Terminal velocity of a coffee filter

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SUMMARY

The discussion revolves around calculating the upward force of air resistance on a coffee filter and a stack of filters as they fall from a height. The individual coffee filter, with a mass of 1.2 grams, reaches terminal velocity, where the upward force of air resistance equals its weight (Fair = mg). For the stack of six filters, the total mass is 7.2 grams, leading to a proportional increase in air resistance. The time taken for the stack to hit the ground is estimated using the drag equation, although the exact calculation requires additional information.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with the concept of terminal velocity
  • Basic knowledge of forces, specifically weight and air resistance
  • Introduction to the drag equation in physics
NEXT STEPS
  • Explore the drag equation and its application in calculating terminal velocity
  • Research the effects of mass on terminal velocity in free fall
  • Investigate how air resistance varies with shape and surface area
  • Learn about the dynamics of falling objects in fluid mechanics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and forces, as well as educators looking for practical examples of terminal velocity and air resistance in real-world scenarios.

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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.
 
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