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What angle should the curve be banked at?

by TheConfewsd
Tags: angles, centripetal foce
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Jan20-10, 11:48 PM
P: 1
1. The problem statement, all variables and given/known data

A 162kg car rounds a curve with a radius of 267 m at 43 m/s. The acceleration of gravity is 9.8 m/s2

a. (already solved) - What force must the road exert on the road to keep the car on the curve.

1121.864 Newtons

b. - At what angle must the curve be banked to give a passenger the most comfortable ride?

2. Relevant equations

Centripetal force = mass x velocity2/radius
Centripetal acceleration = velocity2/radius

3. The attempt at a solution

I have no attempt. I do not understand what part "b" of the problem is asking or how to solve for it.

I don't even really want a solution, I just need someone to explain to me how to solve what angle the curve should be banked at, and I'll solve it myself.
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Jan21-10, 12:07 AM
HW Helper
P: 6,205
The centripetal force should be the same as the component of the weight for a comfortable ride.
Jan21-10, 12:07 AM
HW Helper
P: 4,435
If R is the normal reaction of the road on the car, for comfortable driving, R*cosθ must balance the weight of the car mg, and R*sinθ must provide necessary centripetal force m*v^2/r. Using these hints solve for θ.

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