Bouncing Basket Balls
Name: Jean C.
I just watched Jay Leno and he asked this
question: Let's say you filled one basketball with helium and another
with oxygen. Assuming that both balls have the same pressure and you
drop them from the same height, which ball will be the highest on the
first bounce? Ack!How do you figure this out?
I believe the correct answer to be that there would be very little
difference. Assuming the helium and oxygen act like ideal gases (pV=nRT),
their elastic properties would be identical. That is, the change
in the volume of the basketball as it bounces off the floor would
produce the same change in the pressure of the gas whether it is helium
or oxygen. Actually, the pressure change would be slightly less
(perhaps 1%) for oxygen as oxygen at these temperatures and pressures
deviates slightly from an ideal gas (the molecules attract each other
even when not touching whereas for an ideal gas the forces between the
molecules is zero except when they are in contact.) Another mechanical
difference would be the difference in the masses of the two balls due to
the different masses of the two gases.
Assuming the ideal gas law and that the basketball has a radius of about
1/2 ft = about 1/6 m, the gas inside is at a pressure of 3
atmospheres (45 lb/sq in) and a temperature of 300 K, it contains about
2.4 moles of any ideal gas. For helium, (atomic weight 4 gm/mole) this
means 10 gm and for nitrogen (atomic weight 14 gm/mole) the mass of the
gas inside the basketball would be 56 gm. The difference (40 gm or 1.5
oz) strikes me as very small.
The larger mass of the oxygen filled ball would make it bounce slightly
higher as air resistance is slightly less important. However, the
deviation from ideal gas would make it bounce slightly less high as the
gas does not push back quite as strongly as an ideal gas. This means the
basketball would distort more when in contact with the floor and so would
lose some additional energy since the distortion is not perfectly elastic.
I do not think Jay Leno would be interested in this wordy explanation, but
I hope you found it useful. It could make an interesting experiment or
even science fair project, I would think. You could even use gases which
are much more dense and/or non-ideal to make the effects clearer.
Refrigerant gases meet both criteria.
Best, Dick Plano...
Richard J. Plano
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Update: June 2012