Mathematics/Physics

Bouncing Superball Physics

Objective(s):

1. To explore several striking and unusual properties of bouncing superballs.
2. To measure and understand the elasticity coefficient for a bouncing superball.
3. To understand the role of energy conservation in relation to bouncing balls.

Approximate Level: eighth grade

Materials Needed:

1. A supply of superballs and meter sticks [one per student or one per two students].
2. A collection of balls for bouncing. You may wish to include a ping-pong ball, a tennis ball, a foam ball, a racket ball or squash ball, a rubber ball, a wooden ball, a steel ball, and "happy balls" and "sad balls", and whatever else is conveniently available.

Strategy:

Drop the superball from a measured height h₀ of, say, one meter. The ball will recoil to a height h₁, where h₁ is less than h_0. Let us call the ratio r = h₁ / h₀ the elasticity coefficient of the ball. Drop the ball from several different heights [for example, 0.5 meters, 1.0 meters, 1.5 meters, and 2.0 meters] and measure the bounce heights. You should obtain data somewhat like the following:

h₀ 0.50 meters 1.00 meters 1.50 meters 2.00 meters

h₁ 0.41 meters 0.83 meters 1.24 meters 1.65 meters

When the superball is dropped from a different initial height H₀, it will bounce to a corresponding height H₁, where r = H₁ / H₀ is the same for each bounce. In other words, the coefficient of restitution r determines the ratio of the "drop height" to the "bounce height" for the superball from the surface in question. The elasticity coefficient represents the fraction of the mechanical energy of the ball that remains after the bounce, the remaining fraction being converted into heat. In principle, both the ball and the table become warmer in this process of bouncing.

If the superball is left to bounce several times in succession, the heights h₀, h₁, h₂, h₃, h₄, h₅, … become smaller by the same ratio:

r = h₁ / h₀ = h₂ / h₁ = h₃ / h₂ = h₄ / h₃ = h₅ / h₄ = …

After ten to twenty bounces, the ball stops bouncing.

Take the box of balls, and drop each ball from a height of 1.00 meters. Note that there is a wide variety of bounce heights, but that balls that have the same constitution actually bounce to a similar height, independently of their size.

Take a small superball and balance it on top of a large superball that is held in your hand. [You may find it helpful to dig a small hole in the larger ball, so that the smaller ball is easily balanced.] Make predictions as to what will happen to the balls when they are dropped onto the floor from your hand. Do the experiment, and observe that the small ball tends to bounce very high, whereas the larger ball hardly recoils at all. In other words, energy is transferred to the second ball from the first one after they strike the floor.

Performance Assessment:

1. At the racetrack with a paramutual betting system, the track keeps about 8% of the wager and returns 92% to the participants. In other words, when you bet $100, on the average you get to keep $92 after the first bet. How many times must you bet before your holdings are down to $1? Write an essay on why you should never, never bet at the races.
2. Can you make a superball bounce back and forth about a central location. You should release the ball from a given height with both a spin and a horizontal speed. Practice until you learn to do this with agility.
3. Try throwing a superball off a smooth horizontal surface and then under a table. Notice that the superball will typically come right back to you, boomerang style. Try to explain why this occurs.

Multi-cultural Comment:

Students and teachers of physics have wondered long long and often what would happen if a superball were dropped from the top of a high building, such as the Sears Tower of Chicago. That building, with a height of 440 meters above ground level, has recently lost the designation of world's tallest building to a new structure in Kuala Lumpur, Malaysia on a ridiculous technicality. Fortunately, the fate of the superball can now be known, as a result of experiments done by resourceful team of Australian researchers at a radio antenna tower of comparable height. When they dropped the superball onto the pavement below, the ball shattered into glasslike slivers, which were propelled at great speeds from the impact point. One of the experimenters narrowly escaped injury from the shattered fragments. Alas, it seems that the superball has limited superpower.

References:

Jearl M Walker, The Flying Circus of Physics. This reference contains a variety of applications of superball physics.