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Banked curve with friction, but no angle

  • Thread starter puzzledup
  • Start date
  • #1
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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.
 

Answers and Replies

  • #2
Doc Al
Mentor
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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.
 
  • #3
5
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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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