Thread: Falling bodies

When we are young, we 'know' that heavy things fall faster than lighter things.

Then we learn physics, and are told that in the absence of air, all things fall at the same rate - and we are show the grainy video of Dave Scott dropping the hammer and feather on the Moon.

But on Earth, the hammer and feather fall at very different rates because of air resistance. And then many/most teachers go on to say that two things the same size and shape (e.g. a wooden sphere and a lead sphere of the same size - so both having the same air resistance) would accelerate at the same rate on Earth – usually expressed as hitting the ground at the same time.

But is this last bit correct? I've seen it stated in a paper looking at the science understanding of primary teachers (published in a journal for education, rather than a physics journal). To take the example to extremes, you could have your lead sphere and a balloon of the same size, and no-one would expect those two to fall at the same rate!

My reasoning is:
- initially both will fall at the same rate (because although the lead sphere has a greater weight, it also requires a greater force to accelerate it)
- after a while both spheres will be moving, so there will be air resistance on them. Thus the resultant downwards forces on both will be reduced. But because the air resistance is the same on both (at this point they are both falling at the same speed, and have the same size/shape), the resultant on the wooden sphere will have a greater % reduction, because its weight is less. So now it will accelerate at a lower rate.

Example
Ball A Mass 10 kg, Weight 100 N

Ball B Mass 1 kg, Weight 10 N

Initial acceleration:
A: a = F/m = 100/10 = 10 m/s²
B: a = 10/1 = 10 m/s²

After air resistance is providing 1 N force:
A: a = F/m = 99/10 = 9.9 m/s²
B: a = 9/1 = 9 m/s

And the reason we don't notice this is when we are dropping balls in classroom-demonstration conditions, the difference is too small to be noticed.


Or an alternative way of looking at it:
- a falling object reaches terminal velocity when the air resistance on it balances its weight, giving a resultant force of zero
- the weight of a wooden ball is less than that of a lead ball of the same dimensions, so at terminal velocity its air resistance must also be less
- as both are the same size/shape, the only factor that can cause this difference in air resistance is the speed through the air
- therefore the terminal velocity of the wooden ball must be less than that of the lead ball.


These explanations make sense to me, but I am wondering if I've missed something. Having googled, I find videos like this:
Misconceptions About Falling Objects - YouTube
which are attempting to correct misconceptions, but seem to be introducing some at the same time.

Sorry this is such a long read, but if I'm asking for a sanity check on my reasoning, I need to explain it first!

You seem to be on the ball. I'm a little confused, myself- What is the issue that's actually confusing you?

Just checking that bodies of the same shape/size but different masses really DO fall at different rates, and that my explanations for this make sense.

Originally Posted by Trilobite

Just checking that bodies of the same shape/size but different masses really DO fall at different rates, and that my explanations for this make sense.

Ah, ok. Well, if you figured all that out on your own- you're rockin.'
Here's the quick answer:
When you learn in grade school, basic Newtonian physics, tiny factors that will confuse a young student get ignored.

Such as the Earths gravity being only one factor and the lead weight having gravity as another factor. But the gravity of the lead weight is negligible. It's effect is so tiny, we can ignore it for teaching a grade school student basic Newtonian physics.
If we wanna get all stupid about claiming misconceptions, we can say the gravity of Jupiter effects the falling weight on Earth.
Have fun performing that calculation for totally unsatisfying results...

Terminal Velocity is another factor.

To give a totally different example, think of a grade school student being taught about the Atom.
The teacher shows a model that looks like one blue ball, one red ball and both are together. A wooden dowel extends from this, holding a smaller green ball at very close proximity.
Later, you get to high school chemistry, and they say, "Forget all that crap, it's rubbish." You learn that there is vast space between the nucleus and the electron. You learn that there's something called an electron cloud.
Then you get to University and they say, "Forget all that rubbish, here's a more accurate model of the atom" and so on.

The more you know, the more you can learn. So the basic teachings will ignore factors that will confuse the unready mind.

Hi Trilobite, I think your reasoning is totally sound. What we learn at school (and even at university) is a series of approximations. These get more complex (and therefore more accurate / realistic) as you learn more. But you never get to the "truth" because there are always smaller, subtle effects that could be taken into account.

Some people call this approach "lying to children," which makes it sound like a bad thing. But I think this is the only way of handliong the complexity of the real world.

Originally Posted by Trilobite

These explanations make sense to me, but I am wondering if I've missed something. Having googled, I find videos like this:
Misconceptions About Falling Objects - YouTube which are attempting to correct misconceptions, but seem to be introducing some at the same time.

What misconceptions do you think the video was introducing? The only thing I noticed was that they said the balls would be constantly accelerating, which they wouldn't once they reached terminal velocity.

Originally Posted by Harold14370

What misconceptions do you think the video was introducing? The only thing I noticed was that they said the balls would be constantly accelerating, which they wouldn't once they reached terminal velocity.

I think the video host was nitpicking, to be blunt. He made it sound like people were giving definite answers, yet many of them were shown to say "similar to" etc. The video really struck me as the host patting himself on the back for his super duper smarts.

Wasn't he saying that the balls would fall at the same speed (or accelerate at the same rate)? When I am arguing that they will not?

No, he said they do not have the same acceleration. I didn't watch the video through to it's conclusion, though. I got annoyed with it early on, but aside from being dismissive of those he interviewed, the information on physics was accurate.

OK - I have to admit to getting a bit bored so probably wasn't concentrating very well!

Originally Posted by Trilobite

When we are young, we 'know' that heavy things fall faster than lighter things.

Then we learn physics, and are told that in the absence of air, all things fall at the same rate - and we are show the grainy video of Dave Scott dropping the hammer and feather on the Moon.

Originally Posted by Trilobite

Or if you live near Boston you can go to the Museum of Science and see this in real life. There’s an evacuated tube which crops balls and feathers at the same time in a vacuum. Weird to see a feather fall like it was made of lead.

Originally Posted by Trilobite

But on Earth, the hammer and feather fall at very different rates because of air resistance. And then many/most teachers go on to say that two things the same size and shape (e.g. a wooden sphere and a lead sphere of the same size - so both having the same air resistance) would accelerate at the same rate on Earth – usually expressed as hitting the ground at the same time.

But is this last bit correct?

Originally Posted by Trilobite

No. The force due to air resistane is proportional to v^2. This points up. The force of gravity points down. The total force on a particular ballon or radius R is F = kv^2 where k is a function of the density of air and the radius of the sphere. We now find the total force which is the sum of the two

F = F(friction) + F(gravity) = kv^2 – mg

Since F = ma we have

ma = kv^2 – mg

or

a = (kv^2 – mg)/m

This shows that a is a function of m. Only when k = 0, v = 0 or m is very large does a become -g. The larger the value of m the less a is dependant on it. The larger the mass the less air resistance effects the acceleration.

Thanks for posting this. I always wondered about this but never sat down and did the math. Now I know! And its all thanks to you.

So what they must have been talking about is the simple case of v = 0.

Originally Posted by Trilobite

Wasn't he saying that the balls would fall at the same speed (or accelerate at the same rate)? When I am arguing that they will not?

Actually, you're right. He left out the fact that he was neglecting air resistance. But, for the speed of the balls when dropping a basketball and medicine ball from above one's head, the air resistance is pretty much negligible, which is why they hit the ground pretty much at the same time, at least within the accuracy of the experiment.

Equivalence principle - Wikipedia, the free encyclopedia

Drop a small stone and a large stone outside, notice how they both hit the ground at the same time, being that they have little air resistance due to shape.

Originally Posted by Devon Keogh

Drop a small stone and a large stone outside, notice how they both hit the ground at the same time, being that they have little air resistance due to shape.

And that is how misconceptions come about - if that is all you do, without explaining that their air resistance is different, and if the drop was long enough the big one would hit the ground first.

Originally Posted by Devon Keogh

Drop a small stone and a large stone outside, notice how they both hit the ground at the same time, being that they have little air resistance due to shape.

There's a good amount of drag due to air on objects such as stones moving through them. It'd be wrong to think of them as being little. Hold a ball at the end of a stick out the window of your car. The drag due to the air is pretty strong when the car is going fairley fast.

Originally Posted by pmb

Originally Posted by Devon Keogh

Drop a small stone and a large stone outside, notice how they both hit the ground at the same time, being that they have little air resistance due to shape.

There's a good amount of drag due to air on objects such as stones moving through them. It'd be wrong to think of them as being little. Hold a ball at the end of a stick out the window of your car. The drag due to the air is pretty strong when the car is going fairley fast.

I was only trying to explain that being in a short distance there is little air resistance, and that the objects fall at almost the same time, this proves Galileo's theory to be correct.

Originally Posted by Neverfly

Originally Posted by Trilobite

Just checking that bodies of the same shape/size but different masses really DO fall at different rates, and that my explanations for this make sense.

Ah, ok. Well, if you figured all that out on your own- you're rockin.'Here's the quick answer:When you learn in grade school, basic Newtonian physics, tiny factors that will confuse a young student get ignored.Such as the Earths gravity being only one factor and the lead weight having gravity as another factor. But the gravity of the lead weight is negligible. It's effect is so tiny, we can ignore it for teaching a grade school student basic Newtonian physics.If we wanna get all stupid about claiming misconceptions, we can say the gravity of Jupiter effects the falling weight on Earth.Have fun performing that calculation for totally unsatisfying results...Terminal Velocity is another factor. To give a totally different example, think of a grade school student being taught about the Atom.The teacher shows a model that looks like one blue ball, one red ball and both are together. A wooden dowel extends from this, holding a smaller green ball at very close proximity.Later, you get to high school chemistry, and they say, "Forget all that crap, it's rubbish." You learn that there is vast space between the nucleus and the electron. You learn that there's something called an electron cloud.Then you get to University and they say, "Forget all that rubbish, here's a more accurate model of the atom" and so on.The more you know, the more you can learn. So the basic teachings will ignore factors that will confuse the unready mind.

einstein said something like, most things you learn today is that the things you learned yesteday where wrong.