# Free fall motion

#### werehk

PHF Hall of Fame
It is well-known fact that free fall motion is independent of mass, however, I've got a silly question.

Would the surface area really matter in the speed of free fall motion in
a) Vacuum
b) Air
c) Viscous liquid

#### Twig

hi

Hi!

The surface area wouldn´t affect at all in vacuum, but it will in air.

I can´t imagine that it would not affect in a liquid.

Think of it this way. Using newtons law F=ma
we know that a=acceleration is the derivative of v(t) where t=time

so m*v= mg - kv^2 This is usually presented in high school books as a differential equation for free fall with air resistance.
Where k is a constant, and this constant will include surface, shape etc.
v^2 is simply the speed squared.

Hope I helped somewhat, I am new at this myself.

werehk

#### topsquark

Forum Staff
It is well-known fact that free fall motion is independent of mass...
Actually it does depend on the mass (as well as surface area.) Gallileo's famous experiment at the Leaning Tower of Pisa (which never happened) is not accurate. Two bodies falling in a vacuum have the same acceleration. This has been verified. However if you do Gallileo's experiment and drop two different masses from a decent height you woulld be able to hear two distinct thuds when they hit the ground.

Why is this so? Because the drag coefficient (pick the kind of velocity dependence you wish) does not directly on the mass of the falling object.

-Dan

werehk