Work, power, kinetic and potential energy, conservation, and how heat is measured.
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Work is done when a force moves its point of application in the direction of the force: W = F × s, measured in joule (J). If there is no displacement, no work is done, so a person pushing a wall does no work in the physics sense. Power is the rate of doing work: P = W ÷ t, in watt (W); 1 W = 1 J/s, and 746 W = 1 horse power.
A force of 50 N moves a body 4 m. Find the work done.
W = 50 × 4 = 200 J.
That work is done in 10 s. Find the power.
P = 200 ÷ 10 = 20 W.
A coolie carries a load while walking on level ground. Is work done against gravity?
No: the force (up) is perpendicular to the displacement (horizontal), so the work against gravity is zero.
Energy is the capacity to do work, also in joules. Kinetic energy KE = ½mv² (due to motion); gravitational potential energy PE = mgh (due to height). Energy cannot be created or destroyed; it only changes form. For a freely falling body, PE + KE stays constant, so the gain in KE equals the loss in PE. Common transformations: a dynamo turns motion into electricity; a bulb turns electricity into light and heat.
Find the PE of a 2 kg body at 5 m (g = 10).
PE = 2 × 10 × 5 = 100 J.
It falls to the ground. Find its speed on landing.
½mv² = mgh gives v = √(2gh) = √100 = 10 m/s, so KE = 100 J.
Find the KE of a 1000 kg car at 20 m/s.
½ × 1000 × 20² = 200000 J.
Heat is energy that flows from a hotter to a colder body; temperature tells how hot a body is. Heat needed: Q = mcΔT, where c is specific heat capacity (water 4200 J/kg °C, which is high). Calorimetry: heat lost by the hot body = heat gained by the cold one. Latent heat is the heat taken to change state without a change of temperature: for ice, 336,000 J/kg.
Heat needed to warm 0.5 kg of water from 20 °C to 100 °C (4200 J/kg °C).
Q = 0.5 × 4200 × 80 = 168,000 J.
Heat needed to melt 0.1 kg of ice at 0 °C (L = 336,000 J/kg).
Q = 0.1 × 336000 = 33,600 J.
200 g water at 80 °C is mixed with 300 g at 30 °C. Find the final temperature.
0.2 × (80 − T) = 0.3 × (T − 30) gives T = 50 °C.
1. Define work and its SI unit.
2. A man lifts a 10 kg load through 2 m (g = 10). Find the work done.
3. Define power. What is its unit?
4. Find the power of a motor that does 5000 J in 10 s.
5. Write the formulae for KE and PE.
6. State the law of conservation of energy.
7. Find the KE of a 2 kg body at 10 m/s.
8. Why is water used as a coolant?
9. Heat needed to warm 2 kg of water by 10 °C.
10. What is latent heat?