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Q & A: Big and Small Bouncing Balls

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Most recent answer: 11/06/2010
Q:
Does the size of a ball affect how high it bounces?
- Anonymous
Concord, N.C.
A:
Great question! If a ball were perfectly elastic, and if here was no air resistance or other ways of losing energy, then a it should bounce back to the same height that you dropped it from no matter how big it is. Reality is a bit more complicated, of course. For example:

If you are comparing a big ball and a little ball that have the same mass, air resistance will slow the big one down more than the small one because the big ball has more surface area for the air to be rubbing against. This makes it seem like the small ball should bounce higher.

If you are comparing a big ball and a little ball that are solid and are made of the same material, then air resistance will slow the big one down LESS than the small one because the big ball is so much heavier than the small one. This makes it seem like the big ball should bounce higher.

As you see, its hard to predict exactly what will happen unless you specify exactly what the balls are like.

-Tamara

(published on 10/22/2007)

Follow-Up #1: balls: does size matter?

Q:
My daughter has a science project at school to determine if the size (mass) of a ball will make a difference in how high it bounces. We are using the exact same proportions of each ingredient to make the balls. Does size alone make a difference, we are not testing in a vaccum we will have air resistance. The ball is solid. I am somewhat confussed by the answer given by Tamara in 2006.
- Nancy
Melbourne Beach FL
A:
For your project the mass of the balls is just proportional to the volume, which goes as the cube of the radius. The air friction is approximately proportional to the square of the radius at high speeds, and to the radius at low speeds. So for bigger balls the ratio of gravitational to frictional force goes up, compared to small balls. That would tend to make the large balls bounce higher.

This assumes that the balls really have the same uniform composition. If there's a little difference between them, that can affect how much energy gets lost in internal friction as the ball flexes during the bounce itself. So if you get results that seem complicated, that could be an issue.

Mike W.

(published on 11/06/2010)

Follow-up on this answer.