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Name: Connor
Status: Student
Grade: 9-12
Location: CO
Country: United States
Date: Winter 2009-2010


Question:
Does altitude effect the height of ball bounce? Does a basketball or something similar bounce higher or lower between sea level and mountain levels?



Replies:
Hi Conner,

A ball dropped from the same height, will bounce exactly the same. At first, one would think that because the pull of gravity is VERY slightly less on a mountain top, the ball will bounce slightly higher. But when you drop the ball, the slightly lower gravity will result in the ball hitting the ground a little slower than it would at sea level. The reduced energy the ball gains when falling, cancels out the normally-expected higher bounce one would expect as a result of lower gravity.

Regards,

Bob Wilson


It depends on the details of how the ball is constructed, but probably the ball will bounce higher at a higher altitude.

A perfectly elastic ball, in a vacuum, bouncing on an unyielding surface, will bounce exactly to the height from which it was dropped.

A real ball will lose some energy to friction as the ball's shape is distorted while it bounces. The amount of energy lost depends on how flattened the ball gets, but the dependence is probably not linear. This difference probably favors whichever ball is less flattened as it bounces. I'll argue that this will be the ball at low altitude.

In an atmosphere, the ball will lose energy as it moves, and the rate at which it loses energy increases with speed -- probably not linearly. The thicker the atmosphere, the more drag (air friction). This difference favors the ball at high altitude, and I think it's the biggest effect.

The above difference in air pressure is partly countered by a difference in humidity. Air at lower altitude is more humid, and humidity lessens air density. (H2O is lighter than N2 and O2.) Humidity can have other effects, but I'm going to ignore them.

The surface that the ball bounces from can steal energy from it (try bouncing a ball on your bed). I'll assume the surfaces are the same.

The force of gravity is slightly higher at lower altitude. This has direct and indirect effects. I'm going to ignore the direct effect (the force of gravity on the ball yields a difference in speed, and thus a difference in drag), but I won't ignore the indirect effect (the air is thicker at lower altitude).

The buoyant force on the ball is greater at lower altitude, so it will drop slightly more slowly, and thus be flattened slightly less, than a ball at high altitude. Also, it will lose slightly less energy to air friction than if there were no buoyant force. This difference favors the ball at lower altitude, but it's sort of a second-order effect (that is, it represents two small things multiplied together).

The effects of buoyancy and drag are certainly correlated, but I don't know how.

The ball loses some energy to sound waves as it bounces, and as it continues to oscillate during the rebound. I'll guess this difference favors the ball at high altitude, even though it's flattened more than the ball at low altitude, but I think the effect is small compared to the effect of drag.

Tim Mooney


I suppose the largest factor would be air-pressure in the ball. An under-inflated ball will bounce less than a properly-inflated ball. If you take a ball that is properly inflated at high altitude (lower air pressure), and then move it to sea level, it will seem under-inflated and bounce less.

Technically there would be a little less air resistance at mountain level versus sea level, but for a massive ball like basketball, I would guess that effect would be much smaller than the effect of the condition of the ball (if the rubber is new or old) and the level of inflation. Gravity also changes very slightly from place to place, but not enough to make any significant difference.

Hope this helps,
Burr Zimmerman



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