# Two falling objects

## Main Question or Discussion Point

If I were to drop two objects with equal air resistance from a building, regardless of their differing weights, they would hit the ground at the same time.

However, since they both have different weights, they also will have different masses, and since gravitational attraction is based on mass, wouldn't the heavier one, because it possess more mass, technically fall *slightly* faster? the difference in speed would be invisible to a human watching them fall, but wouldn't it technically fall faster?

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Well, when you deal with energy, say you want to find the speed right before it hits the ground...

potential energy = kinetic energy
mgh = .5mv^2

Notce the mass cancels out

gh = .5v^2

v = sqrt(2gh)

Oh, I see. Now for attractive force the equation is

Force = GMm/D^2
and we know F = ma

so equate GMm/D^2 = ma

Notice the little m for mass cancels out. Just like the energy one. This explains it mathematically, but why disregarding mathematics....hmmmm

Ok, the math makes sense, but logically I don't get there.... how could the falling objects mass not have an effect on the gravitational attraction?

ok, technially, both objects involved in the gravitational attraction (here it's the Earth and the falling ball) exert forces on each other, thus the earth is also simotaniously being attracted to the falling object, the Earth's attraction to the ball will be minute, but nonetheless existant, thus the Earth's attraction will be greater towards the bigger ball and less toward the smaller ball, meaning that the heavier ball will technically fall at the same rate as the smaller one, but the Earth will be attracted to it more, meaning that it has "less" distance to travel before striking the Earth since the Earth moves some microscopic distance toward it.... right?

Well, all objects that have mass have inertia, right? Inertia resists change in velocity. Now since gravity ofcourse is an acceleration, it is ?v/?t or dv/dt.

So it looks like a more massive object does infact feel a greater force, but resists change in dv/dt because it is more massive. A lesser object feels less force but is less hindered by inertia. It's like the inertial and gravitational forces cancel each other out.

This is the best explanation I can think of

Doc Al
Mentor
B-Con said:
thus the earth is also simotaniously being attracted to the falling object, the Earth's attraction to the ball will be minute, but nonetheless existant, thus the Earth's attraction will be greater towards the bigger ball and less toward the smaller ball, meaning that the heavier ball will technically fall at the same rate as the smaller one, but the Earth will be attracted to it more, meaning that it has "less" distance to travel before striking the Earth since the Earth moves some microscopic distance toward it.... right?
Essentially correct, but for normal sized objects (balls and such--as opposed to moons) the acceleration of the earth is ludicrously insignificant. Check this out: https://www.physicsforums.com/showpost.php?p=343562&postcount=16

relativitydude, I coincedentally read the same explanation in Stephen Hawking's "A brief history of time" book just an hour before, that makes sense....

thx Doc, that also helps, and that is truly an "amusing thought experiement".... ;)

krab
B-Con said:
If I were to drop two objects with equal air resistance from a building, regardless of their differing weights, they would hit the ground at the same time.
This is not true; not even close. A pingpong ball and a lead sphere of the same size have, at the same falling speed, the same air resistance. Yet the lead weight will fall to the ground much faster than the pingpong ball.

Doc Al
Mentor
krab said:
This is not true; not even close. A pingpong ball and a lead sphere of the same size have, at the same falling speed, the same air resistance. Yet the lead weight will fall to the ground much faster than the pingpong ball.
Good catch, krab. Only if gravity is the only force on the balls, will their accelerations be equal. This gedanken experiment requires a vacuum.

krab said:
This is not true; not even close. A pingpong ball and a lead sphere of the same size have, at the same falling speed, the same air resistance. Yet the lead weight will fall to the ground much faster than the pingpong ball.
true, I failed to specify in a vaccume, I kinda thought it was assumed.... my bad ;)