# Thread: Do all things fall at the same rate?

1. Ok, first of all, I'm in college, I'm not stupid, I've taken physics, so I'm not a total noob, but I have some questions that I came across when I was doing a lab in my calculus class.

If a baseball and a ping pong ball are dropped at the same place on earth, with no air resistance, they will fall at the same speed and land at the same time. This is what I disagree with/am confused about.

They fall at the same speed because of the earth's gravitational constant (the earth pulls everything equally) no matter what the size/shape/mass of the object is. This is only for earth. On the moon, the gravity is different, thus the constant and the acceleration would be different, correct?

Well doesn't everything that has a mass have gravity? And isn't the amount of gravity something has proportional to how much mass it has?

Say an apple falls from 100 feet. It will land in a specific amount of time. Say an orange is dropped also from a 100 feet. It will land in the same amount of time. But say there is an object that is the size of an orange but has the mass of the sun, thus has the gravitational pull of the sun. If that was "dropped" from a hundred feet from the earth, would it hit at the same time as the orange and apple did? Wouldn't it not, since the earth is pulling on it but it is also pulling on the earth with a tremendous amount of force?

Now back to the fact that everything with mass has gravity. The baseball and the ping pong ball have different masses, thus different amounts of gravity, and although this difference is negligible because the earth's mass/gravity is like a billion times bigger/stronger than the objects', wouldn't the objects fall at SLIGHTLY different times because of the fact that they have different masses? The earth pulls on all objects the same, but the objects don't pull back with the same force.

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4. The force of the pull is symmetrical. The acceleration cancels out each object's own mass though.

Also, the ping-pong ball and the baseball will hit the moon at the same time. Just because there's less gravity doesn't mean any of the laws of physics have changed.

Also also, the "heavier object pulling the ground closer to it" has been discussed before. While theoretically true, assuming the experiment were set up in a way that actually makes sense (not dropping them side-by-side for example), yes, the heavier object would pull the ground towards itself. The practical side of that is that anything that would create a measurable difference would likely destroy the world (or at least the continent) in the process.

5. Originally Posted by xxbluejay21
the amount of gravity something has proportional to how much mass it has?

Say an apple falls from 100 feet. It will land in a specific amount of time. Say an orange is dropped also from a 100 feet. It will land in the same amount of time. But say there is an object that is the size of an orange but has the mass of the sun, thus has the gravitational pull of the sun. If that was "dropped" from a hundred feet from the earth, would it hit at the same time as the orange and apple did? Wouldn't it not, since the earth is pulling on it but it is also pulling on the earth with a tremendous amount of force?

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Short answeer -- The gravitational force exerted on a body is proportional to its mass, but the resulting acceleration is inversely proportional to its mass and the net result is that the acceleration is independent of the mass.

Longer answer -- The short answer works so long as the mass of the object is sufficiently small relative to the Earth that the movement of the Earth can be neglected. In reality you have a two-body problem, and both bodies accelerate towards their combined center-of-mass according to Newton's law of universal gravitation. A somewhat heavier body will approach the Earth very slightly more rapidly than a light body. A really really heavy body will move the Earth with appreciable acceleration and then things are very different from everyday experience. If the orange were the mass of the sun, it would appear to an outside observer that the orange was fixed and the Earth moved.

6. Originally Posted by xxbluejay21
Ok, first of all, I'm in college, I'm not stupid, I've taken physics, so I'm not a total noob, but I have some questions that I came across when I was doing a lab in my calculus class.

If a baseball and a ping pong ball are dropped at the same place on earth, with no air resistance, they will fall at the same speed and land at the same time. This is what I disagree with/am confused about.

They fall at the same speed because of the earth's gravitational constant (the earth pulls everything equally) no matter what the size/shape/mass of the object is. This is only for earth. On the moon, the gravity is different, thus the constant and the acceleration would be different, correct?

Well doesn't everything that has a mass have gravity? And isn't the amount of gravity something has proportional to how much mass it has?

Say an apple falls from 100 feet. It will land in a specific amount of time. Say an orange is dropped also from a 100 feet. It will land in the same amount of time. But say there is an object that is the size of an orange but has the mass of the sun, thus has the gravitational pull of the sun. If that was "dropped" from a hundred feet from the earth, would it hit at the same time as the orange and apple did? Wouldn't it not, since the earth is pulling on it but it is also pulling on the earth with a tremendous amount of force?

Now back to the fact that everything with mass has gravity. The baseball and the ping pong ball have different masses, thus different amounts of gravity, and although this difference is negligible because the earth's mass/gravity is like a billion times bigger/stronger than the objects', wouldn't the objects fall at SLIGHTLY different times because of the fact that they have different masses? The earth pulls on all objects the same, but the objects don't pull back with the same force.

when we say that objects fall at the same speed, we are talking only about their acceleration. The gravitational attraction between them and the Earth cause them to accelerate at the same rate. When we do this, we are ignoring the Earth's acceleration toward the dropped object due to this forces effect on the Earth.

We can get away with this when the dropped objects have a small mass when compared to the Earth, because in this case, the acceleration of the Earth is very, very small. ( for example the force between an 1 kg mass and the Earth at the Surface of the Earth is 9.84 Newtons. This will accelerate the 1 kg mass at 9.84 m/sec². This same force accelerates the Earth at 1.64e-24 m/sec.

It would take 4.5 sec for the kg mass to "fall" 100 m. in that same 4.5 sec the Earth "falls" 1.66e-23 meters towards the 1 kg. A 2 kg mass will have twice the force acting on it, but has twice the inertia, so it will fall at the same rate at the 1 kg mass. The Earth will fall at twice the rate towards it (3.28e-24 m/sec²).

Technically, the 2 kg mass hits the Earth earlier, but twice 1.66e-23 meters is just as infinitesimal compared to 100 meters as 1.66-23 meters for all intents and purposes and so is the difference in timing.

So when does the difference in masses cause a significant difference?, It depends on how accurate you need your answer to be.

Now let's consider what happens when you drop the masses together. Will the 2 kg mass hit first, Even if by an imperceptible amount?

No. As noted above, both masses "fall" at the same rate towards the Earth. The Earth in turn "falls" toward the masses, but the Earth can't fall at two different speeds, it can only fall at one. What it does is accelerate towards the masses at a rate determined by the combined gravitational force between it and both the masses (at 4.92e-24 m/sec²). The masses hit the Earth at the same time.

7. If you put a heavy object and a light object in a bag and drop the bag from height, does the bag rip due to the differential acceleration ??? Or does common sense and observation tell us that the bag drops without ripping ( impact is different ).

Consider a mass m. For a given force, even gravitational force, Fg
Fg=m*Ag where Ag is the acceleration due to gravity
We can also write the force due to gravity as
Fg=G*m*Me/r^2 where G is the gravitational constant, Me is the mass of the earth and r is the radius.

Note that if we set the two equal to each other we get
m*Ag=G*m*Me/r^2 or
Ag=G*Me/r^2

The acceleration due to gravity, Ag, is totally independant of the mass being accelerated, m. It is only dependant on the mass of the earth and the radius. Note that this applies to the moon also, just substitute Mm for Me and, as as DrR has previously stated, this only applies to m<<Me, ie his short answer.

8. I agree with the college boy. It is a shame physics books everywhereput the chapter in about different falling objects falling the same whenthe same physics book assigns different gravitational force to different Masses plain and simple. As said the difference is buried billions of times under due to the mass difference between Earth and these objects. In my opinion they need to "de-emphasize" the statement they masses fall atthe same rate and replace with the real fact it is nearly the same separatedby a billion billion or what ever it is.The sad truth is i believe authors think it novel to put this In the book as an absolute and dont realize the mental anguishthis creates with students myself includes. Unfortunately I think there could be more lessons like this ifThis one lasted this long.

9. Yes all things will fall at same rate if there is no resistense from air etc no matter what heavy thing is I

10. Originally Posted by PhDemon
Why is this? I feel like its good to have all of the info on a single subject together in one thread. Especially on on-going problems; so you can see the work-through and thought process all in one place. And so that the people in the thread are aware of the new ideas being posted on the subject.

11. As well as seeing what all the old people used to say back in the ancient days.

12. Not if a parachute is involved. Drag and terminal velocity must be factored in.

13. in a vacuum?

14. Originally Posted by PhDemon
Welcome to the forum. As a heads up it's considered bad form to "ressurrect" old threads (the last post in this one was 2 years ago). If you would like to start a discussion form a new thread...
Who told you it was considered bad form to open old threads? I've been posting on forums for over 4 years now and your comment is the first I've seen that complains about opening an old thread. I seem to remember in the forum directions they recommend doing a topic search before you open a new thread. Why would they do this if they considered it bad form to open an old thread? Besides this old thread had some very good responses.

15. I've seen the complaint of "thread necromancy" quite often... I don't agree with the complaint but I'm sure those that raise it have their reasons...

16. Originally Posted by Bad Robot
Originally Posted by PhDemon
Welcome to the forum. As a heads up it's considered bad form to "ressurrect" old threads (the last post in this one was 2 years ago). If you would like to start a discussion form a new thread...
Who told you it was considered bad form to open old threads?
Me, wearing my mod hat, and others.
Among reasons it's discouraged are the original contributors are likely long gone--a post is supposed to be a conversation, which obviously doesn't happen to people who've left the forum.
Sometimes it's a pain in the butt to moderate when they run afoul because we have to dig though years of commentary to understand the context before deciding what to do.

Overall it's almost always better to simply start a new thread. It's also a pretty common rule in forums, set in stone in another I moderate and an unofficial in the other four or five I visit.

17. Originally Posted by Lynx_Fox
Me, wearing my mod hat, and others.

Clarification needed.

-Are you wearing your mod hat as well as other hats?
-Are you wearing your mod hat as well as being representative of other people who wear mod hats?
-Are you wearing your mod hat as well as wearing other people?

18. Originally Posted by Lynx_Fox
Originally Posted by PhDemon
Welcome to the forum. As a heads up it's considered bad form to "ressurrect" old threads (the last post in this one was 2 years ago). If you would like to start a discussion form a new thread...
Who told you it was considered bad form to open old threads?
Me, wearing my mod hat, and others.
Among reasons it's discouraged are the original contributors are likely long gone--a post is supposed to be a conversation, which obviously doesn't happen to people who've left the forum.
Sometimes it's a pain in the butt to moderate when they run afoul because we have to dig though years of commentary to understand the context before deciding what to do.

Overall it's almost always better to simply start a new thread. It's also a pretty common rule in forums, set in stone in another I moderate and an unofficial in the other four or five I visit.

Perhaps but I've never considered 2 years to be very old. However, I did notice DrRocket had a post and he's been gone for about 2 years, or at least takes very little part in this forum these days, and his post was confined to his technical knowledge which was fine with me.

19. In this case, it was a good thing to resurrect the old thread, because Dr. Rocket gave the perfect answer. I don't know why there were some people who wanted to continue arguing about it after that.

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