Banked curve with friction, but no angle

AI Thread Summary
A banked curve designed for a vehicle traveling at 70 mph has a radius of 300m, with static and kinetic friction coefficients of 0.80 and 0.60, respectively. A 5512 lb vehicle is instead traveling at 60 mph, prompting calculations for the force exerted by the road and the friction on the tires. Initial attempts to determine the banking angle using the equation v^2/r led to an incorrect steep angle of 19.45 degrees. The correct angle was found by assuming no friction and solving for the normal force, which was then substituted into the force equations. The discussion emphasizes the importance of unit consistency when applying physics equations.
puzzledup
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Homework Statement


A banked curve has been designed so that it is safest for a vehicle going 70 mph. The topography of the land restricts the radius of the road to 300m. Assume mu(static friction) is 0.80 and mu(kinetic friction) is 0.60.
A 5512 lb vehicle travels with a speed of 60 mph on the curve.
1. Calculate the force that the road exerts on the vehicle.
2. Calculate the friction on the tires.


Homework Equations


F=ma
Centripetal acceleration=v^2/r


The Attempt at a Solution




converted all mph's given to m/s and converted weight in lbs to N.
tried to find the angle by:

v^2/r=Wsinθ

I came up with 19.45 degrees. This just doesn't seem right, that's an awfully steep bank.
The rest I'm stumped about.
 
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puzzledup said:
tried to find the angle by:

v^2/r=Wsinθ
How did you arrive at this? Note that the units do not match: The left side is an acceleration, while the right is a force.
 
I was wrong in that angle. I found the correct angle by assuming no friction, solving the y force for Fn and substituting it in the x force equation. This gave me theta.
Then, after figuring out the x y-axis could be rotated to go with the Fn on the car, solved like any other incline plane problem.
 

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