What Should the Banking Angle Be to Prevent a Car from Sliding?

[AHinkle]

Homework Statement

Homework Equations

\SigmaF=ma
a_c=(v^2/r)
f = \muN

The Attempt at a Solution

\SigmaF_radial= (radial-coordinate of normal force) + (radial component of friction) = ((mass)(velocity^2)/(radius))
\SigmaF_y= (y-component of normal force) - (y-component of friction) = (mass)(gravity)

\SigmaF_radial= Nsin\theta+\muNcos\theta = (mv^2/r)
\SigmaF_y=Ncos\theta - \muNsin\theta = (mg)

I divided the equations for F_radial by the equation for F_y
and it yielded...

tan\theta = (v^2-\murg)/(rg+\muv^2)

so in order to find theta which I am looking for

\theta= arctan (v^2-\murg)/(rg+\muv^2)

but I have 2 unknowns...
we know
V_max = 100km/h which is approx 27.78 m/s
g = 9.81 m/s^2 (this is given in the problem)
r= ?
\theta = ?
\mu= 0.22

also I am not sure how to conceptualize the part of the problem where i need to find out what theta needs to be to keep the car from sliding in the ditch.
I feel i can find the upper limit but not the lower. I thought about subbing something in for r to find theta but I'm stumped.

 

[dacruick]

what do you have so far? If nothing mathematical, what concepts are you thinking about?

 

[AHinkle]

im trying to get it to work, and the symbol stuff is screwing up.. how do i delete the post and start over?

 

[dacruick]

Just start A new post I suppose.

 

[AHinkle]

okay i fixed everything, please help me out. The homework is already turned in, I just want the knowledge..

 

[dacruick]

think about the x-direction of the normal force from the bank.