Kinetic and Potential Energy: Quick Revision

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

The big ideas

• Energy is the ability to do work, measured in joules. It has many forms and changes from one to another.
• Kinetic energy is the energy of motion: $KE = \tfrac{1}{2}mv^2$.
• The speed is squared: twice the speed gives four times the kinetic energy.
• The work done on an object equals the change in its kinetic energy.
• Potential energy is stored energy of position or shape: $PE = mgh$ for a height $h$.
• $h$ is measured from a level we choose; the change in $PE$ does not depend on that choice.

The facts at a glance

A worked example

A $70\ \text{kg}$ skier stands at the top of a slope $15\ \text{m}$ high, then reaches the bottom moving at $12\ \text{m/s}$.

1. At the top. $PE = 70\ \text{kg} \times 9.8\ \text{m/s}^2 \times 15\ \text{m} = 10\,290\ \text{J}$, measured from the bottom.
2. At the bottom. $KE = \tfrac{1}{2} \times 70\ \text{kg} \times (12\ \text{m/s})^2 = 5040\ \text{J}$.
3. So about half the potential energy became kinetic energy; the rest went into heat from the snow and the air.

Practice with new numbers

A program to try

The program finds the kinetic and potential energy of a stone at several points.

Mistakes to avoid

• Forgetting the half in $\tfrac{1}{2}mv^2$, or forgetting to square the speed.
• Thinking only moving things have energy. A stone on a roof has potential energy.
• Using km/h in $\tfrac{1}{2}mv^2$. Change to m/s first: divide by $3.6$.
• Arguing about the 'right' reference level. Any level works; only changes of $PE$ matter.

Check yourself

1. Find the kinetic energy of a $0.2\ \text{kg}$ ball moving at $15\ \text{m/s}$.

2. A car's speed is halved. What happens to its kinetic energy?

3. Find the potential energy of a $5\ \text{kg}$ flower pot on a balcony $6\ \text{m}$ up.

4. What kind of energy is stored in a stretched catapult?