A question of physics

[Aeschylus]

Hmm...so after 50-odd posts, nobody knows...or rather, everybody knows, but they all disagre

JM: Some of us know. Others think they know and try to sound sophisticated in their answer. Eventually, those with a willingness to learn and comprehend will quickly come to the same realization as I did when I first waded through all these posts, that most have no clue.

Cheers

Joe Meert

Joe Meert, do you have a degree in physics? I do.

I know I am correct, think about the translation that must be applied in order for the Earth to consider itself staioney, think about the pseudo-force this introduces to the ball.

The translation of the forces on the object becomes:

m d^2x/dt^2 = F

m d^2x'/dt^2 = F - Gm^2/r^2

Now examine post #46 in detail and if you still disagree please point out where exactl;t the problem is.

 

[Mistermystery]

JM: Precisely the same time.

Cheers

Joe Meert

Okay same question, now with air res. What happends then?

 

[Aeschylus]

Okay, so forget air resistance for a moment. Assume a vacuum. Two objects, same size, but one has weighs a ton and the other weighs a billion tons. Drop them both from 1 mile above the earth. Will they hit the ground at PRECISELY the same time? Or different times, but sufficiently close that we wouldn't notice it?

If they are dropped at the same time in the same place yes they will hit the ground at the same time as the pseudo-forces affecting both would be the same. If they were dropped at diffreent times there would be be a differemce in the time that each one took to hit the ground. Even with a sweight of ab billion tons it woul;d still be to small a fraction of the Earth';s weight to have for there to be a perceptible difference.

 

[Mekkala]

I think everyone is confused.

He was referring to pull of the cannon balls on the earth. Basically, the earth and the Cannon balls move towards eachother. The earth accelerates the cannon balls equally towards it, the difference lies in the way the balls accelerate the earth towards themselves.

If you dropped both balls at the same time, there wouldn't likely be any difference, as it seems to me that the gravity of the two balls combine would pull on the earth. However, if you dropped both balls from the same height one after the other, the heavier one would accelerate the earth towards itself slightly faster due to its heavier mass. Essentially, the more massive object would touch the earth more quickly than the less massive object.

This effect is beyond our ability to measure though, so we cannot actually test it.

Actually, it's not beyond our ability. It is if we use the Earth as the object we drop other objects towards, but if we, say, performed the experiment on a very small asteroid and used very heavy cannonballs, the difference would be easily measurable.

 

[Aeschylus]

If anyone still disagree think of this way:

You can get a very, good approximation by ignoring the active mass of the object and it's graviational effects, now if we increase the objects mass lets say to the square of the mass of the Earth (divided by the unit mass obviously, to make sure we still talking about masses) we can effectively ignore the Earth's active mass.

The accelartion of the Earth towards the object is now:

GM^2/r^2

which is a lot larger than

GM/r^2

so the object and the Earth will collide alot sooner than the case where we ignore the active mass of the object.

 

[Mekkala]

I completely understand what Aeschylus is saying, but given the way he's explaining it, I can see why so few others understand him (no offense, man, it's just that your explanation is a bit confusing for the layman).

When you drop an object towards the earth, the object accelerates towards the earth. This acceleration is dependent only on the mass of the earth. That is why, when you drop two objects in the same place at the same time, they will always hit the earth's surface at precisely the same moment.

However, the earth is also accelerating towards the objects you drop. This acceleration is very, very slight, but it does happen. The important point to realize is that the earth's acceleration is dependent only on the mass of the dropped object.

If you drop both objects at once, the earth accelerates towards both objects, and since both objects are at all times at the same distance from earth in the same direction, this acceleration is defined by the sum of the masses of the two dropped objects. However, if drop only the heavier object, the acceleration of the earth will be dependent on the mass of that object. Then, if you drop the lighter object afterwards, the acceleration of the earth at that time will be dependent on the mass of the lighter object -- that is, the earth will accelerate more slowly towards the light object than it will towards the heavy object.

While the acceleration of both objects in such a case (when you drop them at different times) will be the same, the acceleration of the earth will not, and the earth will hit the heavier object slightly sooner than it will hit the lighter object. Again, though, if you drop the objects at the same time (as Galileo did), they will both pull the earth towards themselves simultaneously, and the acceleration of the earth towards each of the objects will be the same.

Hope that makes things a bit clearer, folks. Thanks, Aeschylus, for pointing this fact out -- it's not something I'd ever thought of, but it's quite obvious once you think of it.

 

[vajradhara]

I love all you guys sweating the details. Reminds me of a part of my life long ago and far away there I used to put all this theory into practice.


Disclaimer - I'm not in this photo, it's just representative.

REDLEGS in the House!!!

what unit did you serve in?

i spent my time falling from perfectly good aircraft... in the mighty 101st Air Assault Division. 502d Inf Bdg, 3 Btn, HHC, "Strike and Kill".

my... that was a long time ago

 

[vajradhara]

Namaste all,


i'm sorry for my use of Marlon Bradon in a humorous fasion. no disrespect was intended.

http://apnews.excite.com/article/20040702/D83IP53O0.html

 

[JGMEERT]

I completely understand what Aeschylus is saying, but given the way he's explaining it, I can see why so few others understand him (no offense, man, it's just that your explanation is a bit confusing for the layman).

JM: I also understand what he is saying and understand that what he is saying is wrong. The truth is that if you drop two objects on earth, they fall at the same rate and hit the ground at exactly the same time (assuming no air resistance). However that doesn't mean that they both exert the same force on the earth. The object with the larger mass attracts the earth more strongly than the one with the smaller mass and the earth attracts the more massive object more strongly than it attracts the lesser one which is what several people have been correctly saying. Then the logic and physics takes a wrong turn and leads them to the wrong conclusion that they will hit at slightly (impercebtibly different times). The reason for this error in thought is that although the more massive object weighs more and is pulled downward harder, it is also harder to accelerate and therefore a stronger force is needed to accelerate it at the same rate as the less massive object. The larger weight exactly compensates for the differences and the objects accelerate at the same rate and hit at the same time. I don't know why people are getting this wrong, but if you don't buy my answer feel free to consult a physics professor or Physics 1 textbook.

Cheers

Joe MEert

 

[JGMEERT]

Joe Meert, do you have a degree in physics? I do.

I know I am correct,

JM: I am a geophysicist. While I do not have a formal degree in physics, I have taken ample coursework
in physics and math. I know that you are incorrect and it is a flaw in your logic causing the error.
The difference in masses is exactly compensated for by the fact that the more massive object requires
more force to bring it to earth (see previous comment). I'll make a gentleman's bet with you that if you
ask a physics prof this question, you will discover you are in error.

Cheers

Joe Meert

 

[Aeschylus]

JM: I also understand what he is saying and understand that what he is saying is wrong. The truth is that if you drop two objects on earth, they fall at the same rate and hit the ground at exactly the same time (assuming no air resistance). However that doesn't mean that they both exert the same force on the earth. The object with the larger mass attracts the earth more strongly than the one with the smaller mass and the earth attracts the more massive object more strongly than it attracts the lesser one which is what several people have been correctly saying. Then the logic and physics takes a wrong turn and leads them to the wrong conclusion that they will hit at slightly (impercebtibly different times). The reason for this error in thought is that although the more massive object weighs more and is pulled downward harder, it is also harder to accelerate and therefore a stronger force is needed to accelerate it at the same rate as the less massive object. The larger weight exactly compensates for the differences and the objects accelerate at the same rate and hit at the same time. I don't know why people are getting this wrong, but if you don't buy my answer feel free to consult a physics professor or Physics 1 textbook.

Cheers

Joe MEert

You're still ignoring the effect of the object's (active) graviational mass.

What you're not understanding is there are two forces at work here the force that pulls the object towards the Earth and the force that pulls the Earth towards the object (this is the force you are ignoring). These 2 forces are opposite and equal.

For the heavier object the force that pulls it towards the Earth is greater than than the force that pulls the lighter object towards the Earth, BUT the force is directly proportional to the object's mass so the acceleration is (instaneously) the same for both objects. However the second force that pulls the Earth is also more for the heavier object, but as the Earth's mass is the same in both cases the accelration of the Earth is greater for the heavier object thus the Earth and the heavier object hit each other in a shorter time frame than the lighter object hit's the Earth.

 

[JGMEERT]

You're still ignoring the effect of the object's (active) graviational mass.

What you're not understanding is there are two forces

JM: Nope, I understand quite perfectly what's confusing you so (note in my post I explain that the heavier object pulls on the earth as well). Go ahead, give one of your physics profs a call and let me know who is correct. You obviously won't take my word for it. If I am wrong, I will offer a public apology to you.

Cheers

Joe Meert

 

[Aeschylus]

JM: I am a geophysicist. While I do not have a formal degree in physics, I have taken ample coursework
in physics and math. I know that you are incorrect and it is a flaw in your logic causing the error.
The difference in masses is exactly compensated for by the fact that the more massive object requires
more force to bring it to earth (see previous comment). I'll make a gentleman's bet with you that if you
ask a physics prof this question, you will discover you are in error.

Cheers

Joe Meert

You're not tackling the accelartion of the Earth caused by the object and you're not specifically objecting to anything in my original proof.

You should be famliar with d'Alembert's principle, inertial forces and non-inertial reference frames, so try and solve the problem using these concepts and you will find that the heavier object hits the Eath in a shorter time period.

 

[Aeschylus]

JM: Nope, I understand quite perfectly what's confusing you so (note in my post I explain that the heavier object pulls on the earth as well). Go ahead, give one of your physics profs a call and let me know who is correct. You obviously won't take my word for it. If I am wrong, I will offer a public apology to you.

Cheers

Joe Meert

You explain the object pulls on the Earth, but then you go on to ignore that fact, you need to present your arguments matehmatically.

 

[JGMEERT]

You're not tackling the accelartion of the Earth caused by the object and you're not specifically objecting to anything in my original proof.

JM: I most certainly am considering that acceleration (read my post above). I'm not ignoring anything, but you have a basic conceptual flaw in your thinking. Go ahead, ask a prof.

Cheers

Joe Meert

Here's a site that you might find helpful in clarifying your confusion

http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/newtlaws/efff.html

 

[Aeschylus]

JM: I most certainly am considering that acceleration (read my post above). I'm not ignoring anything, but you have a basic conceptual flaw in your thinking. Go ahead, ask a prof.

Cheers

Joe Meert

You're not though, which of these staements do you disagree with (give reasons):

1) the accelartion of the Earth is Gm/r^2 where m is the mass of the object.

2) therefore when m is larger the accelration of the Earth is larger

3) the accelaration of the objects will instaneously be equal in both cases

4) therefore the heavier object will hit the earth first as though it is accelarting towards the Earth at the same rate as the lighter object the earth is accelarting towards it faster than it accelrates towards the lighter object (see the original proof for a consideration of the dynamics of the situation).

 

[Aeschylus]

JM: I most certainly am considering that acceleration (read my post above). I'm not ignoring anything, but you have a basic conceptual flaw in your thinking. Go ahead, ask a prof.

Cheers

Joe Meert

Here's a site that you might find helpful in clarifying your confusion

http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/newtlaws/efff.html

I will ask a prof if come sto it, but I am sure I can convince you if I can get you to examine your or my arguments in detail.

The link is irrelevant to this discussion as it does not consider the dynamics of the situation.

 

[The Son of Him]

I will ask a prof if come sto it, but I am sure I can convince you if I can get you to examine your or my arguments in detail.

The link is irrelevant to this discussion as it does not consider the dynamics of the situation.

Your assumptions are wrong.

If two objects falling from the same height hit the ground of earth at different speeds it will mean that both objects had different accelerations because accelaration is dependent on distance and time.
That acceleration value is G (gravity), and you do not have two different values for G as demonstrated by Galileo Galilei

 

[Mekkala]

JM: I also understand what he is saying and understand that what he is saying is wrong. The truth is that if you drop two objects on earth, they fall at the same rate and hit the ground at exactly the same time (assuming no air resistance). However that doesn't mean that they both exert the same force on the earth. The object with the larger mass attracts the earth more strongly than the one with the smaller mass and the earth attracts the more massive object more strongly than it attracts the lesser one which is what several people have been correctly saying. Then the logic and physics takes a wrong turn and leads them to the wrong conclusion that they will hit at slightly (impercebtibly different times). The reason for this error in thought is that although the more massive object weighs more and is pulled downward harder, it is also harder to accelerate and therefore a stronger force is needed to accelerate it at the same rate as the less massive object. The larger weight exactly compensates for the differences and the objects accelerate at the same rate and hit at the same time. I don't know why people are getting this wrong, but if you don't buy my answer feel free to consult a physics professor or Physics 1 textbook.

Cheers

Joe MEert

Joe, ask a physics professor about this, please. I can tell you what my physics professors say, but you have no way to know I'm telling the truth, so please, ask a physics professor. I'm sure you can find one in your area.

You are absolutely correct that they will hit at the same moment when you drop both at the same time and in the same place. However, this is not true when you drop them at different times.

You can even solve this for yourself and prove it to yourself. You have the equation for gravitational force (F = (G * M * m) / (r * r)) and acceleration (a = (G * m) / (r * r)) where M is the mass of the object on which the gravitational force is acting. Solve this equation to find the following values:

(1) The acceleration of either cannonball towards the earth, when both are dropped at the same time
(2) The acceleration of the earth towards either cannonball, when both are dropped at the same time
(3) The acceleration of the lighter cannonball when dropped alone
(4) The acceleration of the heavier cannonball when dropped alone
(5) The acceleration of the earth when the light ball is dropped alone
(6) The acceleration of the earth when the heavy ball is dropped alone

(1), (3), and (4) should all be the same. (2), (5), and (6) should *not* be the same. Of those three, (2) should be the highest acceleration, then (6), then (5). See if it doesn't make sense to you once you've found those values for some sample data.

EDIT: Maybe it would help if you understood that all objects dropped towards the earth accelerate at the same rate -- but the earth does not accelerate at the same rate towards all dropped objects.

 

[The Son of Him]

Joe, ask a physics professor about this, please. I can tell you what my physics professors say, but you have no way to know I'm telling the truth, so please, ask a physics professor. I'm sure you can find one in your area.

You are absolutely correct that they will hit at the same moment when you drop both at the same time and in the same place. However, this is not true when you drop them at different times.

You can even solve this for yourself and prove it to yourself. You have the equation for gravitational force (F = (G * M * m) / (r * r)) and acceleration (a = (G * m) / (r * r)) where M is the mass of the object on which the gravitational force is acting. Solve this equation to find the following values:

(1) The acceleration of either cannonball towards the earth, when both are dropped at the same time
(2) The acceleration of the earth towards either cannonball, when both are dropped at the same time
(3) The acceleration of the lighter cannonball when dropped alone
(4) The acceleration of the heavier cannonball when dropped alone
(5) The acceleration of the earth when the light ball is dropped alone
(6) The acceleration of the earth when the heavy ball is dropped alone

(1), (3), and (4) should all be the same. (2), (5), and (6) should *not* be the same. Of those three, (2) should be the highest acceleration, then (6), then (5). See if it doesn't make sense to you once you've found those values for some sample data.

EDIT: Maybe it would help if you understood that all objects dropped towards the earth accelerate at the same rate -- but the earth does not accelerate at the same rate towards all dropped objects.

JOE is still right and he is answering the initial question !!
What is your point ?