would an elephant fall faster than a mouse?

Question

using the law of falling bodies,gravity,mass,surface area, and air, resistnace. Would an elephant fall faster than a mouse?

Answer 1

I hate to do Sarah's homework for her, but I can't resist commenting. When you take into account air resistance, the elephant definitely falls faster than the mouse. This is NOT because of the mouse's "fur". It is because tiny things have a much larger surface-area-to-mass ratio than do larger things of similar shape.

The math is not hard. Instead of elephants and mice, consider two wooden spheres, a big one of radius "R", and a little one of radius "r".

Now let's say that air resistance for spheres is proportional to speed, and proportional to surface area. That's not far off the mark. That means you could express the force of air resistance as:

kvR^2 (for big sphere)
kvr^2 (for little sphere)

where k is some constant and v is velocity. Now, notice that the mass of each object is proportional to the cube of its radius:

big sphere: mass = zR^3
little sphere: mass = zr^3

where z = (4/3*pi*density)

So, the big sphere reaches terminal velocity when this is true:

(zR^3)g = kvR^2

i.e., when v = (zg/k)R

Likewise, the little sphere reaches terminal velocity when this is true:

(zr^3)g = kvr^2

i.e., when v = (zg/k)r

So, you can see that the terminal velocity for the big sphere is greater than the terminal velocity for the small sphere. i.e., the big sphere falls faster. Same for elephants and mice.

Answer 2

The elephant would obviously fall faster. It doens't have much to do with air resistance, but more with boyancy. If you drop a large rock or a pebble in a lake, which will hit the bottom first. We all know the answer to that! Treat the air as a fluid... it's all part of a physics called fluid dynamics.

Answer 3

Actually, although RickB's answer seems mathematically correct, why don't you try doing something like that in real life? Both the mouse and the elephant would land at the same time.

Answer 4

Doubt it. Things fall at an equal speed, regardless of mass. You could argue that surface area is important in this case, but that would mean that maouse would fall quicker. As I see it, the elephant would not fall faster than a mouse. Hope this helps,
-Matt

Answer 5

no. same time.

Answer 6

same.