $h$ from the surface of the earth.

• Applied force required to lift it at constant speed: $F = \text{Weight} = W$
• Displacement of the body: $S = h$

According to the definition of work done:

$\text{Work done} = F \cdot S$

Substituting $F = W$ and $S = h$:

$\text{Work done} = W \cdot h$

Since weight $W = mg$:

$\text{Work done} = mgh$

As we know that the energy stored in a body when work is done on it against the gravitational field is known as Potential Energy, therefore:

$\text{P.E} = \text{Work done}$

$\text{P.E} = mgh$

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