Can a Car Safely Turn on a 40-Degree Banked Road at 30 m/s?

[dk2421]

Homework Statement

Will a road banked at 40 degrees allow cars (u=0.6) to safely make a turn (radius=100m) while traveling at 30 m/s (or 67 mi/hr)?

Homework Equations

f = uN
possibly others

The Attempt at a Solution

I'm really not sure how to get started. This is the only problem I don't know how to do. I would really appreciate any help. Thank you.

 

[LowlyPion]

Welcome to PF.

Draw a force diagram on the car.

Gravity is vertically down, so the components of weight can be resolved as vectors along the incline and normal to the incline.

The centripetal acceleration is acting horizontally. Its components can also be resolved along the plane of the incline and normal to it.

If the downward force of gravity and the additional maximum contribution from the friction component is sufficient to prevent the car from slipping then ...