Gravitational Potential Energy & Kinetic Energy
Derivation of formulas for conservation of energy
- Assume the energy is all gravitational or kinetic energy.
We know vf – vi = g(tf – ti) and hi – hf = ½ (vf + vi)(tf – ti)
Thus hi – hf = ½ (vf + vi)(vf – vi)/g = (vf2 – vi2)/2g And mg(hi – hf) = ½ m (vf2 – vi2)
Then E = mghi + ½ m vi2 = mghf + ½ m vf2