Terminal velocity of a coffee filter

[rkjul]

Homework Statement

You drop a single coffee filter of mass 1.2 grams from a very tall building, and it takes 47 seconds to reach the ground. In a small fraction of that time the coffee filter reached terminal speed.

(a) What was the upward force of the air resistance while the coffee filter was falling at terminal speed?


(b) Next you drop a stack of 6 of these coffee filters. What was the upward force of the air resistance while this stack of coffee filter was falling at terminal speed?


(c) Again assuming again that the stack reaches terminal speed very quickly, about how long will the stack of coffee filters take to hit the ground?

Homework Equations

Fair=mg

The Attempt at a Solution

I got the first two parts by setting Fair=mg since these forces are equal in magnitude once terminal velocity is reached (zero net force) but I am seriously stumped on the third part. I thought about the drag equation but I don't see how it's possible to use that with the amount of information I have.

 

[learningphysics]

Have a look at this thread:

https://www.physicsforums.com/showthread.php?t=190623

I describe how to do that last part.

 

[m2003]

Terminal velocity is the maximum velocity an object can reach when falling through a fluid, such as air. It occurs when the force of air resistance is equal in magnitude to the force of gravity, resulting in a net force of zero and a constant velocity. In this case, the coffee filter has reached its terminal velocity within a fraction of the total time of 47 seconds.

(a) To calculate the upward force of air resistance while the coffee filter is falling at terminal speed, we can use the equation F_air = mg. Plugging in the mass of the coffee filter (1.2 grams) and the acceleration due to gravity (9.8 m/s^2), we get an upward force of 0.01176 N.

(b) When a stack of 6 coffee filters is dropped, the total mass is now 7.2 grams. Using the same equation as before, the upward force of air resistance is now 0.07056 N.

(c) To estimate the time it takes for the stack of coffee filters to reach the ground, we can use the fact that the time it takes for an object to reach terminal velocity is dependent on its mass and the force of air resistance. Since the mass of the stack is 6 times that of a single coffee filter, we can estimate that it will take approximately 6 times longer for the stack to reach terminal velocity. Therefore, it would take approximately 6 x 0.47 seconds, or 2.82 seconds, for the stack of coffee filters to reach the ground. This is assuming that the stack reaches terminal velocity quickly, as stated in the problem.