# Free falling objects

## Main Question or Discussion Point

Hi guys, quick and simple question!

If you allow 2 objects with different weights but exact same shape to free-fall in the presence of air resistance will they hit the ground at the same time (assuming terminal velocity isn't reached by either object). I'm pretty sure the heavier object hits the ground first because even though drag would be the same for both objects it would be relatively larger on the lighter object. Is this correct?
Thanks

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Heavier one hits the ground first.

I'm pretty sure the heavier object hits the ground first because even though drag would be the same for both objects it would be relatively larger on the lighter object.
Is incorrect.

Why is that last part incorrect? The drag will be larger on the heavier object because it will be moving faster but I was talking about the drag relative to the mass of the object...

Ok I see where I'm wrong here:

I'm pretty sure the heavier object hits the ground first because even though drag would be the same for both objects it would be relatively larger on the lighter object.
Drag would be larger on the heavier object at any given moment because it will always be moving faster.

With regards to
"it would be relatively larger on the lighter object".
I guess I could re-phrase the question to:
Would the heavier object have a higher acceleration at all times until both objects reach terminal velocity?

Wouldn't they reach the ground at equal rates?

Generally, free fall implies that no other acclerations are acting other than gravity (objects don't encounter a significant amount of air resistace).

If we considered drag, it would depend on the shape (surface area) of the object, and since they are of differing mass but have the same surface area, they displace the same amount of air and fall at equal rates.

Both objects accelerate towards the Earth at the same rate, but the Earth accelerates faster towards the heavier object. Equal and opposite force are implied by Newton's law. So theoretically a ten pound object will cause the Earth to accelerate ten times as fast as a one pound object. But neither force will affect the Earth measurable even if dropped from interplanetary distances. The result is there mathematically but not realistically. In one discussion someone did the math and came out with a needed accuracy of over 24 places behind the decimal point.

The result is there mathematically but not realistically.
That should be a diamond quote in physics.

Ok I see where I'm wrong here:

Drag would be larger on the heavier object at any given moment because it will always be moving faster.

With regards to

I guess I could re-phrase the question to:
Would the heavier object have a higher acceleration at all times until both objects reach terminal velocity?
I would suggest a simple force balance:

$$F_{net}: m*a=m*g-C_d*s*q$$

or

$$a = g - \frac{C_d*s*q}{m}$$

where q is the dynamic pressure $$q= 0.5* \rho*V^2$$

The heavier object has higher mass, so the fraction of the second term on the left side is smaller as m gets bigger (which results in higher acceleration). But at the same time this higher acceleration results in more drag (the numerator of the second term on the LHS). So its a question of which one wins, the numerator or the denominator.

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Both objects accelerate towards the Earth at the same rate, but the Earth accelerates faster towards the heavier object. Equal and opposite force are implied by Newton's law. So theoretically a ten pound object will cause the Earth to accelerate ten times as fast as a one pound object. But neither force will affect the Earth measurable even if dropped from interplanetary distances. The result is there mathematically but not realistically. In one discussion someone did the math and came out with a needed accuracy of over 24 places behind the decimal point.
This has nothing to do with the question asked.

DaveC426913
Gold Member
This has nothing to do with the question asked.
It does. He is putting it forth as a confounding factor - something that does factor in to the OP's question, since it's such a broad question (he's asking whether the heavier object will hit sooner under the given conditions). It will.

(Assuming you do the experiments seperately, either in time or in distance...) the heavier object will impact the Earth in a miniscule amount of time less than the light object.

It's a vanishingly tiny factor - virtually negligible - granted, but the OP didn't state what scale of measurement he's looking for.

Ok, fine. Relative to the drag forces, this confounding factor is 2nd, possibly 3rd order. In other words, not relevant to the answer.

The OP talked about the presence of drag. This is the primary mechanism for slowing things down.

they will fall at same rate. same shape will cause same amount of drag

D H
Staff Emeritus
I guess I could re-phrase the question to:
Would the heavier object have a higher acceleration at all times until both objects reach terminal velocity?
Yes. Moreover, the heavier object will have a higher terminal velocity.

D H
Staff Emeritus
they will fall at same rate. same shape will cause same amount of drag
No, they won't. If the two objects were at some point moving at the same velocity, both would indeed be subject to the same drag force. They would not be subject to the same drag acceleration because drag acceleration is drag force divided by mass. Atmospheric drag will have a lesser influence in terms of acceleration on the heavier object.

Don't even think about drag. Let's assume the objects are the same shape and be done with that. However, even without drag, the heavier object will hit first. The heavier object pulls on the earth harder than the lighter one does.

That being said, if the objects are dropped at the same time, and relatively close to each other, they will hit at the same time.

If I need to explain that last part, I will.

D H
Staff Emeritus
Don't even think about drag. Let's assume the objects are the same shape and be done with that. However, even without drag, the heavier object will hit first. The heavier object pulls on the earth harder than the lighter one does.
Theoretically, yes, that is true. In practice, no. The difference in timing is immeasurably small. Ignoring air resistance, an object dropped from a height of one kilometer will take 14.28 seconds to hit the Earth. The difference in falling time attributable to gravity between dropping a one gram object down a one km tall cliff and a 10 metric ton boulder: 10-20 seconds.

Drag forces on the other hand can easily result in measurable differences in the time it takes for different objects to fall.

If we considered drag, it would depend on the shape (surface area) of the object, and since they are of differing mass but have the same surface area, they displace the same amount of air and fall at equal rates.
So, would a pingpong ball and another pingpong ball filled with lead hit the ground at the same time?

No, because when you're falling through air, you are falling through a fluid, so your density relative to the density of the fluid also plays a role in how fast you fall.

As far as the friction between the air and the surfaces of the objects, yes, the coefficients of friction would be exactly the same.

Theoretically, yes, that is true. In practice, no. The difference in timing is immeasurably small. Ignoring air resistance, an object dropped from a height of one kilometer will take 14.28 seconds to hit the Earth. The difference in falling time attributable to gravity between dropping a one gram object down a one km tall cliff and a 10 metric ton boulder: 10-20 seconds.

Drag forces on the other hand can easily result in measurable differences in the time it takes for different objects to fall.
Thanks for the numbers! It's cool to see it put in perspective like that. I agree that the difference in gravitational pull is negligible, especially now that I take another look at the OP and see that he specifically mentions air resistance.

But, in my defence, there is a scale at which gravity has more influence than air resistance. Like if one object were a Mars-sized ball of iron and the other were a Mars-sized ball of styrofoam.