What angle should the curve be banked at?

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AI Thread Summary
To determine the angle at which a curve should be banked for a comfortable ride, the centripetal force must balance the components of gravitational force acting on the car. The normal reaction force, R, can be split into two components: R*cos(θ) balances the weight of the car, while R*sin(θ) provides the necessary centripetal force. By setting R*cos(θ) equal to the weight (mg) and R*sin(θ) equal to the centripetal force (mv²/r), the angle θ can be solved. Understanding these relationships is crucial for finding the appropriate banking angle. This approach ensures a comfortable ride by minimizing lateral forces on passengers.
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Homework Statement



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?

Homework Equations



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

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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The centripetal force should be the same as the component of the weight for a comfortable ride.
 
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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