kinetic and potential energy

Kinetic Energy

Objects in motion possess energy and can do work. This energy is called Kinetic Energy.
F = ma.
Also W = F.s
⇒ From the 2nd equation of motion v²−u²=2as,
⇒ we get s = v²−u² / 2a

Substituting equation for work done by a moving body,
⇒ we get W =m.a * v²−u² / 2a

Or

⇒ Kinetic Energy = K.E= 1/2 mv² (taking initial velocity u=0)

When two identical bodies are in motion, the body with a higher velocity has more K.E.

Work-energy theorem

The work-energy theorem states that the net work done by a moving body can be calculated by finding the change in KE.

⇒ W_net = KE_final− KE_initial

⇒ W_net = 1/2 mv²

Factors affecting kinetic energy

• Mass
• Velocity
• Momentum

Potential Energy

Energy can get stored in an object when work is done on it.

For example, stretching a rubber string. The energy that is possessed by a body by virtue of its configuration or change in position is known as Potential Energy.

The potential energy of an object at a height.
When an object is raised to a certain height, work is done against gravity to change its position. This energy is stored as Potential Energy.

⇒W = F.s

⇒F = ma
In the case of increasing the height, F = mg
Therefore, W (P.E) = mgh
⇒ ΔPE = mg(h_final - h_{initial )}