Think of a ball held up in the air. The higher it is, the more “stored” energy it has because it can fall. This stored energy is called gravitational potential energy (GPE).
Mathematically: \$E_g = m g h\$ where \$m\$ is mass, \$g\$ is the acceleration due to gravity (≈9.81 m s⁻² on Earth), and \$h\$ is height above the ground.
When that ball starts to fall, its stored energy turns into motion. The energy of motion is called kinetic energy (KE).
Formula: \$E_k = \dfrac{1}{2} m v^2\$ where \$v\$ is the speed of the object.
⚡️ Example: A 2 kg ball falling at 5 m s⁻¹ has \$E_k = \frac{1}{2} \times 2 \times 5^2 = 25\$ J.
In a closed system (no friction or air resistance), the total mechanical energy stays constant:
\$E{\text{total}} = Eg + E_k = \text{constant}\$
So, as a ball falls, \$Eg\$ decreases and \$Ek\$ increases, but their sum remains the same.
When you see a question about speed or height, decide whether you need \$Eg\$ or \$Ek\$. Write the formula in your scratch work and plug in the numbers.
📝 Quick check: If you’re given mass and speed, use \$Ek = \frac{1}{2} m v^2\$. If you’re given height, use \$Eg = m g h\$.
| Energy Type | Formula | Units |
|---|---|---|
| Gravitational Potential Energy | \$E_g = m g h\$ | J (joules) |
| Kinetic Energy | \$E_k = \dfrac{1}{2} m v^2\$ | J (joules) |