Eliminate friction for banking car

[lemon]

Homework Statement

A corner on a road is banked at an angle of 10° to the horizontal. the radius of the corner is 80m. At what speed should a car make the turn if the driver wishes to eliminate the influence of friction on the car's tyres?

Homework Equations

F=mgsin(θ)

The Attempt at a Solution

I think I need to consider the forces.
The normal contact force is acting upwards perpendicular to the road surface. Weight is acting downwards vertically. Frictional force is acting down the slope of the road. Centripetal force is acting inward horizontally.
F=mgsin(θ) = ? No mass
Simply confused

 

[downwithsocks]

Leave mass in terms of m, perhaps it will cancel out later?

 

[honeyman]

Hello,

I am just, but a student and I think I have a possible solution...Might be wrong though.

F=m*g*sinX
tanX= v^2/r*g
tan10=v^2/800
tan10*v^2=800
v=12m/s

 

[lemon]

F_reaction=80m/cos(80°)
=460.7N
F_friction=80m/cos(10°)

F_reaction+F<sub>friction[/SUB=541.9N
Freaction+Ffriction=mv²/r

I need to get rid of the mass in the above equation in order to equate for the velocity. No idea how to do that. Please help. Need to hand this project in 8 hours from now. Friday morning uk time.

F=ma</sub>

 

[smtcenterchic]

You are trying to find the optimal speed for making the turn without the force of friction. Therefore, this force does not need to be considered in your calculations. You are dealing with the force of gravity and the normal force only. There is centripetal force, of course, but this is equivalent to the sum of all forces in the x direction (because centripetal force is acting horizontally towards the center of the circle, like you said).