Falling objects

Why do objects of different masses dropped from the same height always fall at the same velocity, and experience the same acceleration? I have some vauge idea, but I'm not entirely sure.

Larger masses have a greater force on them, so you'd expect them to fall faster.

My physics teacher couldn't really explain this without showing me two formulas, equating them, and then cancelling out the "m"s. I'd rather have an explaination that gives me an understanding of what's going on.

Oh yeah, neglect air resistance.

they don't actually! heavier objects fall faster.

More mass = more force from the gravitational attraction of the Earth. However, the force is distributed over the mass. Since you have more of both, that evens out, and each bit of mass ends up getting the same acceleration.

As an example, suppose you have two cubes of equal mass, and you let them fall right next to eachother. Obviously, they will land on the ground at the same time. Now, suppose you repeat the experiment, except you glue the cubes together (with glue of negligible weight). The object you drop now has twice the weight of either of the cubes you dropped before, when they weren't attached; Intuitively, however, it will fall just as fast.

I'll forgo the explanation for now and simply say acceleration due to gravity is constant at the same altitude above a mass.  if this and >>3 isnt enough, I'll post in more detail.

actually, no it isn't. F=mg is an approximation of F=G*(m_1*m_2)/r^2, which is an approximation of GR

get a load of legos of equal mass on the moon and join them together and drop them in differnet combos

they all accelerate at the same time

this is Galileo's first experiment, but he was bruned because he couldn't go to the moon, we have just assumed he was right all this time, seems to have worked

i know that some astronaut dropped a feather and a hammer (i think) on the moon and they did land at the same time.

It's quite simple:  more mass = more inertia.  The heavier something gets, the more resistant it becomes to acceleration.

>>8

but then that extra "resistance" is balanced out by the extra force and the acceleration is the same as a lighter object again. i think i got it.

bear in mind the slight difference in gravity due to height from one side of the object to the other

A better model would be a hydrogen nucleus and a deuterium nucleus in which the deuterium nucleus is laid "flat" in relation to the field of gravity it is being attracted by.

If you are a supernatural entity and can place them at exactly the same height and aline the gravity field generating body so that the field of gravity affects them equally, then they will accelerate downards at the same time. Of course this is impossible to prove.

On further note I came and then washed my schlong and it feels very relaxed and fresh now. Things seem.. different... when you're not horny.

Discuss.

>>8 FAIL

The accelleration is due to a mysterious force called gravity. We don't really know much about how gravity works, only that it does and every mass has a gravitational pull. Larger object DO fall faster, but the difference is so small that we can not possibly measure it. "Falling" is a result of the gravitational forces from the planet and the falling object attracting.

say i have two cubes, one is empty inside and another one is bigger. will those also fall at the same rate?

>>12
assuming they are the same weight and 0 air friction, yes.

>>13
assuming they are at the same height and 0 air friction, yes.
fixt

>>14
assuming they are at the same weight, height and 0 air friction, yes.
fixd fixt

>>15
If you're using weight as in the gravitational force then ok, but if you use it as mass then no; this whole thread is about how mass doesn't matter.

>>12
The heavier one will push air out of the way with more force and fall faster.

>>11
You're the one who fails.  You're honestly trying to take into account the *unfathomably* minimal amount of extra gravitational pull that is being generated by the heavier object?  We're talking about things you can hold and drop here, not celestial bodies.  Spare me the asinine nitpicking, please.

This is boring, >>1 obviously just wants an explanation of the terms. >>8 got it right, and >>11 is a dipshit who doesn't really understand what he's saying despite being partially right as well (gravity is quite mysterious by nature, but its effects aren't).

>>1
The formulae are not circular. Let's just take a look at each formul and see what it's saying.

The force pulling the object down towards the earth is its weight
P = m g
where P is the force, m is the objects mass, and g is the "gravitational pull" of the earth. So far, so good. (if not, see note at the end).

But remember, according to Newton's second law, F = m a, where F is the force, m is the mass of the object, and a is the acceleration the force causes on the object. This just goes to show that for objects of different mass, you need to apply more force on the more massive one to produce an equal acceleration.
a = F/m so if m1 > m2, to have F1/m1 - F2/m2 you need F1 < F2 (more specifically F2/F1 = m1/m2). So hopefully your get the whole, F = ma thing.

In the case of weight, F = P.
In short, we can write that the acceleration due to the earth's gravitational pull is equal to a = P / m
so a = (m g) / m
thus a = g (kinda predictable).
g being fairly constant over a small area, and not varying that much over the surface of the globe, aside from the effect of friction objects will fall with the same acceleration and therefore obtain similar velocities simultaneously.

The only thing that can cause objects to fall at different speeds is change in g (for example if I drop a ball in the north pole, and you drop it in North Africa...)

>>19

thank you