Conversion between potential energy and kinetic energy

Mechanical energy

A moving object possesses kinetic energy Ec = (1/2) * m * v^2, in addition to its gravitational potential energy Epp. The sum of the two is mechanical energy: Em = Ec + Epp.

Conservation of mechanical energy

In the absence of friction, mechanical energy is conserved during motion: Em(initial) = Em(final). In other words, any loss of potential energy is entirely converted into kinetic energy, and vice versa.

Example: free fall

A ball of mass m = 0.1 kg is dropped from a height h = 5 m with no initial velocity (g = 10 N/kg, air resistance neglected).

• Initially: Ec = 0, Epp = m * g * h = 0.1 * 10 * 5 = 5 J, so Em = 5 J.
• Upon reaching the ground (reference point h = 0): Epp = 0, so all the mechanical energy has been converted into kinetic energy: Ec = 5 J.

From this, we can work out the velocity on impact: (1/2) * m * v² = 5, so v² = 100, v = 10 m/s.

Summary table

Time	Ec (J)	Epp (J)	Em (J)
Start	0	5	5
Arrival	5	0	5

Common pitfall

This conservation holds true only in the absence of friction. With friction (air, ground), part of the mechanical energy is converted into heat and Em(final) < Em(initial).