[Hiro]

In my daily lesson today I read that heavier objects don't fall faster because gravity pulls on them more, but because their greater mass helps them overcome air resistance better. Therefore, in a vacuum all objects fall at the same speed.

This implies that if two objects, one with large and one with small mass, were hit with the same force in space they would both move at the same speed.

However, my book gives a later example in which an astronaut flicks a ping-pong ball and a brick with the same amount of force, but the brick moves slower than the ball through space.

What is going on here? Are they saying that in order for both the brick and the ball to move at the same speed the same constant force has to applied, instead of the same momentary force? I am greatly confused.

[robertva]

Don't confuse "mass" with "weight". "Weight" is the force that results from gravity attracting an object. Since weight and inertia increase by the same amount when the mass is increased, two objects in a vacuum at the same altitude which are gravitationally attracted by an extremely massive third object (like a planet or moon) will be accelerated towards the third object at the save rate. They will take the same amount of time to fall the same distance. Thus: while the hammer was subject to a higher gravitational force, the feather's lower mass made it easier for the lower gravitational force to accelerate the feather downwards (real Apollo lunar demonstration).

Any differences in an atmosphere are the result of atmospheric drag. Objects with the same shape and size will have the same amount of drag. But a hollow object would have less mass, so the same amount of force (drag) would reduce its velocity quicker. As drag has a connection to velocity, eventually a balance would be reached and the falling object would continue to fall at a constant "terminal velocity".

But when you apply identical forces to objects with different masses the acceleration will be different. Imagine hollow and solid projectiles in identical mortar like launch tubes with identical charges in the base of the mortars. The lighter projectile would be accelerated to a higher velocity, wouldl take longer for the moon's gravity to decelerate to zero vertical velocity and reach a higher altitude.

[ebaines]

It all comes down to applying Newton's famous equation F = ma. In the example of an astronaut throwing a ping pong ball or a brick with the same force, and assuming that the brick has more mas than the ping pong ball, you can see that the resultant acceleration that of the brick will be less than the acceleration or the ping pong ball. Hence the ping pong ball will end up moving faster. That's why you can throw a small rock a lot faster (and farther) than a shot put.

But if you put them in a vacuum and let them fall to earth, the force applied to the objects by the earth's gravity is F = mg. Hence you get:

F = ma = mg;
a = g

So you see that the "m" term cancels out, and regardless of the object's mass it falls with an acceleration of g, or about 9.8 m/s^2 at the earth's surface.

Now for the issue of air resistance. Air resistance is typically modelled as:


where is the density or air, is the object's surface area, is a "shape factor" constant, and is the object's velocity. Since wind resistance slows an object's fall, it opposes the object's acceleration, and the equation is:



Simplifying this:


So the air resistance has a greater effect on slowing objects with a large value of the ratio . You can prove to yourself that smaller objects have a larger ratio of surface area to mass than do larger objects, all else being equal. That's why if you throw a handful of talcum powder in the air you'll see that the large clumps settle to the ground faster than the finer clumps.

[Hiro]

In hindsight I see why I was confused, I had for some reason mixed up velocity and acceleration. Dur. Thanks all for your help.