Help with Mechanics - Circular Motion

So the question states;
"A corner on a flat surface forms a circular arc with the radius 50m. A car travels around the corner at 14m/s without sliding. What information does this give for the value of the coefficient of friction between the tyre and the road surface?"
So far I've discovered the angular velocity which is 0.28rad/s (if I calculated that correctly). But I'm not sure where to go from there?

Think about the centripetal forces involved here. Which centripetal force enables the car to travel through the arc without sliding off it?

Equate this centripetal force with an expression which you should be familiar with:

$F_c = \dfrac{m v^2}{R} = mR\omega^2.$

This is the right idea, but we're looking for an inequality, not an equation. Bear in mind that the coeff. of friction is used in the expression for *limiting* friction.

Thank you all for your help! Any chance I could ask about a few more? I'm finding these questions fairly tricky

Sure, ask away

Ah thank you so so much!
Sorry to be a pain but I have a few more hahah
"One end of a light inextensible string 1m is attached to stationary point A and particle P with mass m is attached on the other side. A second string 1m long is attached to P and stationary point B so that B is lying 1.5m vertically under A. The particle is made to move in a horizontal circle with the uniform angular velocity w. Calculate the lowest value for w so that the strings are tight."

Technically what he says is exactly right, you just introduce the inequality at a later stage.

CF = mrw^2
CF = friction
Friction <= u R (where u is coefficient of friction and R is reaction)
Therefore (CF/R) <= u
u >= (mrw^2)/R

This is true - he wasn't incorrect, but I felt that what he wrote could come across as misleading - the inequality is the crux of the question.



Please don't give complete solutions - they are forbidden by the forum power's-that-be.