Air resistance!! very confusing!!!

[peacefulheart]

22. Two balls are dropped from a tall tower. The balls are the
same size. but Ball X has greater mass than Ball Y. When
both balls have reached terminal velocity, which of the
following is true?
A. The force of air resistance on either ball is zero.
B. Ball X has greater velocity.
C. The Ball X has greater accelet'dtion.
D. The acceleralion of both balls is 9.8 mls'.


1. I have no problem with answer B.

2. I feel very confused about the answer explanation about this question. In Ek book, it says:'"At terminal velocity, acceleration is zero. The force of au resistance counters gravity exactly so the force is equal to the weight for both balls. Ball X requires more collisions with air molecules to compensate for the larger force of gravity. More collisions means greater air resistance."
3. In its text of EK book, it also says" Mass doesn't change the force of air resistance, but it does change the path of the projectile experiencing the air resistance."

4. Does mass change air resistance or not?

5. Could it be possible that air resistance here refers to air resistance coefficient since air resistance coefficient is only related to the density of air and surface area of subject but not the mass of subject.

thanks a lot

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[cheesier]

Air resistance is not directly related to mass, however, air resistance depends on velocity, and terminal velocity depends on mass. So, because one ball is heavier, it has a greater terminal velocity. Because it has a greater terminal velocity, it experiences a greater drag force.

 

[AdrianVeidt]

I didn't really understand this myself. I was under the impression that acceleration due to gravity is the same for any object so why would the answer not be D.

 

[peacefulheart]

I like your explanation. thanks

 

[mcloaf]

I didn't really understand this myself. I was under the impression that acceleration due to gravity is the same for any object so why would the answer not be D.

Because acceleration is only one variable in the equation for terminal velocity.

V = SQRT ( 2mg/(density of fluid through which the object is falling)(cross sectional area of object)(Drag coefficient))

So even though they have the same acceleration, because terminal velocity also depends on mass, they will not have the same terminal velocity.

Also, you could eliminate D because, by definition, at terminal velocity the falling objects are no longer accelerating.

 

[osteosurge]

I didn't really understand this myself. I was under the impression that acceleration due to gravity is the same for any object so why would the answer not be D.

No acceleration at terminal v

 

[peacefulheart]

I didn't really understand this myself. I was under the impression that acceleration due to gravity is the same for any object so why would the answer not be D.

It is only true when there is no air resistance.

 

[vneuro]

22. Two balls are dropped from a tall tower. The balls are the
same size. but Ball X has greater mass than Ball Y. When
both balls have reached terminal velocity, which of the
following is true?
A. The force of air resistance on either ball is zero.
B. Ball X has greater velocity.
C. The Ball X has greater accelet'dtion.
D. The acceleralion of both balls is 9.8 mls'.


1. I have no problem with answer B.

2. I feel very confused about the answer explanation about this question. In Ek book, it says:'"At terminal velocity, acceleration is zero. The force of au resistance counters gravity exactly so the force is equal to the weight for both balls. Ball X requires more collisions with air molecules to compensate for the larger force of gravity. More collisions means greater air resistance."
3. In its text of EK book, it also says" Mass doesn't change the force of air resistance, but it does change the path of the projectile experiencing the air resistance."

4. Does mass change air resistance or not?

5. Could it be possible that air resistance here refers to air resistance coefficient since air resistance coefficient is only related to the density of air and surface area of subject but not the mass of subject.

thanks a lot

Answers A and D are exactly the same. If answer A was true (air resistance on both balls is zero), then the only force (the net force) acting on either ball is the force due to gravity (mg).

mg = ma
a = g

If the force of air resistance on either ball is zero, then the acceleration of both balls is g (9.8 m/s^2), and therefore you can eliminate both A and D because each question can only have a single answer.

Answer C is wrong because both balls reach a terminal velocity. Terminal velocity means that velocity is no longer changing with time (duh!) (i.e. acceleration (dv/dt) is zero). Both balls have zero acceleration at terminal velocity, by definition, and therefore answer C is wrong.

Ideally, it should take you about 20 seconds to read through all 4 answer choices and realize that A and D are the same and therefore both A and D must be wrong. It should take you another 5-10 seconds to realize that "terminal velocity" by definition implies zero acceleration, and therefore answer C is wrong.

Someone who knows the formula for air resistance could - in principle - read through the question and go directly to answer B in about 10-15 seconds, but it's not necessary. A solid understanding of the basics is all you need.

 

[vneuro]

And, like mcloaf, you could also use the fact that "terminal velocity necessarily implies zero acceleration" to rule out C and D, immediately.

In fact, terminal velocity (for MCAT purposes) also implies that air resistance cannot be zero. So the simple term "terminal velocity" can actually allow you to immediately eliminate answers A, C, and D.

There are plenty of ways to answer this question, and most of them don't require detailed knowledge of the formula for air resistance and how it relates to terminal velocity.

 

[peacefulheart]

1. thanks for explanation.

2. Like I said, I have no problem with the answer. Actually, I chose the right answer. I just got confused by the explanation. Just wanna get concepts clear

 

[silverice]

Maybe I can give it a try, I think you are looking for a more intuitive explanation. Excuse my long wordy explanation.

2. I feel very confused about the answer explanation about this question. In Ek book, it says:'"
At terminal velocity, acceleration is zero.-->
I think you know this, terminal velocity means the velocity is not changing anymore, therefore acceleration is zero.

The force of au resistance counters gravity exactly so the force (of air resistence) is equal to the weight(weight) for both balls.-->
The balls was accelerating and then reach an acceleration of zero because Fnet is zero. In this problem there're only two forces acting on the balls, the force of air resistance going up; and the force of gravity going down (aka the weight of the balls).
The reason for the terminal velocity to exist (acceleration is zero) is because net force is zero.

Ball X requires more collisions with air molecules to compensate for the larger force of gravity. -->
The force of air resistance that we usually talk about is talking about the frictional force produced by collision with air molecules. Therefore, the more surface air, the more collision the higher is the resistance. You might also click now, the weight of the object doesn't matter because it doesn't affect collision with the air molecules.

There're two forces acting, air resistance and the gravity. Since the forces of air resistance for both of the balls are the same, only gravity makes a difference. Therefore the one with the higher mass has higher gravity force acting on it.

More collisions means greater air resistance." -->
This sentence is trying to remind us that the air resistance for both of the balls are the same.

3. In its text of EK book, it also says" Mass doesn't change the force of air resistance, but it does change the path of the projectile experiencing the air resistance."
I think it's trying to say if the heavy ball is having a greater velocity it is colliding with the molecule faster? I'm not sure. What do you think it means?

4. Does mass change air resistance or not?
The force of air resistance that we usually talk about is talking about the frictional force produced by collision with air molecules. Therefore, the more surface air, the more collision the higher is the resistance. You might also click now, the weight of the object doesn't matter because it doesn't affect collision with the air molecules. The mass doesn't change air resistance.

5. Could it be possible that air resistance here refers to air resistance coefficient since air resistance coefficient is only related to the density of air and surface area of subject but not the mass of subject.
I don't think so. But I'm not 100% absolutely positive.

thanks a lot

 

[milski]

Here is the abbreviated version:

Terminal velocity => velocity is constant => acceleration is zero, c & d are gone
A is obviously wrong anyway.
acceleration 0 => net force on each ball is 0. The heavier ball has larger gravity force acting on it => air resistance of it is larger. air resistance depends on shape and velocity. Since the balls are the same, the only way to get more resistance for the heavier ball is to have it move faster => b confirmed.