Physics · Grades 8–11
Kinetic and gravitational potential energy
Check squared speed, vertical height and energy reference levels.
Learn the idea
Kinetic energy
Translational kinetic energy is one half mass times speed squared in the classical model.
Gravitational change
Near a surface with constant g, raising a mass by vertical height h increases potential energy by mgh.
Reference level
A potential-energy value depends on the chosen zero. Differences remain physically useful.
Conversion
Energy may move between kinetic and potential stores while some transfers go to the surroundings.
Worked examples
A 2 kg object moves at 5 m/s. Find kinetic energy.
0.5 × 2 × 5² = 25 J.
25 J
A 3 kg object rises 4 m where g = 10 N/kg. Find gravitational potential-energy increase.
3 × 10 × 4 = 120 J.
120 J
Check your understanding
At fixed mass, doubling speed multiplies kinetic energy by what?
- 4
- 8
- 2
Why must the vertical height, not the length of a ramp, be used in mgh?
A 4 kg object has 72 J kinetic energy. Find its speed.
Answers and marking notes
Answers and marking notes
- 4
The squared speed changes by a factor of four.
- Gravitational potential change depends on vertical position change in this model.
Credit vertical displacement and the constant-field model.
- 6 m/s
v² = 2E/m = 144/4 = 36, so speed is 6 m/s.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.