Question

I am doing a physics lab report, but I need some help with the math involved. The lab involves dropping different numbers of coffee filters (n) off a balcony and recording the time of descent. We're talking about terminal velocity and drag forces.

Task 1: Derive a general equation for the velocity v^n of a stack of n coffee filters each of mass m falling through the air after terminal velocity has been achieved.
I really need help understanding what to do. We know that F = bv + cv^2, and that for a slow moving object such as a coffee filter falls, the cv^2 term is effectively 0.

Answer 1

I have more information on what we have to do for this lab, there are 2 other tasks, but as the question box only has so much room I'll wait until they're needed.

Answer 2

Help is sincerely appreciated if you know how to do it!

Answer 3

Hello! Sounds like a fun lab!

There are two ways of looking at this. The first way is more technical, for the lab. The second is for you guys.
1. Usually, a good place to start when studying motion is the "equation of motion."
You know of \(F=ma\) at this point. Now it can be applied! At terminal velocity, velocity is [terminal] unchanging. \(F=m(0)=0\); no acceleration means no net force! So forces must cancel.
2. More intuitively, if there's no acceleration, there's no net force.

So, what are the forces? Because they add up to zero!

Gravitational force, for one, and drag force (that's two).
Gravitational force can be found using gravitational acceleration and mass, which I'm sure you've done.

And your lab has been designed to work nicely with the math!
Since you only care about the situation after terminal velocity is attained, and you will ignore \(cv^2\) at terminal velocity... You can just say \(cv^2\approx0\) when you see it in your equation.

Good luck with your lab! Feel free to ask any questions! If I'm not here, others still will be :)