Air resistance and more massive objects falling faster

[ThujaOccidentalis]

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This question is from EK
"Which of the following is true regarding a tennis ball and a feather dropped from the same height? Assume air resistance acts of 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 falls faster.

The answer is C. I agree. But why are A and D incorrect?

Argument for A: Force of air resistance is not dependent on mass, rather on velocity, surface area, and shape. I get it. But F=ma, so a more massive object (given that the force is constant) will feel less of an acceleration, due to air resistance, in the opposite direction of fall.

Argument for D: An object falls and accelerates until it reaches air resistance of equal magnitude to the force of it's weight. So a heavier object will be able to fall and accelerate more than a lighter object, because it takes a longer time for the force of air resistance to equal the force of its weight.

Is there something I'm misinterpreting?

 

[bee17]

acceleration in this case is constant, because it is equal to gravity (9.8 m/s^2)
In the absence of air resistance, two objects of different masses/weights, when dropped from the same height, will always hit the ground at the same time. Air resistance is what causes the feather and tennis ball to fall at different speeds.
See Galileo: https://en.wikipedia.org/wiki/Galileo's_Leaning_Tower_of_Pisa_experiment

 

[Pediateix]

ye i don't get it. why is air resistance dependent on cross section area. wha tif something small has a greater weight, will it still fall later?

 

[aldol16]

ye i don't get it. why is air resistance dependent on cross section area. wha tif something small has a greater weight, will it still fall later?

Yes. You seem to be missing the key concept here. Everything experiences the same acceleration due to gravity. Therefore, when you drop anything, it will experience at the same rate as anything else, regardless of its mass. Remember when the astronauts on the moon dropped a feather and a hammer on the moon? They hit the ground at the same time because there was no air resistance. Mass doesn't matter because acceleration due to gravity is a constant.

Air resistance is dependent on cross-sectional area because it basically arises due to the upward push of air particles on a surface. The larger the surface, the more area exposed to the particles.

 

[bears1992]

ye i don't get it. why is air resistance dependent on cross section area. wha tif something small has a greater weight, will it still fall later?

This answer in not 100% true. Air resistance is related to the drag coefficient which is dependent upon shape of the object and the surface area (all dependent on the orientation). This force is not proportional to the mass or weight in anyway. The force of gravity is proportional to the mass. Increasing only the mass will make the gravitational force get bigger while not affecting the drag force, thus increasing the speed of the tennis ball (making A and D true). An decrease in the surface area will decrease the drag force while not affecting the gravitational force, thus increasing the speed of the tennis ball (Making C true)

None of the answer choices by themselves will give you any indication of which falls faster with air resistance. The only one that does not make sense is B.

Source: Mechanical Engineer

 

[aldol16]

This answer in not 100% true. Air resistance is related to the drag coefficient which is dependent upon shape of the object and the surface area (all dependent on the orientation). This force is not proportional to the mass or weight in anyway. The force of gravity is proportional to the mass. Increasing only the mass will make the gravitational force get bigger while not affecting the drag force, thus increasing the speed of the tennis ball (making A and D true). An decrease in the surface area will decrease the drag force while not affecting the gravitational force, thus increasing the speed of the tennis ball (Making C true)

The gravitational force getting larger does not affect the acceleration due to gravity. Since F = m*a, when m increases, F gets bigger without necessarily causing an increase in a. That's why a = g for falling objects on Earth - and why g is constant. So the speed of the tennis ball should not increase. This is also the reason why a hammer and feather, when dropped on the moon, hit the ground at the same time.

 

[bears1992]

The gravitational force getting larger does not affect the acceleration due to gravity. Since F = m*a, when m increases, F gets bigger without necessarily causing an increase in a. That's why a = g for falling objects on Earth - and why g is constant. So the speed of the tennis ball should not increase. This is also the reason why a hammer and feather, when dropped on the moon, hit the ground at the same time.

It does not affect the acceleration of gravity but it does affect the acceleration of the tennis ball because the drag force is taken into account. The total force acting on the ball is the force of gravity minus the drag force. The force of gravity will increase with mass while the drag force will not. The total force divided by the mass is the total acceleration which is what is increasing when the mass is increased. The Apollo video is an example of what happens without a drag force. This question stats that drag force is to be taken into account.

I don't really know much more than the basics for chem/bio/english/psych but I've had 5 years worth of fluids classes and this is fluids 101.

 

[aldol16]

It does not affect the acceleration of gravity but it does affect the acceleration of the tennis ball because the drag force is taken into account. The total force acting on the ball is the force of gravity minus the drag force. The force of gravity will increase with mass while the drag force will not. The total force divided by the mass is the total acceleration which is what is increasing when the mass is increased. The Apollo video is an example of what happens without a drag force. This question stats that drag force is to be taken into account.

Ah, I see. Thank you for your insights.

 

[bears1992]

Ah, I see. Thank you for your insights.

This was like the one question in this entire forum that I could actually answer lol.