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

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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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  • #2
mgb_phys
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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.
 
  • #3
russ_watters
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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.
And the derivation of this is very simple: just combine newton's acceleration equation with his graviity equation and solve for "a".
 
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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 ?

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
 
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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 ?
 
  • #6
mgb_phys
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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'.
 
  • #7
ZapperZ
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This is such a common question, I've decided to put an entry on this in our FAQ.

https://www.physicsforums.com/showpost.php?p=2211980&postcount=9 [Broken]

Zz.
 
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The kids a Galileo.
Nice thing you have the courage to ask, its the key to success.
 
  • #9
Andy Resnick
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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 ?

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.
 
  • #10
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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.

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.

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
 
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  • #11
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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.
 
  • #12
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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.

I saw a book point that out by saying:
F = ma, therefore:
a = Flarge / mlarge = Fsmall / msmall
 
  • #13
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Thanks for the FAQ entry Zapper.

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.
 
  • #14
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.
 
  • #15
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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
 
  • #16
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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.
 
  • #17
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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.
 
  • #18
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.
 
  • #19
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Thanks for the reply, coverme. But, I'm afraid what you have written is too subtle for me to understand.


Newton first law of motion states heavier body accelerate less and non heavier accelerate more.This law was made caring the daily experences, and it is clear that these physical forces which we apply are like kicking football, pushing the objects etc

Now the big question is ,is Gravity is same kind of force.In this ,the body acted by gravity
have its every particle devoted to gravity (a kind of interaction)

Remember how would you feel when the gravity would pull only your feet neglecting your other body parts,certainly you would feel the blood drenching your head.But its not your every blood drops ,tissues have similar interaction with gravity ,which makes you are devoted to the earth(means it provides the sense of direction that is up and down)

remember what i told for gravity pulling only feet is like the examples of kicking football and pushing objects

Therefore the gravity and real life physical forces I told is different.Hope you understand what I told
 
  • #20
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Newton first law of motion states heavier body accelerate less and non heavier accelerate more.

With all due respect, I highly recommend that you go back and reread Newton's 1st law of motion, as your explanation makes evident that you do not know its content. Newton's 1st law of motion has nothing to do with the "acceleration" of a mass. In fact, the magnitude of an object’s mass at “constant velocity” or “at rest” is entirely inconsequential per the 1st law of motion.

Newton's 1st law of motion refers to the property of mass-bearing objects that are already in motion (therefore, traveling at “constant velocity”) or “at rest” (hence, no measurable “relative velocity”) to remain in those states unless acted upon via the application of some type of external force, whether it be via air resistance, gravity, a lever, a propulsion system, or what have you.

Newton’s 2nd law of motion deals with the acceleration of mass via his infamous equation, F = ma.

Newton’s 3rd law of motion refers to the consequence of applied force causing an action which results in an equal though opposite reaction.
 
  • #21
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Newton’s 2nd law of motion deals with the acceleration of mass via his infamous equation, F = ma.
Infamous??
 
  • #22
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i am sorry but i said heavier body accelerate less and non heavier accelerate more for same force (is that newtonian law) or what sorry i didnot look book ,(i appologise if that is wrong)
but the above statement is true , isnot it?
 
  • #23
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Infamous??

Yes, infamous, as in "well-known", "legendary".
 
  • #24
HallsofIvy
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Yes, infamous, as in "well-known", "legendary".
Then the word you want is "famous", not "infamous". According to Merriam-Webster Dictionary, infamous means: "having a reputation of the worst kind : notoriously evil <an infamous traitor>".
 
  • #25
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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.

You have a good questioning sense.Keep it up and its your key to success for being successfull physicist
 
  • #26
D H
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Newton first law of motion states heavier body accelerate less and non heavier accelerate more.
Newton's second law, not first: F=ma. Suppose the same force is applied to two objects with different masses. The smaller mass with undergo a greater acceleration.

Now the big question is ,is Gravity is same kind of force.
If, by the "same kind of force" you mean "does gravity obey Newton's laws of motion?" The answer is of course yes.

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.
What contradictory instructions? Look at the gravitational force between two masses:

[tex]F=\frac{Gm_1m_2}{r^2}[/tex]

This is the magnitude of the force that mass #1 exerts on mass #2 and the magnitude of the force that mass #2 exerts on mass #1. The force exerted by mass #1 makes mass #2 accelerate toward mass #1 while the force exerted by mass #2 makes mass #1 accelerate toward mass #2. In other words, the two forces point in opposite directions. Gravitation is consistent with Newton's third law.

How about Newton's second law? The magnitudes of the accelerations of mass #1 toward mass #2 and mass #2 toward mass #1 are

[tex]\aligned
a_1 &=\frac{Gm_2}{r^2} = \frac{F}{m_1} \\
a_2 &=\frac{Gm_1}{r^2} = \frac{F}{m_2}
\endaligned[/tex]

Gravitation is consistent with Newton's second law.
 
  • #27
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Newton's second law, not first: F=ma. Suppose the same force is applied to two objects with different masses. The smaller mass with undergo a greater acceleration.


If, by the "same kind of force" you mean "does gravity obey Newton's laws of motion?" The answer is of course yes.


What contradictory instructions? Look at the gravitational force between two masses:

[tex]F=\frac{Gm_1m_2}{r^2}[/tex]

This is the magnitude of the force that mass #1 exerts on mass #2 and the magnitude of the force that mass #2 exerts on mass #1. The force exerted by mass #1 makes mass #2 accelerate toward mass #1 while the force exerted by mass #2 makes mass #1 accelerate toward mass #2. In other words, the two forces point in opposite directions. Gravitation is consistent with Newton's third law.

How about Newton's second law? The magnitudes of the accelerations of mass #1 toward mass #2 and mass #2 toward mass #1 are

[tex]\aligned
a_1 &=\frac{Gm_2}{r^2} = \frac{F}{m_1} \\
a_2 &=\frac{Gm_1}{r^2} = \frac{F}{m_2}
\endaligned[/tex]

Gravitation is consistent with Newton's second law.

I meant that the gravity is not same kind of force as physical forces in daily life.(not the newtonian concern) Gravity interaction is of different nature than the physical forces

And i am not convinced gravity follows second law of motion
fact for F=ma derivation
acelleration is directly porpotional to force applied(1st statement)
acceleration is inversely porportional to mass of body(2nd statement)
But accerleration due to gravity doesnot follow 2nd statement.does it? this is the main agena of the babai 123 question
 
  • #28
ZapperZ
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I meant that the gravity is not same kind of force as physical forces in daily life.(not the newtonian concern) Gravity interaction is of different nature than the physical forces

And i am not convinced gravity follows second law of motion
fact for F=ma derivation
acelleration is directly porpotional to force applied(1st statement)
acceleration is inversely porportional to mass of body(2nd statement)
But accerleration due to gravity doesnot follow 2nd statement.does it? this is the main agena of the babai 123 question

Er... F=ma even in your second statement. It is directly proportional even when F changes. If not, basic newtonian physics that we ask in undergraduate physics classes will fail. Would you think no one would have noticed this before?

When Put at a location r1 from M. The force that m1 experience is F(r1). If you let go of that mass, it will start accelerating with a1, which is equal to F(r1)/m1. However, when it has moved to another location r2, if you instantaneously measure its acceleration there, you will see that a2 = F(r2)/m. And so on.

This is basic physics. You were applying the wrong thing to the wrong situation.

Zz.
 
  • #29
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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 ?

The shape and size of the object does affect acceleration due to gravity. It is only if you approximate an object by a single point that these effects are ignored.
 
  • #30
f95toli
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I suspect one source of confusion in this thread is that we-although it is rarely explicitly stated- in classical mechanics assume that "heavy mass" (the mass affected by gravity) is equal to the inertial mass (the mass which we use for situation when e.g. two objects collide). We know that they are equal from some very careful measurements (and people are still testing this) but it is not in itself a consequence of the laws; it is an additional assumption (again, verified by experiments). Hence, the reason we can make the connection between Newtons's laws of motion and Newtons law of Gravity is because of this assumption.

Or in other words: whereas the "F" in F=ma and the "F" in Newton's law of gravity are the same (by definition); it is not obvious that the "m" are.

I am not sure if this helps or if it just makes things even more confusing:uhh:
 

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