# Air Resistance Question -- Dropping a tennis ball and a feather....

In summary, the answer to the question in the OP is that a tennis ball falls faster than a feather because the total external force on the ball per unit of mass is greater than that of the feather.
Homework Statement
Which of the following is true regarding a tennis ball and a feather dropped from the same height? Assume that air resistance acts on both objects:
A. The tennis ball has more mass so it will fall faster.
B. The tennis ball has more surface area so it will fall faster.
C. The tennis ball has less surface area so it will fall faster.
D. The tennis ball has more weight so it will fall faster.
Relevant Equations
No relevant equations that I know of except maybe air resistance
I thought the one with more mass would fall faster

No relevant equations that I know of except maybe air resistance
So what equation can you write involving air resistance and acceleration?

Btw, none of the answers is correct.

russ_watters, jbriggs444, pbuk and 2 others
E. None of the the above.

russ_watters and pbuk
Look at the options. Which one(s) (or, as the above posters are trying to make you believe, not a single one) make sense to you.

I thought the one with more mass would fall faster
Why would that be true in general? Do you think a 2oz feather would fall faster than a 1oz ball bearing?

russ_watters
haruspex said:
Btw, none of the answers is correct.
PeroK said:
E. None of the the above.
Hmm, I got the right answer. Remember, air resistance is involved...

PeroK and bob012345
berkeman said:
Hmm, I got the right answer. Remember, air resistance is involved...
You lost me on this one. How do you figure one of those answers is correct? Taken as general statements, it is easy to give counter examples to each of them.

russ_watters and PeroK
phinds said:
You lost me on this one. How do you figure one of those answers is correct? Taken as general statements, it is easy to give counter examples to each of them.
Check PMs...

Think chubby bicyclist on a downhill faster than you can pedal compared to a very light bicyclist with approximately the same surface area/air resistance...

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If you think the answer is C do you think that a feather with a surface area of 1 square centimetre (which is less than that of a tennis ball) will fall faster?

pbuk said:
If you think the answer is C
Who is "you"? The Reply/Quote feature comes in handy sometimes...

berkeman said:
Who is "you"?
Anyone that thinks the answer is "C".

berkeman
Okay, okay. We're clearly not going to help the OP if we keep kidding around. If anybody disagrees with my spoiler hint, please let me know by PM. Otherwise, the OP's answer in post #1 looks correct to me.

bob012345
Apologies, it looks like I managed to lock this thread yesterday -- I don't think I meant to do that. Thread is unlocked again.

phinds said:
You lost me on this one. How do you figure one of those answers is correct? Taken as general statements, it is easy to give counter examples to each of them.
In EMS (EMT, Paramedic) exams, often you have to pick the best alternative of the choices given, even though each one may have issues on its own. That's what I did in this case, since many bird feathers have a ##C_d## that is close to a fuzzy tennis ball.

bob012345
The correct answer is that the tennis ball falls faster because the total external force on the ball per unit of mass is greater than that of the feather. In other words, Newton's second law. The tennis ball falls faster because:
$$\frac{m_tg - f_t}{m_t} > \frac{m_fg - f_f}{m_f}$$where ##f_t, f_f## is the air resistence on the ball and feather respectively. If we take the weight of an object to be ##mg - f##, then there is nothing to say that a large feather weighs less than a small tennis ball. Weight (however you define it) does not determine acceleration.

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bob012345 and berkeman
PeroK said:
If we take the weight of an object to be ##mg - f##, then there is nothing to say that a large feather weighs less than a small tennis ball. Weight (however you define it) does not determine acceleration.
Yes, a parachute could be thought of as similar to a very large feather in this context.

PeroK
Isn't it the one with the higher density.
Think of a table tennis ball, a wooden ball and a solid steel ball, all exactly the same diameter, on a sloping ramp. Which will have the higher terminal velocity (Assuming slope is long enough)?

I use this example to explain why, if you have two identical gliders/sailplanes, but one has its wings full of, say 100kg of water in each one, then the heavier glider will fly down the same slope faster. (For any other pilots, the heavier one will have its best glide at a higher speed).

Note that there is a little bit more required to explain this, but that's what your problem is about.

DrJohn said:
Isn't it the one with the higher density.
That is not an answer to the question in the OP, but if you are asking "will an object with a higher density fall faster than an object with a lower density" then consider a bottle full of water suspended under a parachute and a bottle half full of water with no parachute. Which one has the higher density? Which one falls faster?

phinds
PeroK said:
The tennis ball falls faster because:
$$\frac{m_tg - f_t}{m_t} > \frac{m_fg - f_f}{m_f}$$where ##f_t, f_f## is the air resistence on the ball and feather respectively.
Note that this simplifies to ## g - \dfrac{f_t}{m_t} > g - \dfrac{f_f}{m_f} ##, or even simpler ## \dfrac{f_t}{m_t} < \dfrac{f_f}{m_f} ##.

So the correct answer is "the tennis ball falls faster because it has less air resistance in relation to its mass than the feather", or in the terminology of the OP and noting that air resistance is closely related to surface area, "the tennis ball falls faster because it has less surface area in relation to its mass than the feather".

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PeroK
pbuk said:
That is not an answer to the question in the OP, but if you are asking "will an object with a higher density fall faster than an object with a lower density" then consider a bottle full of water suspended under a parachute and a bottle half full of water with no parachute. Which one has the higher density? Which one falls faster?
Changing the question half way through to make my answer look wrong is really just a bad explanation.
Higher density was a hint to help work out the answer - OP has to make an intelligent guess to which one has the higher density.

For a start, you are deliberately ignoring the mass of the parachute in your rebute (the ones I had for my aircraft were about 15lbs, the one I had on my back on Saturday and Sunday was 18lbs, but I didn't have to jump out, of course)
You are ignoring the volume occupied by the parachute.
You are well aware that the shape of the parachute influences the drag, and I bet you know that a big parachute that doesn't open properly and gets entangled with itself will probably mean the user falls faster than someone using a parachute with 10% smaller total surface area but fully opened. (unless we are talking about tiny parachutes that just will not work)
You are ignoring that as a pilot I am very well aware of the effect of drag in its various types. Your answer is aimed directly at form drag (one type of parasitic drag) - caused by the shape of the object. Form drag, as we all know, increases with speed

Then you reach the same answer as me and say

"the tennis ball falls faster because it has less air resistance in relation to its mass than the feather", or in the terminology of the OP and noting that air resistance is closely related to surface area, "the tennis ball falls faster because it has less surface area in relation to its mass than the feather".

Which is saying the object with the greater density has less drag per unit volume, although the shape and hence drag will complicate things a little bit.

So have a read of my example featuring table tenis ball, wooden ball and steel ball. I know that you will get the correct answer to which will reach the highest velocity, assuming the slope is long enough for all the objects to reach their teminal velocity. But even on a medium length slope, say 10 or 15 or so metres in length, with no ball carrying a parachute just to make things clearer, we both know which one will be traveling fastest at the 10 metre mark - "The one with less air resitance in relationship to its mass". The most dense of the three.Now here's an interesting one, where many glider pilots get the right answer to the first half but give the wrong reason for their answer, but I suspect you will get it correct.

Two identical gliders (ie same model, same shape, same empty mass), with identical weight pilots are flying at the same speed (we will say fast, say 100 knots, to make this more straightforward). And are flying together at the same height. But one glider has 100kg of water ballast in each wing, the other has no water ballast on board (not any other type of ballast). Both pilots pull back on the control column by the same amount / same angle / same stick movement at the same 100 knots speed, and not at an angle that risks stalling the aircraft due to excessive g loading and huge angle of attack. And they dont' adjust the glider's flaps, either. I think I've covered all excuses or silly things and variations that would mess things up.
So.
Which one will pull up by the largest amount, and why?
(Or do they both pull up to the same height?)

Remember PE = mgh and KE = 1/2mv2
h = height of course.

Gone on, give it a try, but the reason why is the important bit ;)

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phinds
DrJohn said:
Higher density was a hint to help work out the answer - OP has to make an intelligent guess to which one has the higher density.
Cross-sectional area is more relevant than volume. The sort of "density" that you want is mass per unit of cross-sectional area in the direction of fall.

A steel wrecking ball has a higher terminal velocity than a spherical fleck of steel dust, despite having the same mass per unit volume. This is a consquence of the cube-square law.

PeroK and DrJohn
DrJohn said:
Then you reach the same answer as me and say
I would just say "shape matters"...

DrJohn and jbriggs444
pbuk said:
That is not an answer to the question in the OP
DrJohn said:
Changing the question half way through
I believe @pbuk was merely pointing out that greater density is not one of the offered answers. This was not changing the question.

DrJohn said:
noting that air resistance is closely related to surface area
DrJohn said:
Then you reach the same answer as me
Not the same. The dimensional difference between volume and area is crucial.

phinds, pbuk and PeroK

## 1. What is air resistance?

Air resistance is the force that opposes the motion of an object through the air. It is caused by the air molecules colliding with the surface of the object, creating a drag force.

## 2. Why does a tennis ball fall faster than a feather?

A tennis ball falls faster than a feather because it has a greater mass and therefore a greater gravitational force acting on it. The air resistance on the feather is also greater due to its larger surface area, slowing it down.

## 3. How does air resistance affect the speed of falling objects?

Air resistance increases as the speed of an object increases. This means that as an object falls, the air resistance also increases, slowing the object down. Eventually, the air resistance will equal the force of gravity, causing the object to reach a constant speed called terminal velocity.

## 4. Can air resistance be reduced?

Yes, air resistance can be reduced by making the object more aerodynamic, such as shaping it like a teardrop. This reduces the surface area and allows the object to move through the air more easily, decreasing the air resistance.

## 5. How does air resistance affect the trajectory of a falling object?

Air resistance can cause a falling object to deviate from its expected trajectory due to the drag force acting on it. This can cause the object to fall at an angle or even change direction. The amount of deviation depends on the shape and mass of the object, as well as the speed and direction of the wind.

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