Conservation of Energy and Power: Quick Revision

A brief note on Conservation of Energy and Power. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• Energy is never made or destroyed; it only changes form.
• In a fall with no air, the potential energy lost becomes kinetic energy: $v = \sqrt{2gh}$, whatever the mass.
• In real life some energy becomes heat and sound, but the total is still the same.
• Power is the rate of doing work: $P = \dfrac{W}{t}$, in watts ($1\ \text{W} = 1\ \text{J/s}$).
• Electricity is sold in kilowatt hours: $1\ \text{kWh} = 3.6 \times 10^{6}\ \text{J}$, one unit on the bill.

The facts at a glance

A worked example

A pump lifts $520\ \text{kg}$ of water $10\ \text{m}$ in $2$ minutes, twice a day, for $30$ days. One unit costs ₹$6$.

1. Work each time. $520\ \text{kg} \times 9.8\ \text{m/s}^2 \times 10\ \text{m} = 50\,960\ \text{J}$.
2. Power. $\dfrac{50\,960\ \text{J}}{120\ \text{s}} = 425\ \text{W}$.
3. Energy in a month. $60$ runs $\times 50\,960\ \text{J} = 3.06 \times 10^{6}\ \text{J} = 0.85\ \text{kWh}$, costing about ₹$5.10$ (if the pump wasted nothing).

Practice with new numbers

A program to try

The program checks that the total energy stays the same as a stone falls, then finds a power.

Mistakes to avoid

• 'The energy is used up.' It changes form, often into heat.
• Using minutes with watts. Change the time to seconds for joules, or to hours for kWh.
• 'More power means more work.' It means the same work in less time.
• Calling a kWh a unit of power. It is a unit of energy.

Check yourself

1. A stone is dropped from $11.25\ \text{m}$. How fast is it moving when it lands?

2. A crane does $36\,000\ \text{J}$ of work in $45\ \text{s}$. What is its power?

3. How many units does a $500\ \text{W}$ heater use in $6$ hours?

4. A pendulum slowly stops swinging. Where did its energy go?