Linear and Angular motion and Friction

[Sparky500]

Homework Statement

Calculate the maximum speed with which a vehicle can travel round a horizontal bend of radius 40m without skidding if the coefficient of friction between the tyres and the road is 0.6.

Homework Equations

v=sqrt μrg

The Attempt at a Solution

v=sqrt 0.6 x 40m x 9.81m/s^2

v=15.34m/s

Therefore the maximum speed would be 15.34m/s

Can someone please confirm that this is correct and if not please point me as to which i have gone wrong, i am not looking for the answer just direction.

Many thanks

 

[berkeman]

Your answer looks correct to me. Do you understand how to derive the equation for v directly?

 

[Sparky500]

Thanks for your prompt response.

The equation was given in the question and i only had to apply the numbers correctly so i guess the answer would be no.

 

[berkeman]

Thanks for your prompt response.

The equation was given in the question and i only had to apply the numbers correctly so i guess the answer would be no.

Well, it's good to understand where the equation came from, because it will help you in the future as you work through more problems.

The centripetal force to make the object go in the circle is $$F = \frac{m v^2}{r}$$

and that force is supplied by the horizontal friction force $$F = \mu N$$

where N is the normal force down by the mass into the ground (which generates the horizontal friction force).

That normal force is just the weight of the object, $$F = m g$$

So now you should be able to do the algebra to derive the equation that you used for the max velocity that can be sustained for the given coefficient of friction mu...