Falling objects: Tennis ball vs. feather

[Bailey]

Assuming air resistance, when a tennis ball and a feather are dropped from the same height? Which statement is true:

A: Tennis ball has more mass so it will fall faster.
B: Tennis ball has less surface area so it will fall faster

I think the answer should be A, but the textbook say B is true base on the reasoning that surface area is proportional to air resistance. My arguments are as follows:

1. The question does not suggest a feather have a greater surface area than a tennis ball. I can picture the size of a tennis ball, but size and shape of feather varies depending on the source.

2. Assuming if they explicitly state that cross-sectional surface area is greater for the feather, wouldn't the mass still play a greater effect due to the greater difference in mass between the objects vs. the difference in cross-sectional areas.

Thank you.

 

[Nugatory]

Neither A nor B are correct; if your book says B either it's wrong or you're misunderstanding what it's saying. What matters is the ratio of mass to surface area, and that is greater for the tennis ball.

 

[Bailey]

Neither A nor B are correct; if your book says B either it's wrong or you're misunderstanding what it's saying. What matters is the ratio of mass to surface area, and that is greater for the tennis ball.

But in this case, wouldn't the mass is the main factor in contributing to the difference in ratio? So wouldn't A be "more" correct than B given those two choice.

Here is the full solution in the book:
The force of air resistance is dependent on the surface area, the shape, and the velocity of an object; the object's mass does not affect it. Surface area is directly proportional to air resistance. The feather has a larger surface area and experience greater resistance, or upward force. This results in smaller net force and smaller acceleration downward. Acceleration due to gravity is the same for all objects near Earth's surface regardless of mass.

Edits:
Here a link I found that kinda explain why it is the mass that play a bigger role:
http://www.physicsclassroom.com/mmedia/newtlaws/efar.cfm

 

[Drakkith]

But in this case, wouldn't the mass is the main factor in contributing to the difference in ratio? So wouldn't A be "more" correct than B given those two choice.

No. It just happens to be the case that the tennis ball is much more massive than the feather, but I can easily imagine an object with the same mass as the tennis ball yet a hundred times its surface area. The surface area is just as important as the mass of the object. Neither one has a greater effect than the other unless you directly specify some arbitrary criteria.

Here is the full solution in the book:
The force of air resistance is dependent on the surface area, the shape, and the velocity of an object; the object's mass does not affect it. Surface area is directly proportional to air resistance. The feather has a larger surface area and experience greater resistance, or upward force. This results in smaller net force and smaller acceleration downward. Acceleration due to gravity is the same for all objects near Earth's surface regardless of mass.

In my opinion, you should probably burn this book and never look at it again. This is a ludicrous explanation. As Nugatory explained, it's the ratio of the mass to the surface area that determines the acceleration through the air. This comes about because the downward force of gravity increases with mass while the force from air resistance increases with surface area. I have no idea why they are even bringing in the acceleration of gravity as part of the explanation. You aren't even using the acceleration under gravity, but the force.

I cannot stand these 'cause and effect' style question. They are absurdly easy to mislead students with. For one, there usually isn't a single cause, as the question in your example shows. Both A and B are potentially true.

 

[A.T.]

Here is the full solution in the book:
...The feather has a larger surface area ...

There are feathers smaller than a tennis ball, but still fall slower.

 

[russ_watters]

Here is the full solution in the book:

But what was the exact question?

 

[Jobrag]

Go back to basics, if you're on the moon which would drop faster, the feather or the tennis ball, Google hammer and feather on the moon, there must be a you tube video out there. Having seen what happens on the moon think about what would happen on Earth.

 

[PeterDonis]

if you're on the moon

The moon has no air, so no air resistance. The OP explicitly said "assuming air resistance".

 

[PeterDonis]

the textbook say B is true base on the reasoning that surface area is proportional to air resistance.

To see the flaw in this argument (which is basically that the mass of the object doesn't matter), consider a tennis ball and an oversized ping-pong ball that's the same size as the tennis ball (but obviously much less massive). If surface area were the only factor that mattered, both of these would fall at the same rate. Do they?

Or, to be even more extreme, consider a ping-pong ball and a ball of lead of the same size.

In fact, you could do the experiment with an actual tennis ball and an actual ping pong ball; if smaller surface area means falling faster, the ping pong ball should fall faster than the tennis ball. Does it?

 

[Jobrag]

The moon has no air, so no air resistance. The OP explicitly said "assuming air resistance".

Yes it does, but by considering the case without air resistance you can dismiss answer A, and then unpick the bad wording of answer B.

 

[A.T.]

by considering the case without air resistance...

...you fail to answer the question.

 

[my2cts]

A rocket can have a large surface and still meet relatively little resistance.
Burn the book.

 

[litup]

Or, alternatively, you could just get a couple of feathers of different sizes and a tennis ball and drop them about 7 or 8 feet off the ground, inside with no wind, and just watch. My incredibly intuitive prediction: Tennis ball 1, feather 0. Tennis ball gets down faster. For one thing, the feather won't even fall straight down, it will wiggle from side to side on its way down so it will travel more distance than the ball which will fall more or less straight down. THEN throw out the book.

I assume you know you drop the same objects on the moon with no air they hit the ground at the same time, no matter how high they are dropped.

 

[PeterDonis]

by considering the case without air resistance you can dismiss answer A

No you can't. The mass of an object does affect how fast it falls when air resistance is present, even though it doesn't when air resistance is not present.

 

[Glurth]

>>The force of air resistance is dependent on the surface area, the shape, and the velocity of an object; the object's mass does not affect it.

Note it is referring to the FORCE of air resistance. The actually change in the velocity of this object, because of this force, will depend upon the mass of the object. ( F=ma )
So I'd have to say this text is technically correct.

 

[A.T.]

So I'd have to say this text is technically correct.

"Surface area is directly proportional to air resistance. The feather has a larger surface area and experience greater resistance, or upward force. This results in smaller net force..."

This assumes that all other forces (like weight) are the same. Otherwise you know nothing about the net force.

 

[Glurth]

>>This assumes that all other forces (like weight) are the same. Otherwise you know nothing about the net force.

I don't see why that statement needs to make any such assumption. I agree that to compute the actual NET force you will need to know the weight. However, it is true to state that, regardless of the weight, the greater the air resistance upward, the less the NET force downward. F_net = F_weight + -F_{airresistance}

Don't get me wrong, the initial question from the textbook is awful. The only way it makes sense is if you use the statement-part of the answers, as information available to answer the question: "Tennis ball has more mass", and "Tennis ball has less surface area"

 

[A.T.]

regardless of the weight, the greater the air resistance upward, the less the NET force downward.

No, you cannot say that the net force is less, without making any assumptions about weight.

 

[nasu]

Note it is referring to the FORCE of air resistance. The actually change in the velocity of this object, because of this force, will depend upon the mass of the object. ( F=ma )
So I'd have to say this text is technically correct.

The question is about which go faster so exactly about the change in velocity you mention. It is not about comparing forces of resistance but velocities

 

[Glurth]

You are right; I was assuming weight stayed the same, and air resistance changed!

Still, I don't see why the book statement I vouched for needed to make that assumption, it doesn't even reference the net force:
>>The force of air resistance is dependent on the surface area, the shape, and the velocity of an object; the object's mass does not affect it.

 

[A.T.]

I was assuming weight stayed the same...

That's what the book author apparently assumed too, to then conclude that the weight plays no role.

 

[nasu]

He assumed that a tennis ball and a feather have the same weight?

 

[A.T.]

He assumed that a tennis ball and a feather have the same weight?

And the same shape. That's the only way to conclude that only the surface area affects the falling velocity.

 

[nasu]

This look like trying to find some contorted way to make a holy book right when it is actualy just simply wrong.

 

[Lsos]

Go back to basics, if you're on the moon which would drop faster, the feather or the tennis ball, Google hammer and feather on the moon, there must be a you tube video out there. Having seen what happens on the moon think about what would happen on Earth.

The video you speak of is now obsolete :

 

[Chestermiller]

Let's see what the math tells us. The force balance on the falling object is pretty simple:

$$ma=W-F$$

where F is the drag force and W=mg is the weight of the object. Rewriting the equation a little differently, we obtain:

$$\frac{a}{g}=1-\frac{F}{W}$$

So, the downward acceleration in g's is equal to 1 if the air drag force is zero. But, if it is not zero, the downward acceleration is determined by the drag force divided by the weight. This is the key dimensionless group. Note that both the drag force and the weight are important. The drag force is determined by the shape of the object (including surface area), and the weight is determined by its mass. Clearly the ratio of the drag force to the weight is less for a tennis ball than for feather. Big surprise. But it is neither the drag force nor the weight alone that tells the whole story. It is their ratio that matters.

Chet