Galilean CannonBeta
Stack balls and drop them to launch the top one many times higher
This tool is a beta version still being stabilized. Please let us know if a result looks off.
A classic science-museum demo: a tennis ball sits on a basketball and both are dropped from 1 m. On its own a tennis ball bounces about 56 cm. Together? The faded ball on the left is a tennis ball dropped alone.
Goal Make a guess, then drop to check
Slow motion ×1/40
Guess first: dropped from 1 m, how high will the tennis ball go?
Pick balls — each tap adds one on top
Your stack (top → bottom)
- Top ball's peak
- –
- Dropped on its own
- –
- Theory
No air drag (vacuum) - –
Where did the energy go?
Each ball's share of the total energy before the drop (= 100), kinetic + potentialConditions
Previous tries
Why does the top ball fly so high?
Just before landing every ball falls at the same speed v. The bottom ball bounces off the floor first and heads up at v while the ball above is still coming down at v — they run head-on into each other.
If the bottom ball is much heavier it acts like a moving wall. Riding on it, you'd see the top ball arrive at 2v and leave at 2v; from the ground that's 2v + v = 3v. Bounce height goes with speed squared, so up to 3² = 9 times higher. Add more balls and it grows 3v → 7v → 15v.
No energy is created. The lower balls bounce far lower than usual, or nearly stop, handing their energy upward. With two perfectly elastic balls where the bottom one is exactly 3× heavier, the bottom ball stops dead and all the energy goes to the top ball.
Real balls lose energy to heat and sound when they squash (restitution), touching balls collide in overlapping ways, and light balls are slowed quickly by air. So real heights fall short of theory. The same idea is often used to picture a supernova: a collapsing star's core rebounds and blasts the outer layers away.
v_top = (3m_bottom − m_top) / (m_bottom + m_top) · vh ∝ v² → 3v gives 9×m_bottom = 3 m_top → bottom stops, top leaves at 2v
Working…
0.0
It hasn't frozen — the result will appear when the calculation finishes.
About Galilean Cannon
Drop a tennis ball sitting on top of a basketball and the tennis ball bounces several times higher than it would on its own. This tool computes that experiment in one dimension. The balls are stacked in a column and fall straight down. Each contact, whether ball on floor or ball on ball, is modelled as a spring and damper that compresses and releases over about 2 ms. The spring stiffness and damping for every pair are tuned so the contact reproduces that pair's coefficient of restitution exactly.
Masses and diameters are close to regulation values (basketball 620 g, tennis ball 58 g, table-tennis ball 2.7 g and so on). The restitution coefficients are rough figures, taken as the square root of bounce height over drop height on a hard floor. Real balls vary with wear, pressure and surface.
3v and nine times the height: the idealised argument
Let both balls arrive at the floor moving at speed v. The bottom ball bounces first and heads up at v while the top ball is still coming down at v. If the bottom ball is far heavier, then in its frame the top ball approaches at 2v and, in an elastic collision, leaves at 2v. Add back the bottom ball's own v and the top ball leaves the ground frame at 3v. Bounce height scales with speed squared, so it rises nine times as high.
With a finite mass ratio and perfectly elastic balls, the top ball leaves at v × (3m_bottom − m_top)/(m_bottom + m_top). A basketball is about 10.7 times the mass of a tennis ball, which gives 2.66v, well short of 3v. At a ratio of exactly 3 the bottom ball stops dead and the top ball leaves at 2v, reaching four times the height. That ratio hands over every bit of the bottom ball's energy.
Stack more balls and the ideal limit climbs as 1, 3, 7, 15v (2ⁿ − 1). Three balls give seven times the speed and 49 times the height. Harter (1971) measured the effect by sticking a pen in a ball, and compared the results with a more detailed model that allows the contacts to overlap in time.
Three reasons the real bounce falls short
- Restitution. The tennis ball (0.75) and basketball (0.84) lose energy each time they squash. Dropped together from 1 m, the theory panel (no drag) gives the tennis ball 8.94 m/s, 2.02 times its impact speed, and a peak of 4.31 m measured at the ball's underside. Switch on Perfectly elastic and it becomes 11.77 m/s and 7.30 m.
- Air drag, which matters most for light balls. The tool uses a drag coefficient of 0.47 and air density of 1.2 kg/m³. With those values a table-tennis ball's terminal speed is only about 8.7 m/s, so one launched at 18 m/s slows down very quickly.
- Collision order. The theory assumes the collisions happen strictly in sequence: floor with bottom ball, then bottom ball with the one above, and so on. When the balls are touching, the contacts overlap in time and the outcome shifts. Opening up the gap between balls lets the collisions run in order, and the result moves closer to the theory.
Choosing a stack
Each ball should be much lighter than the one beneath it. Basketball, tennis ball, table-tennis ball dropped from 1 m reaches 4.23 times the impact speed in theory (an 18.2 m peak), yet basketball, tennis ball, superball manages only 2.84 times. The 25 g superball is nearly half the mass of the 58 g tennis ball, so the second collision adds little.
Flip the order, with the light ball at the bottom, and the amplification disappears. A tennis ball under a basketball cannot throw the heavy ball back up. The predicted speed for the top ball comes out negative, meaning it is still moving down.
Worked examples
Basketball + tennis ball from 1 m
- Input
Restitution 0.84 / 0.75, no drag (theory panel)- Output
Top ball 8.94 m/s (2.02×), peak about 4.31 m. The tennis ball alone reaches about 0.56 m
More than seven times its solo bounce. The simulation with air drag switched on comes out a little lower.
Hitting the third-floor window (6.9–8.1 m)
- Input
Basketball, tennis ball, table-tennis ball, dropped from 0.4 m- Output
Theory: 11.84 m/s, peak about 7.45 m
That lands inside the window on paper. The table-tennis ball feels a lot of drag, though, so on screen you may need to raise the drop height slightly.
The special mass ratio of 3
- Input
Perfectly elastic, m_bottom = 3 m_top, colliding at speed v- Output
Bottom ball 0, top ball 2v, four times the height
The centre-of-mass velocity is (3v − v)/4 = v/2. An elastic collision reverses each velocity relative to the centre of mass, so the bottom ball ends at v/2 − v/2 = 0 and the top ball at v/2 + 3v/2 = 2v.
How to use it
- Pick a scenario: Basketball + tennis ball, the third-floor window, the record attempt or free play.
- Choose balls from the tray to build the stack and set the drop height.
- Optionally change the gap between balls, air drag or Perfectly elastic, then drop.
- Compare the top ball's peak with the theory prediction.
Frequently asked questions
Doesn't this break energy conservation?
No. The top ball gains height because the bottom ball bounces far lower than usual or nearly stops. Energy moves from the lower ball to the upper one.
Can it really reach nine times the height?
Only in the limit of perfectly elastic balls with a top ball of negligible mass. Real balls lose energy as they deform, and light balls also lose a lot to air drag.
Why is this linked to supernovae?
It is a popular analogy: a heavy core rebounds and drives lighter outer layers outward. The tool only computes the mechanics of balls.
Is it safe to try at home?
The top ball can fly off faster and at a steeper angle than you expect. Keep your face clear and do it away from anything breakable.
Sources
- W. G. Harter, Velocity Amplification in Collision Experiments Involving Superballs, Am. J. Phys. 39, 656 (1971)
- Harter (1971) full text, University of Arkansas
Last reviewed: