Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Drag force/difficult integral.

  1. Sep 3, 2008 #1
    1. The problem statement, all variables and given/known data
    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


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

    newton's second law



    3. 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.
     
  2. jcsd
  3. Sep 4, 2008 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Maybe you can use
    [tex]\frac{\mathrm d}{\mathrm dx} \operatorname{arctanh}(x) = \frac{1}{1 - x^2}[/tex]
     
  4. Sep 4, 2008 #3
    yeah, i was able to get it to that form and it worked. Thanks.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook