Dropping Lead

Dunners

Hey all,

A quick question if you please. If I have two spheres roughly the same size, say a ping pong ball and a ball of lead or some other heavy substance, and dropped them from the same height at the same time (on Earth) which would hit the ground at first?

I think the lead would hit first as it has greater mass and thus can overcome the drag of air resistance with greater ease and so drop faster hitting the ground first, I cite F=ma as my evidence that the heavier object can overcome air resistance with greater ease.

My associate however believes that they will both fall at the rate as they are both the same or roughly the same size and surface area and so wouuld have the same air resistance acting upon them and as acceleration due to gravity is the same for both they would fall and hit the ground as one.

We both agree however that on the moon with no air resistance they would hit the ground at once.

Any help and relevant links/equations to settle this debate would be greatly appreciated.

Cheers!

themole

afaik,

is they are both identical in every way except weight they will hit the ground at the same time.

but the heavier one will hit the ground with more "force", so if say they hit soft ground the heavier one will impact the ground more and leave a deeper hole

ApeXaviour

Dunners wrote:

Hey all,

A quick question if you please. If I have two spheres roughly the same size, say a ping pong ball and a ball of lead or some other heavy substance, and dropped them from the same height at the same time (on Earth) which would hit the ground at first?

I think the lead would hit first as it has greater mass and thus can overcome the drag of air resistance with greater ease and so drop faster hitting the ground first, I cite F=ma as my evidence that the heavier object can overcome air resistance with greater ease.

My associate however believes that they will both fall at the rate as they are both the same or roughly the same size and surface area and so wouuld have the same air resistance acting upon them and as acceleration due to gravity is the same for both they would fall and hit the ground as one.

We both agree however that on the moon with no air resistance they would hit the ground at once.

You're more correct than your friend. Ok I'm gonna do a couple handwaving derivations/explanations. Of course air resistance would be a factor, if you ever wonder about these things just take an extreme example: say two feathers of equivalent shape and volume. One made from steel and one a regular feather. Drag is obviously going to be a factor there.
But for most regular examples it is usually safe to take drag as negligible. Say a wooden and steel ball dropped from 10m (height of a building), they will for all intents and purposes hit the ground at the same time. We do this with many other things like bouyancy. I mean say you had a large steel ball and a balloon full of helium, bouyancy is going to be a major factor there. But we usually count it out.

This all well and good, qualitative examples. I'll approach it more quantitatively. Right, air resistance at low velocities (gets into complicated fluid mechanics at higher velocity) is proportional to velocity.

So for a falling object the upward force acting on it is Fu = A*v (A being an arbitrary constant, I'm assuming everything else is constant).
The downward force, Fd = m*a (a is acceleration due to gravity, also assumed a constant).
When Fd = Fu you no longer have acceleration, you will still have velocity simply that it will be constant. See terminal velocity. So at terminal velocity m*a=A*v, and since a and A are constants it's quite obvious that the terminal velocity for a smaller mass is gonna be small aswell.

Ok that's great but it doesn't really explain what's happening up til terminal velocity does it?

ad (downward acceleration) is constant (9.81 ms^-2). Fu = m*au =A*v. Therefore au (upward acceleration) is gonna be proportional to v/m. So if we vary the mass, say make it larger, the upward acceleration is gonna be less. While the downward acceleration does not depend on mass and is as such a constant. Of course for actual acceleration we must take the resultant of these... ad + au (the latter being of negative value) = atotal

Again i'd like to emphasize that this is a very hand-waving derivation. In truth it would be a lot more complicated, but it gives you the idea.

Civilian_Target

A simpler handwaving argument is this.

If you're dropping them off a table, they'll both land at the same time, because they'll both accelerate at the same speed.

If you're dropping them from a cloud, the lead ball will land first. This is because of the momentum difference between the two. The lead ball weighs more so will have much more momentum than the ping pong ball, and momentum is proportional to force. As they gather speed, friction will play an increasingly important role as an upward force against both balls, but the lead ball has more momentum and thus exerts more force against the air - so it will fall more quickly because it falls with more force.

Dunners

Cheers guys, looks like we might have to call this one a draw. I was right for some situations and he was right for other situations

DjDangerousDave

Civilian_Target wrote:

If you're dropping them off a table, they'll both land at the same time, because they'll both accelerate at the same speed.

Im the person that thinks they will hit the ground at the same time. The orignal arguement was, will one abject accererate faster than the other because it has a greater mass and thus can overcome air resistance better than the other. This is not the case, accereration due to gravity is a constant of about 9.81 m/s^2 and is independant of the mass of the object.

Civilian_Target: They will both accelerate at the same rate no matter where you drop them from.

I believe my friend is confusing the concepts of accereration due to gravity and the concepts of terminal velocity. In your extreem example with the birds feather and the steal feather they will both accelerate at the same rate until the birds feather reaches its terminal velocity, at this stage the steal feather will keep accelerating at 9.81 m/s^2 while the birds feather will drop at whatever speed it was at when it reached its terminal velocity.

Dunners wrote:

I think the lead would hit first as it has greater mass and thus can overcome the drag of air resistance with greater ease and so drop faster hitting the ground first, I cite F=ma as my evidence that the heavier object can overcome air resistance with greater ease.

Above my friend uses the term "Drop Faster" i think this is where he is confusing the two concepts.

Thanks for the input lads.....

Dave.

ApeXaviour

DjDangerousDave wrote:

Im the person that thinks they will hit the ground at the same time. The orignal arguement was, will one abject accererate faster than the other because it has a greater mass and thus can overcome air resistance better than the other. This is not the case, accereration due to gravity is a constant of about 9.81 m/s^2 and is independant of the mass of the object.

Civilian_Target: They will both accelerate at the same rate no matter where you drop them from.
...
at this stage the steal feather will keep accelerating at 9.81 m/s^2 while the birds feather will drop at whatever speed it was at when it reached its terminal velocity.

Not exactly. An object's acceleration will not just instantly go to zero once it reaches its terminal velocity. It happens a little more gradually than that, though not a whole lot. You say they will both accelerate at the same rate? Their acceleration due to gravity will be the same yes (as it would for all objects) but their resultant acceleration would not be the same once they are travelling at some velocity.

For instance: you drop two balls from a plane, one steel and one wooden. At 0.5 seconds before the wooden one reaches terminal velocity (a significant timescale for something travelling >100m/s), the steel ball will be below it. Thus will have a greater magnitude of acceleration.

I'd say your friend (Dunners) is more correct. Though for small scales (balls off a house rooftop) drag is as negligible as bouyancy.

Dunners

DjDangerousDave wrote:

Im the person that thinks they will hit the ground at the same time. The orignal arguement was, will one abject accererate faster than the other because it has a greater mass and thus can overcome air resistance better than the other. This is not the case, accereration due to gravity is a constant of about 9.81 m/s^2 and is independant of the mass of the object.

As I said before I agree that acceleration due to gravity is the same for both and independant of the mass, the argument was not necessarily that one will accelerate faster than the other but that the object with greater mass will hit the ground first. My point being that one will reach a greater velocity than the other (as it can overcome greater drag due to additional mass).

DjDangerousDave wrote:

Civilian_Target: They will both accelerate at the same rate no matter where you drop them from.

Going to have to agree with Civilian_Target Dave, they won't always accelerate at the same rate as drag increases it will slow them down, the one with less mass being slowed at a greater rate. If it was a no atmosphere planet then acceleration would be constant and equal for both.

DjDangerousDave wrote:

I believe my friend is confusing the concepts of accereration due to gravity and the concepts of terminal velocity. In your extreem example with the birds feather and the steal feather they will both accelerate at the same rate until the birds feather reaches its terminal velocity, at this stage the steal feather will keep accelerating at 9.81 m/s^2 while the birds feather will drop at whatever speed it was at when it reached its terminal velocity.

I think you've just admitted defeat there Dave. The inital argument was two pennies one of plastic and one of something super heavy which would hit the ground first. I never questioned acceleration due to gravity I merely said the one with greater mass would hit the ground first as it would end up going at greater speed. Barry can back me up on this one!

DjDangerousDave wrote:

Above my friend uses the term "Drop Faster" i think this is where he is confusing the two concepts.

Given that I was and am suffering from flu when I used that term I don't think it's fair to try and use it to unravel my argument. Furthermore if the object with greater mass does hit the ground first (whoch I think civilian_target has proved with his equations) then who cares if I said drop faster or falls with the speed of Mercury the God of messaging - when push comes to shove the terminology matters little in that case.

Now I'm going to dive into another Lemsip...

Gurgle

Dunners wrote:

I think the lead would hit first as it has greater mass and thus can overcome the drag of air resistance with greater ease and so drop faster hitting the ground first, I cite F=ma as my evidence that the heavier object can overcome air resistance with greater ease.

Yep!

F1=ma -> Force of acceleration due to gravity: mass x acceleration
F2=µv -> Force of deceleration due to air friction: friction co-efficient x velocity

When F1=F2 you're at terminal velocity. This will happen at a lower velocity (v) for the lighter sphere.

µ = 0 for a vacuum, so with no atmosphere the two spheres will continue to accelerate equally.

Civilian_Target

OK - lets sort it out from the original question.

Dunners wrote:

A quick question if you please. If I have two spheres roughly the same size, say a ping pong ball and a ball of lead or some other heavy substance, and dropped them from the same height at the same time (on Earth) which would hit the ground at first?

The answer is - how high are you dropping it from? Once friction becomes an more-than negligable factor, the object with most momentum will always land first. That simple.

We both agree however that on the moon with no air resistance they would hit the ground at once.

Same argument applies. There's still atmosphere on the moon and there's much less gravitational acceleration to counter the friction due to atmospheric resistance there too, so again, height will be a factor. Gas gathers wherever gravity exists in the universe, so unless you create a man-made vacuum you'll always have a terminal velocity.

DjDangerousDave

We aggread to drop a golf ball and a ping pong ball from the 3rd floor of our college.

Dunners

DjDangerousDave wrote:

We aggread to drop a golf ball and a ping pong ball from the 3rd floor of our college.

Actually the original question was two pennies, one plastic, one lead from the top of the Empire State Building. Given that we can't get two pennies as described and I don't like travelling to America the ping pong and golf ball were a mediocre solution...

ApeXaviour

Dunners wrote:

Actually the original question was two pennies, one plastic, one lead from the top of the Empire State Building. Given that we can't get two pennies as described and I don't like travelling to America the ping pong and golf ball were a mediocre solution...

Also a golf ball is so designed as to have less drag so the experiment would be tainted. Those dimples allow airflow past it easier..

Gurgle

ApeXaviour wrote:

Also a golf ball is so designed as to have less drag so the experiment would be tainted. Those dimples allow airflow past it easier..

I thought that was more to do with applying spin to the ball?

ApeXaviour

Gurgle wrote:

I thought that was more to do with applying spin to the ball?

It's definitely more to do with length of trajectory and reduction of drag:

"One effect of dimples is a reduction of drag, contributing to the increased length of flight of dimpled balls compared with smooth ones."
- http://en.wikipedia.org/wiki/Golf_balls#Aerodynamics

Though it seems modification of lift/direction with spin is also an aspect.

Capt'n Midnight

Oddly enough in a vacuum on earth the lead ball might be slower than the ping-pong ball due to the earths magnetic field http://www.rare-earth-magnets.com/magnet_university/magnetic_levitation.htm


The moon has no appreciable magnetic field so ping pong and golf ball should fall at same rate.They did a drop test with a feather and something else on the moon to show that ( how did the conspiracy people debunk that one ? )

Dunners

Capt'n Midnight wrote:

how did the conspiracy people debunk that one ?

They were all on pieces of string or some such!