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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