Finding the Angle for Safe Max Speed on Unbanked Curve

[aimslin22]

A car can negotiate an unbanked curve safely at a certain max speed when the coefficient of static friction between the tires and the ground is 0.88. At what angle should the same curve be banked for the car to negotiate the curve safely at the same maximum speed without relying on friction?

Homework Equations

Normal force = N
angle = Q
friction = f

NycosQ = mg + fsinQ

NxsinQ + fcosQ = mvˆ2/r

The Attempt at a Solution

Both equations simiplify to:

vˆ2 = gr*((sinQ + μcosQ)/(cosQ - μsinQ))

I know I am suppose to find the speed first, which I have no idea how to find. Then, how would I find the angle?

 

[alphysicist]

Hi aimslin22,

What is the angle for the first situation (the unbanked curve)? What is the coefficient of friction for the second situation (the banked curve)?

 

[aimslin22]

That was all the info I was given, but my teacher went over it today. Thanks though!