Banked Curve with Friction Problem

AI Thread Summary
The discussion revolves around calculating the maximum speed a car can take on a banked curve without skidding, given specific parameters like friction coefficient, angle, radius, and mass. The user has attempted to solve the problem using a free body diagram, calculating the normal force and friction force, but is unsure if they accounted for all necessary components, particularly the sine component of weight. Clarifications are sought regarding the forces acting on the car, emphasizing the need to consider both horizontal centripetal acceleration and vertical equilibrium. The user reports an incorrect result of approximately 18 m/s according to their online homework. Understanding the interplay of these forces is crucial for accurately determining the car's speed on the curve.
ruck101
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Hey all! Brand new to PF. Anyway, I'm having trouble with a problem involving centripital force. Here are the givens:

Friction coefficient = .49
Angle = 19 degrees
Radius = 46m
mass= 1200 kg

Question - How fast can the car take the curve without skidding to the outside? Thanks ahead of time!

By the way, yes, I have attempted this problem, just so nobody thinks I'm trying to get my homework done for me. :biggrin:
 
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Show us your attempt then. and Welcome to PF!
 
Banked Curve

Hehe, guess I should have done that in the first part. Anyway, I drew a freebody diagram and got the Normal Force = 11119 N, and the Friction force = Normal x Coefficient = 5448 N. Is that the only centripital force or is there also the sin component of the weight? I've added sin (mg) and the friction force together and plugged it into V^2= Centripital Force x radius/ mass. And I get the wrong answer, or so my online homework says. I get around 18 m/s.
 
How did you find the normal force?

Realize that when the car moves at maximal speed, there are three forces acting on the car: weight, friction (which way does it act?), and the normal force. In the horizontal direction, there is centripetal acceleration; in the vertical direction, equilibrium.
 
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