The ball has mass m = 1 kg. Its gravitational potential energy relative to the floor is Ep = mgh, and its kinetic energy is Ek = ½m|v|². While airborne, no energy leaves the system: Ep and Ek trade places continuously and Ep + Ek stays constant, exactly the first law ΔE = Q + W with Q = W = 0.
Ep = m·g·h Ek = ½·m·v²
Impact: v_after = e · v_before (normal component)
v_after = (1-μ) · v_before (tangential component)
Heat generated per bounce:
ΔQ = ½m·v_before² − ½m·v_after²
Every time the ball hits the floor, the restitution coefficient e (0<e<1) shrinks the rebound speed along the impact normal, and the friction coefficient μ shaves off part of the sideways speed. Both losses are real: the kinetic energy that vanishes from the mechanical budget is added, bounce by bounce, to a running heat counter Q — representing the sound, deformation and micro-friction that actually warm the ball and floor on contact.
- Drop height / gravity — set the initial potential energy E₀ = mgh₀, the total energy budget for the whole run.
- Restitution e — how much vertical kinetic energy survives each bounce; e → 1 is a perfectly elastic (bouncy) collision, e → 0 is nearly dead.
- Floor friction μ — how much horizontal speed is scrubbed off on contact, feeding the same heat counter.
The energy bar always sums to 100% of E₀: watch the red "heat" segment grow and the ball's bounces get shorter and lower — mechanical energy is not disappearing, it is becoming heat, exactly as the article's ΔE = Q + W predicts.