The potential energy | POINT classical mechanics

When work is done on an object to change its position, this work is stored inside the object in the form of energy called potential energy.

Potential Energy: The energy that an object possesses as a result of its position or state.

Examples of Potential Energy:

1- Potential energy stored in a taut or compressed spring coil (elastic potential energy):
Contraction or Elongation of a Spring Its molecules gain a new position thus storing elastic potential energy. Then the spring does work until it gets rid of this energy in order to return to its resting position.

2- Potential energy stored in a taut rubber string (elastic potential energy):
Elongation of a Rubber String: Its molecules gain a new position and thus store elastic potential energy. Therefore, the taut rubber string moves when the force acting on it is removed until it gets rid of this energy in order to return to its resting position.

3- Potential energy stored in an object lifted from the Earth's surface (gravitational potential energy):
Gravitational potential energy is related to the position of objects relative to the Earth's surface relative to the gravitational field.

4- Potential energy stored in the electrons inside the battery(Chemical potential energy):
Electrons move when the battery is connected and the circuit is closed.

Deduction of the potential energy of the body:

When a body of mass m is lifted a vertical distance h above the surface of the Earth, the work done W is determined from this equation: W = Fh

where F is the force needed to lift the body upwards against gravity and is equal to its weight w:
F = w = mg
W = mgh

The work done is stored inside the body as potential energy: PE = mgh

*In the opposite figure, the work done to lift a body of mass m from position A to position B is:
W = mgh - mgh
W = mg(h - h) = mgΔh
W = Δ(PE)

Life Applications:

• When a box weighing 450N is lifted vertically upwards by a distance of 1m

The work done is: W = wh = 450 × 1 = 450J

This requires a force equal to the weight of the box: F = W/d = 450/1 = 450N

• And when the same box is lifted vertically upwards by a distance of 1m using an inclined plane of length 3m

The work done is: W = wh = 450×1 = 450J

This requires less force than the weight of the box, but it will require a greater displacement: F = W/d = 450/3 = 150N