What a learner can do afterwards
- Calculates the kinetic store of a moving object and the gravitational store of a raised one
- Equates the two stores to find a landing speed or a rise height
- Explains why doubling the speed makes the kinetic store four times larger
1 · Read
Movement carries kinetic energy for you: half times mass times speed squared, in joules. The squaring is the surprise: doubling the speed makes the store four times larger. A car at 60 mph holds four times the motion energy it has at 30.
Lifted objects hold gravitational potential: mass times g times height, with g = 10 N/kg. A 0.2 kg ball at 1.8 m stores 0.2 times 10 times 1.8 = 3.6 J. Only the height change matters, so pick a zero level and stay with it.
A falling ball swaps one store for the other, joule for joule, ignoring air resistance. The 0.2 kg ball lands with 3.6 J of kinetic energy: half times 0.2 times v squared = 3.6 gives v squared = 36, so v = 6 m/s. Set the loss equal to the gain and the mass cancels out.
Read the question for which swap it wants: falling asks for landing speed, launching asks for rise height. Write both stores first, then equate them. Speed is squared, so small speed slips cost big energy errors.
Half m v squared for motion, m g h for height, and falls swap one for the other.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.