recall and use EK = 21mv2
Gravitational Potential Energy & Kinetic Energy
What is Gravitational Potential Energy?
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.
What is Kinetic Energy?
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.
Energy Conservation
In a closed system (no friction or air resistance), the total mechanical energy stays constant:
$$E_{\text{total}} = E_g + E_k = \text{constant}$$So, as a ball falls, $E_g$ decreases and $E_k$ increases, but their sum remains the same.
Exam Tip: Remember the Formula
When you see a question about speed or height, decide whether you need $E_g$ or $E_k$. Write the formula in your scratch work and plug in the numbers.
📝 Quick check: If you’re given mass and speed, use $E_k = \frac{1}{2} m v^2$. If you’re given height, use $E_g = m g h$.
Step‑by‑Step Example
- Identify what energy type the problem asks for.
- Write down the relevant formula.
- Insert the given values (remember units).
- Calculate the result.
- Check units: J = kg m² s⁻².
Quick Formula Summary (Table)
| 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) |
Exam Tip: Check Your Work
- Verify that you used the correct formula.
- Make sure all units are consistent (kg, m, s).
- Remember that speed $v$ is always positive in kinetic energy.
- When in doubt, double‑check the sign of $h$ (height above the reference point).
Revision
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