What is meant by kinetic energy? State its unit. Describe how it is determined.
Definition
The energy a body has because of its motion. SI unit: joule (J).
Principle
A moving body can do work as it is brought to rest. So its kinetic energy equals the work done by the force that stops it.
Derivation
- A body of mass m moves with speed v. A steady opposing force F stops it over a distance S, so Ek = F × S ...(i)
- By Newton's second law, F = ma, where a is the deceleration.
- The speed falls uniformly from v to 0, so the average speed is v/2 and S = (v/2) × t.
- Putting these in (i): Ek = ma × (v/2) × t ...(ii)
- From the velocity-time graph, a = v/t. Putting this in (ii): Ek = m × (v/t) × (v/2) × t = ½mv².
Example
- Ek = ½ × 0.05 × 300².
Answer2250 J
Kinetic energy depends on mass and on the square of the speed.