| MadSci Network: Physics |
Hmm. It sounds to me like your coworkers are correct.
Let's consider the contributions to Newton's law for a
metal ball of radius R and mass M, falling through the air.
The force due to gravity is
F_gravity = M*g
where g is the acceleration due to gravity in a vacuum (g = 9.80 m/s^2).
Since the density of metals is typically more than 1000 times
greater than the density of air, we can neglect the boyancy force here.
However, boyancy will be important for a styrofoam ball.
The force due to air resistance is more difficult. It depends
on the velocity and the radius of the ball in a complicated way.
However, at low speeds it is approximately linear in the velocity V and
the radius R:
F_air_resistance = -A*V*R
where A = 0.00037 kg/(m*s)
and the negative sign indicates that the force opposes the motion.
The acceleration of the ball can be found using Newton's law:
acceleration = (sum of forces)/(mass)
= (M*g - A*V*R)/M
= g - A*V*R/M
While the mass cancels out of the term due to gravity, it ends
up in the denominator of the term due to air resistance.
Other things being equal, a less massive ball will fall slower!
This is generally true even at high speeds, where the force
of air resistance increases like the *square* of the velocity.
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