Air Resistance Question

[dray5150]

Question from EK 1001 Physics:

Person A and Person B parachute from a plane. Person A weighs twice as much as person B. Both move at a constant velocity once their shutes open. Compared to the force of air resistance on the chute of Person B the force of air resistance on the chute of Person A is:

a. half as much
b. the same
c. twice as much
d. four times as much

C is the right answer which is confusing b/c I though Mass does not affect air resistance and the answer would be the same. Only things like surface area, shape, and velocity I though affects air resistance.

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[MBHockey]

Mass doesn't affect air resistance per se. But mass does affect the force of gravity on each person, which is what drag is equal and opposite to when one has reached terminal velocity.

The question is referring to terminal velocity. This is the fastest speed you can reach when free falling towards earth (relatively speaking). To really understand terminal velocity, you have to understand why you don't perpetually speed up until you crash into land.

When you first jump out of the plane, your initial velocity (y-direction) is zero. You immediately begin speeding up (accelerating at g) towards earth. So why would you ever stop accelerating? It might seem that you'd keep speeding up until you hit the ground. But this is not the case.

The whole time you are in free fall air resistance is opposing your downward motion (it's just friction, so it acts just as friction does upon a block moving along a surface to the right -- friction acts to the left). You keep accelerating the opposing drag force is equal to your body weight. Once this point has been reached, you are moving at a constant terminal velocity.

Even though air resistance isn't a function of mass it is equal to your body weight (mg) at terminal velocity and that is how it's related. The heavier person must experience a higher drag force than a skinner one once both have reached terminal velocity.

Think of it on land. Say you are trying to pull a rope attached to a Mini Cooper and then one that is attached to an 18-wheeler. It takes a lot more force (analogous to the force of gravity opposing the drag force in the parachute example) pulling on the rope to get the 18-wheeler moving at a constant velocity than it would to get the mini cooper going at a constant velocity.

Don't confuse this force with acceleration. Assuming no air resistance (or equal drag coefficients), two objects chucked out of a plane will hit the earth at the same moment. Acceleration due to gravity does not depend upon mass, but the force of gravity does...but force does not equal speed.

 

[dray5150]

Great explanation!! Really appreciate you clearing that up. Makes total sense now.

 

[MBHockey]

I'm glad you could make some sense out of that long-winded story. I wasn't sure how clear it was