01 Key Concepts
Kinetic Energy (KE)
The energy of motion: KE = (1/2)*m*v^2.
Potential Energy (PE)
Stored energy due to position or configuration; gravitational PE = m*g*h, where h is height above a reference point.
Conservation of Energy
In a system with no external losses (like friction), total mechanical energy (KE + PE) stays constant, even as it converts between forms.
Energy Transformations
Energy constantly converts between forms -- a falling object converts PE into KE; a pendulum swings between KE and PE at each end and midpoint of its swing.
Units of Energy
Measured in joules (J), the same unit as work, since work is the transfer of energy.
02 Key Formulas
- KE = (1/2)*m*v^2
- PE = m*g*h
- Total mechanical energy = KE + PE (conserved without friction)
03 Solved Examples
Example 1 Find the kinetic energy of a 4 kg object moving at 5 m/s.
- Apply KE = (1/2)*m*v^2 = 0.5*4*5^2 = 0.5*4*25.
- = 2*25.
Answer: 50 J
Example 2 Find the potential energy of a 3 kg object held 10m above the ground (g=10 m/s^2).
- Apply PE = m*g*h = 3*10*10.
Answer: 300 J
Example 3 A 2 kg ball is dropped from a height of 5m (g=10). Use energy conservation to find its speed just before hitting the ground.
- Initial PE converts entirely to KE at the bottom: PE = KE.
- m*g*h = (1/2)*m*v^2. Mass cancels: g*h = 0.5*v^2.
- 10*5 = 0.5*v^2, so 50 = 0.5*v^2, v^2=100.
Answer: v = 10 m/s
04 Practice Questions
1Find KE of a 2 kg object at 10 m/s.
100 J
2Find PE of a 5 kg object at height 4m (g=10).
200 J
3A ball is dropped from 20m (g=10). Find its speed at the bottom using energy conservation.
v^2=2*10*20=400, v=20 m/s
4What is the SI unit of energy?
The joule (J)
5In a frictionless system, what stays constant?
Total mechanical energy (KE+PE)
📄 Energy — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.