Galileo's Falling Bodies — Race a Ball Down a Ramp

Aristotle said heavier objects fall faster; around 1600 Galileo said they fall together. Test it: hold a heavy ball and a light one at the same height and drop them at the same instant. They land together (as long as neither is fluffy enough for air to slow it). Heaviness does not win the race.

Free fall is too fast to time by hand, so do what Galileo did: prop up a smooth board as a gentle ramp and roll a ball down it. The ball follows the same speeding-up pattern as a fall, only slower. Mark distances along the ramp with a tape measure — say 10, 20, 30, 40 cm from the start.

Release the ball from the top and time how long it takes to reach each mark. Repeat a few times and average — timing rolling balls by hand is tricky, so several tries help. Write down each time and distance. You should find the ball covers far more than double the distance when you double the time.

What your ramp reveals. (1) Distance grows as time SQUARED (d = one-half g t-squared), so in equal seconds a falling object covers distances in the ratio 1, 3, 5, 7 — Galileo's famous odd-number rule, and the odd numbers add to the perfect squares. (2) The MASS never enters the formula, so without air everything falls at the same rate — the astronaut David Scott proved it on the airless Moon in 1971 by dropping a hammer and a feather together. (3) A steeper ramp accelerates faster; a vertical 'ramp' is just free fall, with acceleration g about 9.8 metres per second every second. (4) This single law, wrung from a rolling ball, was the first piece of the mechanics Newton would complete, and it still describes every dropped object, thrown ball and launched rocket.