why do two objects fall same rate in a vacuum

[trevorjohnson32]

Does anybody know the answer?

Google searching why do two objects fall at the same rate in a vacuum, I found this:

 

"The mass, size, and shape of the object are not a factor in describing the motion of the object. So allobjects, regardless of size or shape or weight, free fallwith the same acceleration. In a vacuum, a beach ballfalls at the same rate as an airliner."

 

The three objects: the earth, a feather, and a cannonball, would all move toward each other in ratio to there size? So if you replace the earth with say a brick, and you put each thing at the corner of an equilateral triangle, the three objects wouldn't meet in the middle, the feather would move the most and the brick second but all three would move towards each other. Same thing with the earth, except the earth is so big it appears that the two objects fall and land at the same time, while in reality all three objects move towards each other.

 

[swansont]

They would have identical accelerations under gravity. The gravitational mass and inertial mass are the same.

F = GMm/r^2 and F= ma

Thus the acceleration is independent of the object's mass.

8 minutes ago, trevorjohnson32 said:

 The three objects: the earth, a feather, and a cannonball, would all move toward each other in ratio to there size? So if you replace the earth with say a brick, and you put each thing at the corner of an equilateral triangle, the three objects wouldn't meet in the middle, the feather would move the most and the brick second but all three would move towards each other. Same thing with the earth, except the earth is so big it appears that the two objects fall and land at the same time, while in reality all three objects move towards each other.

This is not the same as the scenario described in the title 

[Strange]

The force exerted on an object by the Earth is proportional to its mass (from Newton's law of gravity). So more massive objects experience a greater force.

The acceleration of an object is proportional to the force and inversely proportional to the mass.

So these two things exactly cancel out: the more massive object experiences a greater force, but that force is just enough to cause something with that mass to fall at 9.8 m/s².

[trevorjohnson32]

6 minutes ago, Strange said:

The force exerted on an object by the Earth is proportional to its mass (from Newton's law of gravity). So more massive objects experience a greater force.

The acceleration of an object is proportional to the force and inversely proportional to the mass.

So these two things exactly cancel out: the more massive object experiences a greater force, but that force is just enough to cause something with that mass to fall at 9.8 m/s².

So the force of gravity coming out of the earth is in proportion to the amount needed for an object depending on its mass so that it will fall at 9.8 m/s? Now who bases there logic only on what they can see? 

I suppose you thing gravity waves move at light speed as well....

[swansont]

21 minutes ago, trevorjohnson32 said:

So the force of gravity coming out of the earth is in proportion to the amount needed for an object depending on its mass so that it will fall at 9.8 m/s? Now who bases there logic only on what they can see? 

Yes. Gravity is pretty well-tested.

21 minutes ago, trevorjohnson32 said:

I suppose you thing gravity waves move at light speed as well....

Gravitational waves move at c. Experimentally confirmed.

[Strange]

22 minutes ago, trevorjohnson32 said:

So the force of gravity coming out of the earth is in proportion to the amount needed for an object depending on its mass so that it will fall at 9.8 m/s?

I wouldn't put it like that. The force isn't "coming out of the Earth". The force is between the Earth and the object so the magnitude of the force depends on both masses. (https://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation)

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Now who bases there logic only on what they can see? 

What is the relevance this question?

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I suppose you thing gravity waves move at light speed as well....

That is predicted by theory and consistent with the evidence. What speed do you think they move at?

And I assume you mean gravitational waves (gravity waves are much, much slower).

[Area54]

23 minutes ago, trevorjohnson32 said:

So the force of gravity coming out of the earth is in proportion to the amount needed for an object depending on its mass so that it will fall at 9.8 m/s? Now who bases there logic only on what they can see? 

I suppose you thing gravity waves move at light speed as well....

I'm curious as to what your 'logic' is based on. Would you care to expound? It might help explain your apparent difficulty with received theory.

[beecee]

38 minutes ago, trevorjohnson32 said:

So the force of gravity coming out of the earth is in proportion to the amount needed for an object depending on its mass so that it will fall at 9.8 m/s? Now who bases there logic only on what they can see? 

I suppose you thing gravity waves move at light speed as well....

Hmmm, it appears you have a chip on your shoulder...or perhaps an agenda?  

And yes, it has now been experimentally shown that gravitational waves do propagate at "c"

 

 

Edited January 14, 2018 by beecee

[trevorjohnson32]

I guess sometimes the three objects meet in the middle of the triangle created by there three centers of gravity, and sometimes a line to the middle of the earth is longer considerably then a line between the feather and the cannonball. as such the two fall between almost two parallel lines causing them to appear to fall straight down like other things the big earth does like create flat earth blah bleh blehhhhhhhhh 

[Mordred]

Umm that makes little sense sorry.

Why not start with the Einstein elevator...

https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.einstein-online.info/spotlights/equivalence_principle.html&ved=2ahUKEwjLu9DkpNnYAhVX5WMKHWjTCdUQFjALegQIERAB&usg=AOvVaw3wQjN9cBIl1_t24KBW1ij6

Which is the principle of equivalence. The latter portion is the principle of covariance (tidal forces due to intrinsic curvature) which isn't required to understand why all objects fall at the same rate.

(particularly since the title of this thread specified in a vacuum lol). Which requires parallel freefall paths.

However lets start with the basics

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Free-Fall-and-Air-Resistance

Notice how mass affects the rate of freefall? ie counters it to the point where the mass term cancels out of the equations?

[math] a=\frac{F_{net}}{m}[/math] you can see two examples ie elephant and mouse in that last link.

Ie that basic definition of mass I posted in your other thread... mass is resistance to inertia change ie acceleration.

Edited January 15, 2018 by Mordred

[studiot]

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why do two objects fall same rate in a vacuum

 

To answer this you need to understand what is meant by the word 'fall'.

 

Falling, of course, refers to motion, specifically its acceleration and velocity.

Now velocity is the rate of change of distance (position) with respect time.

And acceleration is the rate of change of velocity with respect time.

 

As such their units are LT^-1 and LT^-2 respectively.

So it can be seen that these quantities only depend upon length and time and are independent of mass.

 

As a matter of interest, falling on Earth does depend upon position or location.

Two objects at the same location will be subject to the same acceleration and therefore fall at the same rate.

However if those two object are located at the Pole and the Equator respectively they will fall at different rates because the acceleration they experience is not due to gravity alone but is a compound of gravity and centripetal acceleration.
So in this case a body's motion at right angles to the direction in which it falls affects its rate of falling.

[Strange]

3 minutes ago, studiot said:

So it can be seen that these quantities only depend upon length and time and are independent of mass.

That argument doesn’t make sense to me. The acceleration due to gravity on the Moon is less than on Earth so mass obviously does play a role. 

And acceleration is dependent on force, which also doesn’t appear in your dimensional analysis. 

[swansont]

3 hours ago, Strange said:

That argument doesn’t make sense to me. The acceleration due to gravity on the Moon is less than on Earth so mass obviously does play a role. 

Independent of the mass of the object.

[Strange]

1 minute ago, swansont said:

Independent of the mass of the object.

Hmmm.... yeah.... But I still don't find the argument from dimensional analysis very compelling - and it doesn't explain the reason, either. It just argues from the result: it's independent of mass because it is independent of mass.

[StringJunky]

4 minutes ago, Strange said:

Hmmm.... yeah.... But I still don't find the argument from dimensional analysis very compelling - and it doesn't explain the reason, either. It just argues from the result: it's independent of mass because it is independent of mass.

It just is.

[studiot]

7 hours ago, Strange said:

That argument doesn’t make sense to me. The acceleration due to gravity on the Moon is less than on Earth so mass obviously does play a role. 

And acceleration is dependent on force, which also doesn’t appear in your dimensional analysis. 

 

Would you say the volume of an object depends upon its density or just the linear dimensions of that object?

In other words is it necessary to know the density (or mass) of that object in order to completely know its volume?

In the same way I can measure the velocity and acceleration of an object, without knowing anything about its mass or any forces impelling it.

[Strange]

3 minutes ago, studiot said:

In the same way I can measure the velocity and acceleration of an object, without knowing anything about its mass or any forces impelling it.

But that doesn't tell you anything about the reason it has that velocity or acceleration. It certainly doesn't tell you that two objects with different mass must have the same velocity or acceleration. Because, of course, they can have any velocity or acceleration.

[MigL]

"As a matter of interest, falling on Earth does depend upon position or location.
Two objects at the same location will be subject to the same acceleration and therefore fall at the same rate."

That is inherently true, however...

The acceleration, a=G*Me/(r^2) , is the same because inertial mass and gravitational mass are equivalent, as is the force.
I.E.    m*a = F = (G*Me*m)/(r^2)

So that, although dimensional analysis can help verify the above, it does not show dependence.
( I think that's the issue Strange has )

Oh, and I think Trevorjohnson32 is just about ready for his first spanking.

Edited January 15, 2018 by MigL

[studiot]

49 minutes ago, Strange said:

But that doesn't tell you anything about the reason it has that velocity or acceleration. It certainly doesn't tell you that two objects with different mass must have the same velocity or acceleration. Because, of course, they can have any velocity or acceleration.

Talking of reason, yes a body can have any velocity or acceleration with reason, regardless of its mass.

Just as a body can have any volume within reason, regardless of its mass.

Yet there are other properties that connect volume and mass or velocity/acceleration and mass viz density and force.

So it is true that these connective properties must alter if we select a volume or velocity/acceleration and then change the mass.

 

So what?

 

Swansont has already suggested you concentrate on the object, not the property.

[Strange]

5 minutes ago, studiot said:

Yet there are other properties that connect volume and mass or velocity/acceleration and mass viz density and force.

And that connection is what the OP was asking about; i.e. why the acceleration is what it is for different masses.

[Endy0816]

There's parallels to the more relatable strain.

A stressed board for example. Though curved it isn't responsible for that curvature.

Edited January 15, 2018 by Endy0816

[studiot]

1 hour ago, Strange said:

And that connection is what the OP was asking about; i.e. why the acceleration is what it is for different masses.

 

Yes and this has been answered several times.

 

There is only one acceleration available at each and every point, whether you are an elephant or a mouse.

That is the nature of a vector field (acceleration is a vector).

 

Do you prefer mathematics?

 

[math]F \propto \frac{{{M_{earth}}{M_{body}}}}{{{r^2}}}[/math]

Since the mass of the Earth is constant, and r is constant at any one point.

[math]F = W{M_{body}}[/math] , where W is a constant.

Since force = mass x acceleration

[math]{M_{body}}*acceleration = W{M_{body}}[/math]

or acceleration = w = a constant, independent of mass.

 

 

 

Edited January 15, 2018 by studiot

[Strange]

2 minutes ago, studiot said:

Since the mass of the Earth is constant

F=WMbody , where W is a constant.

Since force = mass x acceleration

Mbody∗acceleration=WMbody

or acceleration = w = a constant, independent of mass.

And all of that useful information (which was included in the first reply) is lost when you reduce it to dimensional analysis.

Edited January 15, 2018 by Strange

[John Cuthber]

"why do two objects fall same rate in a vacuum?"

What else could they do? 
The "obvious" answer is that a heavy thing would fall faster.
Well, let's think about that; what would happen...?

Lets get two different rocks (say 1Kg and 2Kg) and tie them together with a string,  then drop them.

The heavy rock falls faster- and so it pulls on the string and that makes the light rock also fall at the same speed as the big rock.

But, considered together the thing is now a 3Kg "thing made from 2 rocks + some string" so it should fall even daster than the 2Kg rock.

How can that work?  The little rock is being dragged down and, consequently, it's pulling back on the string.

Yet somehow, by pulling back (up) on the 2 kg rock it makes it fall down faster (so that the whole 3kg  collection falls faster than a 2kg rock).

 

That makes no sense at all.

It also didn't make sense to Galileo, and that's what he pointed out to people  at the time.

They didn't believe him, and that's why he did his famous experiment; not because he wanted to know the answer (which he had already worked out) but to convince the other "philosophers" of the day who accepted everything that Aristotle told them.

It also doesn't work if you assume that lighter things fall faster; the only way that it makes sense is if everything falls at the same rate.

 

[studiot]

14 minutes ago, John Cuthber said:

"why do two objects fall same rate in a vacuum?"

What else could they do? 
The "obvious" answer is that a heavy thing would fall faster.
Well, let's think about that; what would happen...?

Lets get two different rocks (say 1Kg and 2Kg) and tie them together with a string,  then drop them.

The heavy rock falls faster- and so it pulls on the string and that makes the light rock also fall at the same speed as the big rock.

But, considered together the thing is now a 3Kg "thing made from 2 rocks + some string" so it should fall even daster than the 2Kg rock.

How can that work?  The little rock is being dragged down and, consequently, it's pulling back on the string.

Yet somehow, by pulling back (up) on the 2 kg rock it makes it fall down faster (so that the whole 3kg  collection falls faster than a 2kg rock).

 

That makes no sense at all.

It also didn't make sense to Galileo, and that's what he pointed out to people  at the time.

They didn't believe him, and that's why he did his famous experiment; not because he wanted to know the answer (which he had already worked out) but to convince the other "philosophers" of the day who accepted everything that Aristotle told them.

It also doesn't work if you assume that lighter things fall faster; the only way that it makes sense is if everything falls at the same rate.

 

 

I've not heard that approach before, but i like it.

And since I'm always glad to learn new things +1