# Do heavier objects fall faster?

Discussion in 'Physics & Math' started by mountainhare, Aug 2, 2004.

1. ### mountainhareBannedBanned

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I know that objects with the same surface area but different densities fall at the same speed in a vacuum.

However, there is actually a bit of an argument between my science teachers.

One science teacher thinks that heavier objects do fall faster (he provided calculations). The other one (appears) to think that this is nonsense.

I decided to try it for myself. I dropped a piece of paper, and a piece of cardboard with similiar SA. The cardboard fell much faster.

I could explain this by stating that heavier objects have more force to 'push' air molecules out of the way.
In otherwords, heavier objects are not as affected by air resistance.

3. ### BlindmanValued Senior Member

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1,425
Yes.. The acceleration due to gravity is a result of the total mass of the two objects.

5. ### dmcm01Guest

is this in air or in a vacuume?

i know that the speed it falls at is affected by weght, gravity and air resistance,
.....(put very simply)....air reistance is created by surface area. Ther similar SA effectivly counts for nothing as it is the same on both if u get me?
so the heavier object should fall faster as that is the only 'difference' between the two objects.
also paper and card is not a good way to test it as the paper tends to float about and go wierd places, try two boxes with one empty and one full of stuff.....

and yes, put in school terms N=Kg X M/s/s
force = wieght x acceleration
so the heavier one would have more force or 'pushing power'

7. ### Blue_UKDrifting MindValued Senior Member

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I hate this one, it's so obvious.

Code:
[B]Force = G * (m1.m2 / d^2)[/B]
G = constant
m1 = mass of earth
m2 = mass of object
d = distance between them
Force does not = acceleration (F = ma)

Heavy objects will have a force applied by grav proportional to their masses. So objects will fall towards the earth at the same speed.

However,

The earth will also be drawn to the objects in question with accel proportional to mass of object. So assuming you drop one after the other and have a very accurate timer to hand you will notice the heavier object fall faster if you reference the earth as a fixed point.

Last edited: Aug 2, 2004
8. ### RickॐValued Senior Member

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Was leaning Tower Of P. the actual place where Galileo performed his experiment?...I wonder...

bye!

9. ### James RJust this guy, you know?Staff Member

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28,676
The force of air resistance on an object is usually given as:

F = apAv<sup>2</sup>

where a is a constant which depends on the shape of the object, A is the cross-sectional area of the object, p is the density and v is the speed.

The rate of fall in air is affected both by gravity and the air resistance on an object. Since the air resistance is somewhat complex, it is not surprising that paper and cardboard fall at different rates.

Astronauts on one of the Apollo missions actually did the experiment on the Moon in a vacuum, using a feather and (I think) a rock. Both fell at the same rate and hit the ground at the same time.

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It was Dave Scott, commander of Apollo 15, and it was a falcon feather and a geology hammer.

11. ### Blue_UKDrifting MindValued Senior Member

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Had he conducted the experiment by dropping the hammer and the feather seperatly there would have been a (immeasurably small, but present) difference.

12. ### MacMRegistered Senior Member

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I have seen this arguement before and have posted it here about a year or so ago. It was done by a guy named Eric. I had his e-mail and used to be in contact with him but due to having to have my hard drive replaced after a crash, I have lost contact.

He made a strong arguement for the different rate of fall but I still am not convienced. The issue of the earth moving toward the free-falling object is a good one but I suspect that the formula is correct and that it represents the "Closure Rate" between the earth and the object, which means they actually close at the same rate and if the imperceptable motion of the earth could be measured (which it is in a timing free-fall to contact) the times would be the same.

The (what I believe is a falacy) idea that an object falls at a given (equal rate) but that the earth responds to different mass with different counter motion creates the illusion that the rate should be different. But if you treat the problem symmetrically and view it as a formula for "Closure Rate" between the object and Earth then the result changes and is consistant with the idea that the free-fall time to contact is the same.

Take a bowling ball (bb) and a soccer ball (sb) of the same size and shape. Compared to the earths mass the difference in the earth's response to such objects is negligable but whatever it is, it is the closure rate that determines the apparent free-fall rate.

That is expressed as F = G*m1*m2/r^2 and F=ma. The truth of the matter can better be visualized if you forget earth and consider cases of bb's and sb's in deep space.

Two bb's will close in a given amount of time. Two soccer balls will close in the same time given the same seperation. Likewise you can see that if you release one of each, the bb and a sb will close at the same rate regardless of which one is to the left or right on your graph and assumed to free-fall. Granted the amount of motion of the objects varies with its mass but the closure time is the same.

Last edited: Aug 2, 2004
13. ### mountainhareBannedBanned

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3,287
Oh, I tried a different experiment. I dropped a cube of metal and wood, and they both hit the ground at the same time.

Contradicts my paper and cardboard experiment (pretty crap, I admit. But it's all I had on hand.)

14. ### PeteIt's not rocket surgeryModerator

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I've seen an extremely rigorous treatment of this problem somewhere on the web. Let me see if I can find it.

I recall that it considered the case of dropping the two items as the same time on different parts of the globe!

15. ### PeteIt's not rocket surgeryModerator

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Nope... can't find it quickly.

But! I did find this gem published in the European Journal of Physics in 1987:

Aristotle was right: heavier objects fall faster
Donoghue, JF & Holstein, BR, European Journal of Physics, Vol 8 Issue 2, April 1987

16. ### Blue_UKDrifting MindValued Senior Member

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MacM, I have to admit I don't really understand the last paragraph of your post.

I will use the two forumlas you have given to show that 'closure time' will be shorter for objects of greater mass.

For simplicities sake, lets make up the constants so they are easier to work with:
Earth = 100kg
Bowling ball = 10kg
Soccer ball = 1 kg
Distance (r) = 1m
G = 1 (instead of 6.6742 × 10^−11)

So we have our made up world, Nonceworld.

Force = G. m1.m2 / r^2

Bowling Ball

Force = 1 . 100 . 10 / 1 = 1000 Noncicles of force

F = ma, so a = 1000/10 = 100 m/s^2

Soccer Ball

Force = 1 . 100 . 1 / 1 = 100 Noncicles of force

F = ma, so a = 100/1 = 100 m/s^2

So they accelerate at the same rate towards earth

THE EARTH

OK, this bad boy when placed a metre away from the BB
F = ma, so a = 1000/100 = 10 m/s^2

and from the SB
F = ma, so a = 100/100 = 1 m/s^2

So the earth accelerates towards the BB faster than towards the SB.

And so the heavier object lands first.

This is Nonceworld, so the figures will be different in the real world but only in scale. And if the objects were dropped at the same time, they would both land at the same time, it's only if dropped seperately that this happens.

Last edited: Aug 3, 2004
17. ### MacMRegistered Senior Member

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Ok. I surrender.

I agree it appears to be so. I remember that I also agreed with Eric at the time but had forgotten the details of his presentation which were simular to yours and was swayed to think it was in error.

My last paragraph really wasn't that important in that it merely showed the closure rate between two masses were always idendtical but the inclusion of the third mass restores the arguement.

18. ### Blue_UKDrifting MindValued Senior Member

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One thing I don't understand though, is Pete's link. I have no knowledge of quantum mechanics what so ever. I've heard of spin and understand what it means to say 1/2 spin, but it obviously contradicts what our brains would like us to think of the world. I'll wait until uni before pretending to know anything about that.

19. ### MacMRegistered Senior Member

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Yea, I'm not into the mathematical solutions either but I couldn't get to the paper. It requires subscription.

20. ### PeteIt's not rocket surgeryModerator

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I could neither understand the abstract nor access the paper...

21. ### Alpha«Visitor»Registered Senior Member

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All their papers are unavailable ATM:
"Brief interruption to IOP Electronic Journals due to essential maintenance
Access to Electronic Journals will be temporarily interrupted to enable vital maintenance work to be undertaken. This work is part of a programme of updates designed to maximise the reliability and performance of IOP's Web services."

Don't see any copies elsewhere either.

22. ### FacialValued Senior Member

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Hmmm... I wonder what the terminal velocity of a 30lb bowling ball is...

23. ### shmoeRegistred UserRegistered Senior Member

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I could access the paper just fine. The paper has the abstract in a language that I don't know (looks like Spanish?) in addition to the English version. I got as much out of the Spanish side as I did the english. :bugeye: