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Hollow Ball Bounce Height and Altitude
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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