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Finding the radius of a curve

  1. Oct 16, 2004 #1
    can someone please help me, i can't figure out where the angle on the free body diagram for this problem. i was thinking of using newton's second law with a = v(squared)/R would this work?

    A car goes around a curve on a road that is banked at an angle of 27.0°. Even though the road is slick, the car will stay on the road without any friction between its tires and the road when its speed is 23.0 m/s. What is the radius of the curve?
     
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  3. Oct 16, 2004 #2

    Pyrrhus

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    Do the forces analysis and find which force component is working as the centripetal force.
     
  4. Oct 16, 2004 #3
    well there is no friction force so the only thing pushing it to the center would be the acceleration, is that right?
     
  5. Oct 16, 2004 #4

    Pyrrhus

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    Actually it will be a component of the normal force, try to draw all the forces on our particle, Normal and weight.
     
  6. Oct 16, 2004 #5
    oh ok so
    sumF = Ncosθ = m ((v^2)/R)

    sumFy = Nsinθ - mg = 0

    i used this and i solved for R = (v^2)/cotθ but i didn't get the correct answer. can you please tell me what i did wrong?
     
  7. Oct 16, 2004 #6

    Pyrrhus

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    [tex] Ncos\theta = mg[/tex]

    [tex] Nsin\theta = ma_{c}[/tex]

    Look at the triangle....
     
  8. Oct 16, 2004 #7
    oh i get it. its R = (v^2)/(tanθ g)
    thank you for your help!
     
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