Terminal Velocity Lab: Finding Constant C in Fdrag=Cv^N

[dranseth]

Homework Statement

We did a lab that was about terminal velocity; we had to drop coffee filters from different heights, and we had to take down data.

We were given a formula

Fdrag=Cv^N
where C is a constant, and N=1.

I have no clue how to find the constant C, can someone help?

Homework Equations

The Attempt at a Solution

 

[hunter151]

Assuming you took data of how long it takes the filter to fall from a given hight, I would do it like this:

Find the velocity the filter falls with. You can assume it reaches terminal velocity immediately, so the velocity you find is the terminal velocity. The filter is then falling at constant velocity (acceleration = 0), so you are faced with a body in equilibrium (net force = 0). Look at the forces acting on the body, equate them, and the solution presents itself.

 

[dranseth]

thanks a lot. What type of relationship relates between Fdrag and velocity (the mathematical relationship?)

 

[hunter151]

You wrote it in your post, Fdrag=Cv^N...

 

[dranseth]

I know, I forget the mathematic terminology though. I don't know how to describe the relationship. Also, when it says find the constant, the constant is going to be different when we use one filter than if we use two filters (one on top of the other) right?

 

[hunter151]

Fdrag is directly proportional to v.

From a physical standpoint, the constant shouldn't be different. You will have a larger terminal velocity, but the mass is also larger, thus Fdrag will be larger. Experimentally your constant will differ of course, but I would expect it to be somewhat close.

 

[dranseth]

My teacher was extremely vague for this experiment. He asked us to calculate what C is, but we have four different velocities for both the single filter and the double. I'm guessing he wants us to calculate the value of C for all of them... but I am not sure

 

[hunter151]

I would average the velocities for the single filter and find c for that. Then average the velocities for the double filter and find c for double. The coefficient of drag (c) is mainly dependent on the cross sectional area of the object, and in your case it doesn't change much from one filter to two. Thus it may make sense to average out the two cs you get for single and double filters.

 

[dranseth]

One last question. What does the constant C represent anyways? I calculated everything, and the units were kg/s in the end.

 

[hunter151]

Its the drag coefficient. It represents how hard air will slow the object down when it is being pushed through. Its kind of like the coefficient of friction, only friction here is with air. The higher the coefficient, the harder it is to move the object through air (or any other fluid).

 

[mysqlpress]

at time = infinity
the v would become a constant and equal to mg/C (the weight is balanced by the drag force)
and in fact, what kind of data did you gather?
what measurements did u use?