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Drag force/difficult integral.

  • #1

Homework Statement


If a ping pong ball is released from rest, how long does it take for the ping pong ball to reach 90% of its terminal velocity?

m=2.2g, density(air)=a.29kg/m^3, Cw=.5, diameter=.38mm


Homework Equations


Fd=1/2*C[tex]_{w}[/tex]+[tex]\rho[/tex]*A*v^2

newton's second law



The Attempt at a Solution



I set up newtons second law for the going down case. I wanted to get v in terms of t.
I can't solve the integral though.

Fd-mg=m*dv/dt

[tex]\int \frac{dt}{m}[/tex]=[tex]\int \frac{2*dv}{C_{w}*\rho*A*v^2-mg}[/tex]

Please help.
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
47
Maybe you can use
[tex]\frac{\mathrm d}{\mathrm dx} \operatorname{arctanh}(x) = \frac{1}{1 - x^2}[/tex]
 
  • #3
yeah, i was able to get it to that form and it worked. Thanks.
 

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