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Banked car without friction

  1. Dec 18, 2008 #1
    1. The problem statement, all variables and given/known data
    A curve of radius r is banked at angle θ so that a car traveling with uniform speed v can
    round the curve without relying on friction to keep it from slipping to its left or right.
    The acceleration of gravity is 9.8 m/s2. If r = 50 m and v = 64 km/hr, what is θ?
    Answer in units of ◦.

    For this one, I drew a FBD. In my picture, Fny and Fg canceled each out, so the unbalanced force was Fnx. I used N2nd Fnet=ma and used components:
    Fnx=max
    Fnsintheta=max
    Fny= mg
    Fncostheta=mg
    then i divided them:
    Fsintheta max
    --------- = --------
    Fcostheta mg
    The masses canceled out on the right and on the left I had tantheta.
    on the right, ax/g= v^2/rg
    When I plugged in numbers, I got theta= approx 90 degrees. However, when I submit this answer, it is wrong..could someone help me find out where I messed up?
     
  2. jcsd
  3. Dec 18, 2008 #2

    jgens

    User Avatar
    Gold Member

    It's hard to follow your work but it looks like your resultant equation is correct: tan(x) = v^2/rg. Make sure to convert the km/hr to m/s before doing the calculation.
     
  4. Dec 18, 2008 #3

    LowlyPion

    User Avatar
    Homework Helper

    The force down the bank will be m*g*sinθ and the force from centrifugal acceleration is your m*v²*cosθ/r

    That means that you have v²/(r*g) = tanθ

    So to find θ that would be the tan-1( v²/(r*g)) = θ
     
  5. Dec 18, 2008 #4
    oh that would be the problem, not converting the units >< thanks to both of you for your help! :)
     
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