A BRIEF HISTORY OF TIME, question

[mchammer9111]

I just started reading A BRIEF HISTORY OF TIME and I am having a problem understanding Stephen Hawking explanation of why all bodies fall at the same rate. If I weigh twice as much as someone else and we both jump off a cliff at the same time I would tend to think that I would fall faster because I have twice the mass. I pull on the Earth more than he does and it pulls on me more. I know that the rate at which things fall is constant in a vacuum I just don't understand why.

Thanks

 

[junglebeast]

Nobody knows why the laws of physics are what they are, we only know what they are. And the laws are:

Newton's 2nd law:
F = MA

Gravity:
Fg = g m1 m2 / r^2

Let m1 be the mass of the Earth, then consider two objects X and Y with different masses mx and my. Now plug into find the acceleration of the X object:

g m1 mx / r^2 = mx ax
g m1 /r^2 = ax

Now you see the mass mx cancels out, so the acceleration of the object (ax) depends only on the mass of the planet it's falling towards and the distance. Thus ax = ay and both objects fall at the same rate regardless of how heavy they are.

 

[Battlecruiser]

Your pull on the Earth is extremely negligible. If you (mass of 150 kg) and a friend (mass of 75 kg) both jumped off a cliff at different times, but someone else (presumably because you and your friend would be dead) timed how long it takes to reach the ground, you would reach the ground first by perhaps a billionth of a second faster (I actually just made that number up, but it would nonetheless be a very small number that is almost 0, like .000000001 s). You will have a very very slightly stronger pull than your friend does on the Earth, which will make the distance you fall very slightly smaller.

However, I don't think that is what you meant when you started including forces. I haven't read A Brief History of Time, but I don't think you need to include forces in this discussion. The force your body has on the Earth is insignificant. What we are concerned about is acceleration, and what has been proved is that acceleration in vacuums is not related to mass. So whether you are 20 kg or 400 kg, you will fall at the same rate. Why is this? Well that is like asking questions like why are we here? (which, by the way, isn't an entirely unreasonable question, but I hope you get my point)

EDIT: Feel free to correct me if I'm wrong. My physics is a bit rusty.

 

[Nanyang]

mchammer9111:

Let me try to explain this as simple as possible...

Indeed the Earth pulls heavier objects more (otherwise they wouldn't be called heavy in the first place!)

However, even though the pull is more, don't forget that the mass is also more. So by the law of inertia, that things that are heavier tend to translate a smaller distance than lighter objects for the same pull, the result is that objects fall at the same rate to Earth, no matter their masses.

Alternatively, you can think of the big guy as made up of many small masses. So if the small guy falls at a certain rate, the smaller masses in the big guy will fall at that same rate*! Therefore, the big guy and the small guy falls the same rate.

*The shape of the big guy doesn't change for the same reason.

That is true, neglecting the movement of the Earth due to the big guy or the small guy. If you start to consider that the Earth moves as well, then indeed the big guy will reach the Earth first (since the Earth is going to move faster towards the big guy compared to a smaller guy). But reaching the Earth first does not mean that the big guy moves faster. Furthermore the motion of the Earth is very small if it arises from the pull of any normal human being, as mentioned by the poster above.