What is the range of speeds for a car on a banked curve with friction?

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The discussion focuses on calculating the range of speeds for a car on a banked curve with a radius of 30 meters and a coefficient of static friction of 0.32. The angle of the bank is determined to be 22.78 degrees, allowing for the calculation of forces acting on the car. Key equations involve the balance of forces, including friction and gravitational components, to prevent skidding. The problem emphasizes finding the maximum speed using the frictional force when the road is not icy. The solution requires understanding the relationship between speed, angle, and friction on a banked curve.
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banking curve problem cont'd ?

1. Homework Statement [/b]

a curve of radius 30m is banked so that a 950kg car traveling 40 km/h can round it even if the road is so icy that the coefficient of static friction is approximately zero. Find the range of speeds at which a car can travel around this curve without skidding if the coefficient of static friction between the road and the tires is 0.32. Homework Equations
I've already solved for the angle and my problem is only how to equate^^
3. The Attempt at a Solution
Given

km/h = ?
angle of slope = 22.78 degrees
coefficient of friction = .3
mass = 950 kg
weight = 9310 N
radius = 30m

coefficient of friction X Normal Force = Force of Friction

n sintheta + f costheta = mv^2 divided by radius

sorry can't figure out latex
 
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In LaTeX, the theta (or greek symbols) is preceeded by a \ , e.g. \theta.


Here is the PF tutorial on LaTeX - https://www.physicsforums.com/showthread.php?t=8997


One should solve for an angle such that the inward component of the weight of the car keeps it on the road, i.e. when ice is present and the coefficient of friction \mu = 0.

Then with that angle, solve for the higher speed when the coefficient of friction \mu = 0.3.
 
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