Question

If two objects have different masses (where the mass of object A>mass of object B) and therefore have different inertia (where the inertia of A>inertia of B), why do both objects reach the ground at the same time? Shouldn't the more massive object take slightly longer to begin falling and therefore reach the ground a measurable amount of time later than the less massive object?

Answer 1

I think you're mistaking the meaning of inertia. Inertia is an object's resistance to change. It will take more force to accelerate object A than it will take to accelerate object B, but the acceleration due to gravity on Earth is constant. Therefore, while the momentum of object A will be greater than that of object B, due to it's increased mass, the acceleration of both objects is the same at 9.8 m/s^2 and therefore both objects dropped from the same height will reach the ground at the same moment. Remember, velocity = acceleration * time
Hope this helps.

Answer 2

acceleration = F/m, so the gravitational field is the force experience or unit mass which is constant for the two objects. The more massive object experiences a greater attractive force as a whole towards the centre of the Earth (weight) but the force per unit mass is the same for both objects remains constant as explained above so they accelerate the same.

Answer 3

Errata - above should read "force experienced per unit mass"

Answer 4

Thanks guys, dcabeche I think your stated definition of inertia is the same as my understanding of it when i posted the question. I was thinking that, since object A has more inertia than object B, that it will experience more resistance to change in its translational motion, and therefore take a little longer to start moving (please correct me if my understanding of inertia still seems wrong). Wjames I was still a little confused after reading your response, but you helped me to find the answer another way. I noted that the experienced gravitational force should be greater for the larger object (as explained by IFgI=GMm/r^2), which may explain why the objects reach the ground at the same time. Then I used a=(-GMm/r^2)/m=-GM/r^2 to confirm that the acceleration of an object in free fall is independent of the mass of said object. Does that sound right? Hopefully i'm not missing something.

Answer 5

ateije. Your derivation is absolutely fine but notice that you are deriving the gravitational field strength with your formula, the gravitation field strength is the same for both objects because it is independent of their mass, it is only dependent on the mass of the Earth in this case. Using the formula GM/r^2 where M is the mass of the Earth (6x10^24) and r its radius (6.378 x 10^6 m) you will find that it yields 9.8m/s^2, look familiar? Note that it is the Earth generating the gravitational field and causing the acceleration. On a more abstract note you should appreciate that the Earth is also accelerating towards the smaller mass but with negligible effect!

The more massive object requires a greater force to overcome its inertia and this force is indeed provided by the gravitational field of the Earth. Again we see that force per unit mass is maintained by the gravitational field so two masses will simply fall at the same rate.

Answer 6

We just started doing electric fields about a week ago, and now I get what you're saying about the gravitational field strength. Thanks man. Even though i saw the units N/kg, i thought that was just maybe an accident. Now I see what you meant about the Earth's gravitational field strength. It was hard to visualize at first, as it seemed weird that the earth would have its own field set up without any other mass nearby... but if that wasn't the case then the masses would have no way of 'knowing' the other is nearby... and to boot they would then then interact via action-at-a distance, which is impossible haha. Thanks man.

Answer 7

Glad it was helpful, electromagnetism will really make the point about fields, it is a field theory after all, and a unified one!