Circular Motion of a motorcycle

[clipperdude21]

Circular Motion! :)

1. 12. A motorcycle moves in a horizontal circular path on the inside surface of a vertical
cylinder of a radius 8 m. Assuming that the coefficient of static friction between the
wheels of the motorcycle and the wall is 0.9, how fast must the motorcycle move so that
it stays in the horizontal path?



2. Fc=mv^2/R, Force friction= uN, Fg=mg



3. The way I did it was I did the sum of forces in the y direction as sum of forces in the y direction=uN-mg=0. I solved for N and got N=mg/u.

I then plugged it into Force centripetal=N. I got mv^2?r= mg/u. I solved for v and got +/- 9.333 m/s. Did I do this right? :) Thanks!

 

[Astronuc]

Yes, the answer is correct. In this case the motorcyclist could travel in either direction with the same magnitude of tangential velocity.

A more straightforward approach to the problem would be to realize that

$$\mu \frac{mv^2}{r}\,=\,mg$$ and the m's divide out so

$$\mu \frac{v^2}{r}\,=\,g$$ or

$$v\,=\,\sqrt{\frac{gr}{\mu}}$$