Banked curve with friction, but no angle

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SUMMARY

The discussion focuses on calculating the forces acting on a vehicle navigating a banked curve designed for a speed of 70 mph, with a radius of 300m and friction coefficients of 0.80 (static) and 0.60 (kinetic). A 5512 lb vehicle traveling at 60 mph is analyzed, with the participant initially miscalculating the banking angle as 19.45 degrees. The correct approach involved resolving forces without friction to find the normal force and subsequently determining the angle of the banked curve accurately.

PREREQUISITES
  • Understanding of centripetal acceleration and its formula: a = v²/r
  • Knowledge of force resolution in inclined planes
  • Familiarity with converting units from imperial to metric (mph to m/s, lbs to N)
  • Basic principles of friction (static and kinetic coefficients)
NEXT STEPS
  • Study the derivation of forces on banked curves without friction
  • Learn about the effects of friction on vehicle dynamics in banked turns
  • Explore the relationship between speed, radius, and banking angle in circular motion
  • Investigate real-world applications of banked curves in road design and safety
USEFUL FOR

Students in physics or engineering courses, automotive engineers, and anyone interested in vehicle dynamics and road design principles.

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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