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

[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?

 

[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)

 

[Nugatory]

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?

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.

 

[ddnath]

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.

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

 

[arildno]

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.

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

The force of gravity equals m*g.

Thus, in F=m*a, we get: m*g=m*a, that is g=a, irrespective of what the mass of the given object is.

 

[ash644499]

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.

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

Here is what he said:

F=GMm/d2.
F=ma.
Substitute ma to first equation.
ma=GMm/d2

a=GMm/d2.

This equation gives that it is dependent on the mass of the Earth and not individual body... Look how object's mass effect is cancelled... shorter one is canceled because it is the one that gets acceleration.

 

[ash644499]

The force of gravity equals m*g.

Thus, in F=m*a, we get: m*g=m*a, that is g=a, irrespective of what the mass of the given object is.

 

[DrGreg]

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?

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.

 

[davenn]

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.

I like that analogy sweet...

mite have to steal it one day ;)


Dave

 

[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?

 

[davenn]

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?

if they both start at zero speed/velocity and ignoring air resistance ... yes
But don't forget that in an atmosphere there's going to be significant wind resistance against the 100ton rock.

you used the term meteorite ... hopefully you weren't implying it was already traveling 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

 

[davenn]

A meteor entering the atmosphere is already traveling between 20 and 40 km/sec and so can't be compared to something just being dropped at height and being accelerated by gravity alone.


Dave

 

[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.

 

[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

 

[jimmyly]

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.

Davenn is correct.

 

[jtbell]

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?

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

 

[ddnath]

many many thanks for these replies.I got it.

 

[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.