Why is Acceleration Due To Gravity Constant For All Bodies Irrespective Of Mass ?


by babai123
Tags: acceleration, bodies, constant, gravity, irrespective, mass
babai123
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#1
May25-09, 09:01 AM
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I have been reading about Acceleration Due To Gravity. All sources including Fundamentals Of Physics By Resnik say that ' Acceleration due to gravity does not depend on the object's properties like mass , density , shape etc '. The magnitude of 'g' is 9.8 m/s^2 for all bodies ? But I can not understand why is it the same for all bodies ? Why doesn't it increase or decrease according to the mass of the body ?
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mgb_phys
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May25-09, 09:06 AM
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Simplest way to think about it is probably:
Massive bodies get more pull from gravity, but it also takes more force to accelerate a more massive body so this cancels out and all objects fall at the same speed.
russ_watters
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#3
May25-09, 09:23 AM
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Quote Quote by mgb_phys View Post
Simplest way to think about it is probably:
Massive bodies get more pull from gravity, but it also takes more force to accelerate a more massive body so this cancels out and all objects fall at the same speed.
And the derivation of this is very simple: just combine newton's acceleration equation with his graviity equation and solve for "a".

coverme
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#4
May25-09, 09:31 AM
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Why is Acceleration Due To Gravity Constant For All Bodies Irrespective Of Mass ?


Quote Quote by babai123 View Post
I have been reading about Acceleration Due To Gravity. All sources including Fundamentals Of Physics By Resnik say that ' Acceleration due to gravity does not depend on the object's properties like mass , density , shape etc '. The magnitude of 'g' is 9.8 m/s^2 for all bodies ? But I can not understand why is it the same for all bodies ? Why doesn't it increase or decrease according to the mass of the body ?
It is because the each unit mass is affected by same gravitational force.

But in normal life for example
when we hit the ball by our hand,only some part of the ball gets this external energy directly and this energy is distributed to whole spherical ball .This makes the less heavy material to accelerate more and heavier material to accelerate less.
But the gravity is interaction with each unit mass,where each unit suffers 9.8m/s^2
babai123
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#5
May25-09, 09:40 AM
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Than you everyone, I got it. Let me now explain and tell me if I am right or wrong :

We know , w = mg---> Eq (1)

From Newton's second Law , we come also come to know that F = ma --->Eq (2)

Now the Force acting in case of free falling acceleration is the same force as ? ( can't understand this part , pls explain )



By comaring Eq 1 and Eq 2, we get : mg = ma
or, m = a

Please explain why F is the same as g or why F is same as weight ?
mgb_phys
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#6
May25-09, 10:34 AM
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The force of gravity on an object of mass 'm' a distance 'r' from the centre of the planet of mass 'M' is, F = GMm/r^2
And acceleration is F = ma
so ma = GMm/r^2
The mass of the object cancels giving you a = GM/r^2
which when you make r=the radius at the surface of the planet gives you the value of 'g'.
ZapperZ
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#7
May25-09, 10:34 AM
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This is such a common question, I've decided to put an entry on this in our FAQ.

http://www.physicsforums.com/showpos...80&postcount=9

Zz.
ank_gl
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#8
May25-09, 10:47 AM
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The kids a Galileo.
Nice thing you have the courage to ask, its the key to success.
Andy Resnick
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May25-09, 12:02 PM
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Quote Quote by babai123 View Post
I have been reading about Acceleration Due To Gravity. All sources including Fundamentals Of Physics By Resnik say that ' Acceleration due to gravity does not depend on the object's properties like mass , density , shape etc '. The magnitude of 'g' is 9.8 m/s^2 for all bodies ? But I can not understand why is it the same for all bodies ? Why doesn't it increase or decrease according to the mass of the body ?
Your question is one of the most fundamental in all of physics. That materials of diverse composition fall with the same acceleration has been hypothesized and tested since Aristotle; modern limits on the null experiment are on the order of [itex]\delta[/itex]g/g ~ 10^-12 or better.

That observed fact, codified into physical law, leads to general relativity.
Hertz
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#10
May25-09, 12:31 PM
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Just so you know, F = ma and N = mg are the same equation.
Newtons(Force) are what weight is measured in, and "g" is nothing more than a variable representing the "acceleration" due to gravity(9.8.))

So when you added the two equations together, you were actually adding the same equation.

Quote Quote by mgb_phys View Post
Simplest way to think about it is probably:
Massive bodies get more pull from gravity, but it also takes more force to accelerate a more massive body so this cancels out and all objects fall at the same speed.
This is all the answer you need.

The object has more mass, so theoretically it should fall faster, but because it has more mass it also has more inertia, so it is harder to move to begin with.

Quote Quote by mikelepore View Post
If the acceleration depended on mass, we would get different values if we think of a 1 kg object as being two 1/2 kg objects next to each other, or think of it as being four 1/4 kg objects next to each other, etc. That would produce the impossible result that the behavior of a collection of particles depends on what we decide to name it.
Wow, I've never thought of this before. That's some amazing logic O_O
mikelepore
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#11
May25-09, 12:42 PM
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If the acceleration depended on mass, we would get different values if we think of a 1 kg object as being two 1/2 kg objects next to each other, or think of it as being four 1/4 kg objects next to each other, etc. That would produce the impossible result that the behavior of a collection of particles depends on what we decide to name it.
mikelepore
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#12
May25-09, 12:51 PM
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Quote Quote by mgb_phys View Post
Simplest way to think about it is probably:
Massive bodies get more pull from gravity, but it also takes more force to accelerate a more massive body so this cancels out and all objects fall at the same speed.
I saw a book point that out by saying:
F = ma, therefore:
a = Flarge / mlarge = Fsmall / msmall
TurtleMeister
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#13
May25-09, 02:07 PM
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Thanks for the FAQ entry Zapper.

Quote Quote by Hertz View Post
Quote Quote by mikelepore View Post
If the acceleration depended on mass, we would get different values if we think of a 1 kg object as being two 1/2 kg objects next to each other, or think of it as being four 1/4 kg objects next to each other, etc. That would produce the impossible result that the behavior of a collection of particles depends on what we decide to name it.
Wow, I've never thought of this before. That's some amazing logic O_O
That's the same logic Galileo used to determine that Aristotle was wrong.
Cantab Morgan
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#14
May25-09, 06:07 PM
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Quote Quote by coverme View Post
But in normal life for example
when we hit the ball by our hand,only some part of the ball gets this external energy directly and this energy is distributed to whole spherical ball .This makes the less heavy material to accelerate more and heavier material to accelerate less.
But the gravity is interaction with each unit mass,where each unit suffers 9.8m/s^2
Sorry, but I have to quibble with this. I'm afraid it's more misleading than helpful.

It's hard to know where to begin, but I think we're confusing the terms energy and impulse here. The former is a force applied over a distance, while the latter is a force applied over a time. When you're writing energy above, I think you meant impulse.

The ball's inertia, or resistance to acceleration, comes from its mass, not from it's shape. Imagine a flat palm print of the same mass as the round ball. Your hand would push on much more of it than the spherical ball, but it would be just as hard to accelerate because it had the same inertia.
coverme
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#15
May25-09, 08:53 PM
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Quote Quote by Cantab Morgan View Post
Sorry, but I have to quibble with this. I'm afraid it's more misleading than helpful.

It's hard to know where to begin, but I think we're confusing the terms energy and impulse here. The former is a force applied over a distance, while the latter is a force applied over a time. When you're writing energy above, I think you meant impulse.

The ball's inertia, or resistance to acceleration, comes from its mass, not from it's shape. Imagine a flat palm print of the same mass as the round ball. Your hand would push on much more of it than the spherical ball, but it would be just as hard to accelerate because it had the same inertia.
I didnot meant the shape actually,I only meant how gravitational force and the actual force which human apply in daily life are different.
the force of gravity interacts with unit mass,that means each unit mass suffers 9.8N.And the whole body suffers 9.8+9.8+9.8+9.8+..... depends upon the total number of unit mass



But is there any normal daily life experience where the force interacts with each unit mass directly
thats the difference
Newtons first law of motion goes for the daily life of forces not for the gravitational force.Because how the gravity and daily life force acts are different
babai123
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#16
May26-09, 03:42 AM
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Thanks for explanation , I now got it. Will read more about inertia and resistance and come back with a bunch of questions.

Now , I know these are very basic questions. I am a student of 9th standard and in our country these things are in the syllabus of 11th standard. Actually , proper Physics starts in 11th standard only.I was just having some interest in the subject and finishing parts of the syllabus of higher classes which I think I can grasp without a teacher. I feel the books , the internet and this forum is enough for a clear idea beforehand.

Thanks again.
mikelepore
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#17
May26-09, 09:59 AM
P: 567
Perhaps this comparison will help someone. Consider a way in which gravity is different from the electric force on a charge.

A charged particle has an electric force on it because it has a charge. But what about the inertia that has to be overcome in order to accelerate it -- is that also due to it having a charge? No! It's inertia is due to its mass only, and its charge has nothing to do with that.

Note how that's different from gravity. An object has a grav force acting on it due to mass, AND the inertia that has to be overcome is also due to it mass. I'm saying "mass" is both places: in one cause that makes it do something, and also in another cause that makes it resist doing that very thing.

Sorry about my habit of anthropomorphizing inanimate objects, but... It's like giving someone contradictory instructions. "Because you're a big mass, accelerate more than the other guy", and, "because you're a big mass, accelerate less than the other guy". You have two opposite tendencies that cancel each other.
Cantab Morgan
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#18
May26-09, 07:55 PM
P: 261
Quote Quote by coverme View Post
Newtons first law of motion goes for the daily life of forces not for the gravitational force.Because how the gravity and daily life force acts are different
Thanks for the reply, coverme. But, I'm afraid what you have written is too subtle for me to understand.


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