# Why all free falling bodies reach the ground at the same time?

1. Nov 23, 2012

### ddnath

If you drop your shoe and a coin side by side, they hit the ground at
the same time. Why doesn't the shoe get there first, since gravity is
pulling harder on it?

2. Nov 23, 2012

### DrewD

Why is it that pushing harder on a truck does not make it move faster than pushing less hard on a shopping cart?
(that's not my only answer, but I bet you'll figure it out without more help)

3. Nov 23, 2012

### Staff: Mentor

The shoe has more mass than the coin, so it takes more force to accelerate the shoe than it does the coin. The two effects (more force needed to accelerate heavier object, and force of gravity on heavier object is greater) exactly balance out.

Mathematically, you can write down the equation for the acceleration of an object of mass m being accelerated by a force F: $F=ma$ and the the equation for the force of the earth's gravity acting on that same mass m: $F=\frac{mGM_e}{r^2}$ where $M_e$ is the mass of the earth and G is the gravitational context, do some algebra, and you'll end up with a value of a that is independent of m.

4. Nov 24, 2012

### ddnath

The statements is not clear to me.Would you please explain more rigorously?

5. Nov 24, 2012

### arildno

6. Nov 24, 2012

### ash644499

7. Nov 24, 2012

### ash644499

Last edited: Nov 24, 2012
8. Nov 24, 2012

### DrGreg

Here's another way to think about it. Suppose you drop 3 identical shoes side-by-side. All 3 shoes hit the ground at the same time. Now glue 2 of the shoes together and repeat the experiment. Wouldn't you still expect all 3 shoes to reach the ground at the same time? So the pair of glued-together shoes, with twice the mass of the single shoe, falls at the same rate as the single shoe.

9. Nov 25, 2012

### davenn

I like that analogy sweet....

mite have to steal it one day ;)

Dave

10. Nov 25, 2012

### Crazymechanic

So basically if we ignore the heating up effects and possible destruction dropping a coin from stratosphere and a 100 ton meteorite they would both land at the same time?
That would imply that they are traveling with the same speed I guess that is the interesting part how can a giant piece of rock travel through air at the speed of a little coin but I guess it's because it has so much more mass?

11. Nov 25, 2012

### davenn

if they both start at zero speed/velocity and ignoring air resistance .... yes
But dont forget that in an atmosphere there's going to be significant wind resistance against the 100ton rock.

you used the term meteorite ... hopefully you werent implying it was already travelling at huge velocity when it hit the atmosphere.... that is a different situation completely
you should probably have used 100 ton lump of rock ;)

Dave

12. Nov 25, 2012

### davenn

A meteor entering the atmosphere is already travelling between 20 and 40 km/sec and so cant be compared to something just being dropped at height and being accelerated by gravity alone.

Dave

13. Nov 25, 2012

### Crazymechanic

Nah I wasn't thinking the already speeding meteorite but something like you described a lump of rock or whatever.
But basically dropping a huge rock and a coin both from say 50km above ground is it really that sure that they will hit the ground at the same time or is it more that they should theoretically but practically assuming the wind resistance and pattern it could turn out a little different?
It's like a bullet traveling through air having specially shaped front to minimize the air resistance and even then strong winds affect snipers very much.

14. Nov 25, 2012

### davenn

it was well proved that totally different masses dropped together will hit the ground at the same time in the absence of air resistance.

In one of the early Apollo moon landings one of the astronauts ( google it) did the classic hammer and feather drop. Two items of very different size, shape and mass, yet they hit the moon's surface at the same time.

Dave

15. Nov 25, 2012

### jimmyly

Davenn is correct.

16. Nov 25, 2012

### Staff: Mentor

This is addressed by the first item in the FAQ at the top of this very forum.

17. Nov 29, 2012

### ddnath

many many thanks for these replies.I got it.

18. Dec 1, 2012

### ParamTv

Actually you can say heavy mass object have more inertia then littler objects. More will be the mass of object it will take more force to get accelerate. In case of low mass object it will take less force to get accelerate.