Friction problem with banked curve given static friction coefficient

  • Thread starter zenith12
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  • #1
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Homework Statement



What is the maximum speed with which a 1200 rubber-tired car can take around a banked curve with radius of 80.0 meters an angle of 19.0 degrees? (static friction coefficient is 1.0)


Homework Equations


Fs=mu*F(normal)
F(netxdirection)/m=acceleration
acceleration=velocity2/radius


The Attempt at a Solution


I tried answering this problem several times and I failed at each; although I swear my first answer was correct (31.6 m/s). My professor's answer was 40.1 m/s and I have no idea how he got that.

Please help....

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Doc Al
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Show how you solved it. What are your vertical and horizontal force equations?
 
  • #3
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Hey....sorry for being so short. I was in a hurry to just get the question asked. I spent all day on homework and no time to fully explain.

Here are my notes on this problem:

Known:
incline angle=19.0 degrees
Radius of turn=80.0 m
Mass of car=1200 kg
mu(s) tire on cement road=1.0

Forces:
Normal
Weight
Friction

Find:
Max velocity without slipping on cement

Steps:
1. Find Friction force by finding the Normal force for the y-axis by adding up the forces in the y direction. This was done by F=ma. Acceleration=zero, so solved for Normal.
2. Enter Normal in Friction equation (F=mu*N) to get Friction force.
3. Enter Friction force in F(netx)=ma for x-axis to solve for acceleration in the x direction which is also the radial/centripetal direction btw.
4. Use a=v^2/r to find the velocity.

Maybe this velocity is not the maximum? Am I missing something conceptual?
 
  • #4
Doc Al
Mentor
45,140
1,442
1. Find Friction force by finding the Normal force for the y-axis by adding up the forces in the y direction. This was done by F=ma. Acceleration=zero, so solved for Normal.
Careful! The acceleration is horizontal, so you cannot say that the acceleration is zero normal to the incline.

Instead, analyze vertical and horizontal force components. Set up two equations and solve them together.
 

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