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Double the speed — four times more Ek to scrub off. At the top of a throw the same amount sits in Ep.
Part 8 (last) of Physics without mysteries. Map: kinematics from scratch.
Kinetic energy Ek = ½mv² grows with the square of speed. A ~1400 kg car at ~14 m/s (about 50 km/h) is on the order of 140 kJ — that much must be scrubbed by brakes or deformation. That is why stopping distance hurts more than “only twice as fast”.
Gravitational potential energy Ep = mgh tracks height change. In a vertical throw Ek vanishes at the apex and Ep = mgH_max; on the way down it becomes Ek again. Work W = F·s is the bridge: a constant force along a path changes mechanical energy.
Leibniz spoke of “living force”; the nineteenth century closed the energy language that crash tests and homework balance sheets still use. On Calcboxer three calculators keep separate intents: Ek, Ep and work.
| Goal | Formula | When |
|---|---|---|
| Motion energy | Ek = ½mv² | Car, ball, throw launch |
| Height energy | Ep = mgh | Throw apex, lifting |
| Constant-force work | W = F·s | Brakes, dragging a crate |
| Balance | ΔEk + ΔEp = W′ | When you join motion and forces |
A car of mass m = 1400 kg travels at v = 13.9 m/s (about 50 km/h). Find the kinetic energy Ek.
Steps
Answer: Ek ≈ 1.35·10⁵ J
A body of mass m = 2 kg is raised to h = 5 m. Take g = 9.81 m/s². Find Ep.
Steps
Answer: Ep = 98.1 J
