Friction problem with banked curve given static friction coefficient

[zenith12]

Homework Statement

What is the maximum speed with which a 1200 rubber-tired car can take around a banked curve with radius of 80.0 meters an angle of 19.0 degrees? (static friction coefficient is 1.0)

Homework Equations

F_s=mu*F(normal)
F_{(netxdirection)}/m=acceleration
acceleration=velocity²/radius

The Attempt at a Solution

I tried answering this problem several times and I failed at each; although I swear my first answer was correct (31.6 m/s). My professor's answer was 40.1 m/s and I have no idea how he got that.

Please help...

 

[Doc Al]

Show how you solved it. What are your vertical and horizontal force equations?

 

[zenith12]

Hey...sorry for being so short. I was in a hurry to just get the question asked. I spent all day on homework and no time to fully explain.

Here are my notes on this problem:

Known:
incline angle=19.0 degrees
Radius of turn=80.0 m
Mass of car=1200 kg
mu(s) tire on cement road=1.0

Forces:
Normal
Weight
Friction

Find:
Max velocity without slipping on cement

Steps:
1. Find Friction force by finding the Normal force for the y-axis by adding up the forces in the y direction. This was done by F=ma. Acceleration=zero, so solved for Normal.
2. Enter Normal in Friction equation (F=mu*N) to get Friction force.
3. Enter Friction force in F(netx)=ma for x-axis to solve for acceleration in the x direction which is also the radial/centripetal direction btw.
4. Use a=v^2/r to find the velocity.

Maybe this velocity is not the maximum? Am I missing something conceptual?

 

[Doc Al]

1. Find Friction force by finding the Normal force for the y-axis by adding up the forces in the y direction. This was done by F=ma. Acceleration=zero, so solved for Normal.

Careful! The acceleration is horizontal, so you cannot say that the acceleration is zero normal to the incline.

Instead, analyze vertical and horizontal force components. Set up two equations and solve them together.