Energy Revision

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1. For a body rising or falling, while gravity is the only force acting on it, the total mechanical energy (potential + kinetic) remains constant. That is, mechanical energy is conserved. This is assuming no air resistance or friction is opposing the motion

$E_p+E_k=E_m=\text{constant}$

$mgh+\frac{1}{2}m{v}^2=E_m=\text{k}=\text{constant}$

2. If a body is rising (e.g. arrow shot upwards), its potential energy increases while its kinetic energy decreases (i.e. its speed decreases). Kinetic energy is being transformed into potential energy

3. If a body is falling (e.g. arrow now falling down), its potential energy decreases while its kinetic energy increases (its speed increases). Potential energy is being transformed into kinetic energy

4. In many situations, height and speed are independent of the body’s mass