A runner of mass 60 kg moves at 5.0 m/s. What is the kinetic energy of the runner?
- Write the equation: Ek = ½ × m × v2.
- Square the speed: 5.02 = 25.
- Multiply: ½ × 60 × 25 = 30 × 25 = 750.
Answer: 750 J
Energy stores, energy changes and specific heat capacity
Physics · Energy. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
Energy is kept in stores: kinetic (moving objects), gravitational potential (raised objects), elastic potential (stretched or squashed objects), thermal, chemical and others. When a system changes, energy moves from one store to another. A ball thrown upwards loses kinetic energy and gains gravitational potential energy. A car that brakes moves energy from its kinetic store to the thermal store of the brakes and the surroundings.
You can calculate how much energy is in a store. The amount moved out of one store equals the amount moved into the others.
Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 °C.
Rules to remember
- kinetic energy = ½ × mass × speed2 (Ek = ½mv2), mass in kg, speed in m/s, energy in J
- gravitational potential energy = mass × gravitational field strength × height (Ep = mgh), with g = 9.8 N/kg
- elastic potential energy = ½ × spring constant × extension2 (Ee = ½ke2), k in N/m, e in m
- change in thermal energy = mass × specific heat capacity × temperature change (ΔE = mcΔθ), c in J/kg °C
- Doubling the speed makes the kinetic energy 4 times bigger, because speed is squared
- With no air resistance, Ep lost in a fall = Ek gained
- In the specific heat capacity practical, insulate the block so less energy escapes to the surroundings
Common mistake
Students forget to square the speed in Ek = ½mv2, or they square the whole of ½mv. Square the speed first, then multiply by the mass and by ½.
Worked example
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