Gravity

[CaldasGSM]

I'm reading a book about science.. there was a topic about "weight vs mass"..

And it referred that old experience of galileu in which 2 objects of the same shape, but with different masses fall at the same time.. now my question is..

 

if weight is a product of the attraction of masses..

earth may be attracting the 2 objects with the same force..

but the 2 objects are also attracting earth? right?

and since one of the objects as more mass.. it should attract earth with more force.. so.. fall faster..

 

of course the force of the earth is so great that the other force is ignorable..

but shouldn't at least mathematically one fall faster..

I searched the internet and found nothing about this.. Am I wrong? or does science ignores this last step?

 

1 common sense says heavier objects fall faster

2 the way the forces work make them fall as the same time (in vacuum)

3? but if you do the math one actually get to the ground a tiny bit faster?

[SunLight]

if I recall correctly (it's been ages since I studied those things) F = ma, so a = F/m

the force is greater, the mass is greater, but the acceleration will stay the same, because the ratio will be the same.

 

So both objects will reach the ground together (well, not if there is friction with the air).

[Pepperonipizza]

1 common sense says heavier objects fall faster

 

Common sense says heavier objects fall faster because they suffer less from air resistance (assuming they have the same shape).

 

But since the reasoning in your first post only goes for vacuum settings, this does not hold, because in vacuum settings there is no air resistance.

[Fb!N!nJa]

when i throw paper in the air it like flys around then falls, but if i throw a cardboard paper then it just falls

[Saizou]

It's what SunLight said. Average acceleration caused by gravity on Earth is about 9.81m/s^2 so if you drop multiple things from the same height they should all hit the ground at the same time (in vacuum as already pointed out before). Density, air friction and buoyancy affect the acceleration of different things more or less.

[rolf]

if I recall correctly (it's been ages since I studied those things) F = ma, so a = F/m

the force is greater, the mass is greater, but the acceleration will stay the same, because the ratio will be the same.

 

So both objects will reach the ground together (well, not if there is friction with the air).

I agree. The problem is that there are usually multiple forces.

 

Attracting the earth to the object is one of them, but most of the times insignificant (unless the object is the sun ). Attracting the objects to each other, most of the times also not relevant (but comparable with the earth attracting the moon, but the moon deciding the tide). More interesting in situations close to real life is the air resistance. But since you are playing in a vacuum, there is none. However, with the same shape, the air resistance is equal too. (But can be calculated, based on speed and shape I believe but I'm not an physicist. But shape is equal, and so is acceleration, so so is speed)

 

So, what we keep, is only the gravitation law with F=mg (g=9.81m/s² for the earth). Filling that in in the equation of sunlight, and you can see that the acceleration does not depend on the mass, but only on the time. We actually get a = g =9.81m/s². Note that if there would be friction, as in Galileo's experiments, the friction would be equal. However, it would change the acceleration.

 

 

However, if you get really large objects such that they will influencing each other, (choose objects with the size and weight of the earth), it might become a difference. Look here http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation for more information about that

[Vanaraud]

if weight is a product of the attraction of masses..

earth may be attracting the 2 objects with the same force..

but the 2 objects are also attracting earth? right?

and since one of the objects as more mass.. it should attract earth with more force.. so.. fall faster..

 

The thing is, two objects haveing gravitational force between them is measured by F= G[m*M\ r(square)] so m1 and M as earth are pulling themselves with force F1 as stated up, and m2 and M with force F2. So if both objects were to pull themselves to each other so they would meet somewhere in middle. The force that m1 has to earth F\m1=G[m1\ r(square)] and earth has to m1 F\M=G[M\ r(square)], so earth would gain acceleration

aM=G[m1\ r(square)] and object nr1 am1=G[M\ r(square)] and with 2nd obj a2M=G[m2\ r(square)] and a2m2=G[M\ r(square)] respectively. As the acceleration objects would gain are the same am1=G[M\ r(square)]=am2=G[M\ r(square)] we have to look a2M=G[m2\ r(square)] > aM=G[m1\ r(square)] as it would be because F1<F2.

 

So what about the time on case of object nr1: t1=tm1+t1M=squareroot(r\am1)+ squareroot(r\aM)

object nr2: t2=tm2+t2M=squareroot(r\a2m2)+ squareroot(r\a2M)

So as a2M>aM t2M<t1M as a2M is what you are dividing with. so t2<t1 really in theory?!!! In case of earth and 2 objects t1M=squareroot(r\a2M)=squareroot[r\G[m2\ r(square)] and t2M=squareroot(r\aM)=squareroot[(r\G[m1\ r(square)] m1 and m2<<<<<<<M, so m1~0 and m2~0 and t1M~8 and t2M~8, that means it isn´t moveing at time being.(8 as infinity) But in theory with objects with similiar masses your logic is true as t2<t1?!

 

But as earth wouldn´t move from its position for minor force a2M~G[m2\ r(square)]~0 and aM~G[m1\ r(square)]~0 are irrevelant and am1=G[M\ r(square)]=am2=G[M\ r(square)] on condition that M is massive and wouldn´t move am1=am2=g on earth. I think its the same with the Sun and the Earth. Sun just wouldn´t move because its millions of times bigger?

 

Hope I didn´t mess up with copy\pasteing and with english as its not my first language and missing characters.

[Razzled]

Simple, what goes up must come down. I never liked science much, but took a few forensic science courses and what I have retained i have yet to use. History was my fav.

[T.A.Rockstead]

I'm reading a book about science.. there was a topic about "weight vs mass"..

And it referred that old experience of galileu in which 2 objects of the same shape, but with different masses fall at the same time.. now my question is..

 

if weight is a product of the attraction of masses..

earth may be attracting the 2 objects with the same force..

but the 2 objects are also attracting earth? right?

and since one of the objects as more mass.. it should attract earth with more force.. so.. fall faster..

 

of course the force of the earth is so great that the other force is ignorable..

but shouldn't at least mathematically one fall faster..

I searched the internet and found nothing about this.. Am I wrong? or does science ignores this last step?

 

1 common sense says heavier objects fall faster

2 the way the forces work make them fall as the same time (in vacuum)

3? but if you do the math one actually get to the ground a tiny bit faster?

[T.A.Rockstead]

GALILLEO States that variables in mass & attraction all FALL at same RATE .

when on the moon a feather & Hammer both falling the same distance distance begin and end simultaneously.

[Waster]

Basically Gravity acts on all object the at the same rate. If the object is big enough it has its own gravity that also attracts as well the you get additional attraction ( with something the size the moon or small planetoid). something smaller needs to be VERY dense (great mass). so something the size of a mac truck wouldnt have its only gravity or rather its gravity wouldnt be something that would affect gravitational attraction rate. (note: it does have a very small gravitational attraction) so in an airless environment a mac truck would still fall as fast (or slow) as a feather.