How to solve for drag coefficient/terminal velocity?

[jonny7777]

[SOLVED] How to solve for drag coefficient/terminal velocity?

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i was told by a classmate that all i need to do is take distance over time. :)

thanks anyway







I am doing a lab and I need to solve for both the drag coeffient and the terminal velocity for dropped coffee filters. I have values for the drop height (4.66m), (and also the resisitive force) the cross-sectional area (1.2 m^3), the time (varies, but let's say 1.47s), and the mass (also varies, will say .0046 kg), and also the density of air (1.2 kg/m^3). I can't seem to figure out the drag coeefecient or the terminal velocity, although my teacher seemed to indicate that the terminal velocity must be found first. Any help would be much appreciated.

I have a feeling i must use Tao, if you know what that is. I believe it is 63% of the time it takes to reach terminal velocity. I also know the equation V = Vterm (1-e^(-t/tao)). but i don't know how to use it. Then there is the equation D = (2mg)/(Vterm^2*pA). Aany help would be great as i have been stumped for hours

Please help me, I've tried a lot of things but how do you solve for two unknowns?
Thanks in advance

 

[lippyka]

!To solve for the drag coefficient and terminal velocity, you can use the equations V = Vterm (1-e^(-t/tao)) and D = (2mg)/(Vterm^2*pA). You can rearrange the V equation to solve for Vterm, and then substitute that value into the D equation to find the drag coefficient. To solve for Vterm, first isolate Vterm on one side of the equation. Then, take the natural logarithm of both sides. This gives you ln(V/Vterm - 1) = -t/Tao. Rearrange this equation to make Vterm the subject. This gives you Vterm = V/(1-e^(-t/Tao)). Substitute the values you know (drop height, cross-sectional area, time, mass, and density of air) into the equation and solve for Vterm. Once you have Vterm, substitute it into the second equation to solve for the drag coefficient. This gives you D = (2mg)/(Vterm^2*pA). Again, substitute the values you know into the equation and solve for D.