What is the minimum radius that cyclist can ride around without slipping a 10 km/hour if the coefficient of friction between his tires and the road is .5?

The answer is 4.1 m

How do you do this problem I am pulling my hair out with these kind of physics problems. Any help would be appreciated. Thank you

This is in relation to centripetal force. They basically want you to relate how the static coefficient of friction and centripetal force work. It sounds kind of tricky, but if you just draw a diagram, the answer will come to you.

The coeffecient of friction is what is making the cyclist stay inside of the circle, and the equation is equal to uk * Fn. The only other force is the F = m x a and the acceleration is the centripetal force.

Thus

fn = F

ukFn = m x a

uk mg = m a (a = centripetal force = v^2/r)

The masses cross each other out and you have

ukg = a

now all you need to do is calculate for R. Remember, you also need to convert km/h into m/s.

0.5 x 10 = X/R

10 km/hr * 1000m/km * 1hr/60min * 1min/60 seconds = 2.8 m/s

- edit -

wait 4.1 m/s? Did you give us the correct values?