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!