Equation for Solving v: Steps, Tips & Results | Did I Solve it Right?

  • Context: Undergrad 
  • Thread starter Thread starter ektrules
  • Start date Start date
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
1 reply · 2K views
ektrules
Messages
35
Reaction score
0
Here's the equation.
[tex]\frac{mv^{2}}{r}=\frac{mg+C_{a}v^{2}cos\vartheta}{cos\vartheta-\mu sin\vartheta}\left(\mu cos\vartheta+sin\theta\right)-C_{a}v^{2}sin\vartheta[/tex]
After trying to solve for v, I got this:
[tex]v=\sqrt{\frac{mg\mu cos\vartheta+mg sin\vartheta}{-2\mu C_{a}cos\vartheta-2\mu C_{a}sin\vartheta+\frac{mcos\vartheta-\mu msin\vartheta}{r}}}[/tex]
I'm not sure if this is correct though. I never took trig, so all the sin's and cos's confuse me, and I'm not exactly sure how to perform algebra on them.
 
Physics news on Phys.org
I haven't checked your result. However, solving for v doesn't require knowing trig. Just put all the v2 on one side of the equation, and put all the other terms on the other side. Then divide by the coefficient of v2 and take the square root.