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Just need a confirmation (Force in uniform circular motion)

  1. Aug 13, 2006 #1
    I'm a little unsure with my some of my answers here, mainly because it seems too simple. The Questions ask:

    A race car driver is driving her car at the record breaking speed of 225 km/h. The first turn on the course is banked at 15 degrees, and the car's mass is 1450 kg.

    a) Calculate the radius of curvature for this turn.

    v = 225 km/h = 62.5 m/s
    m = 1450 kg
    theta = 15 degrees

    Since, v^2 = grtan theta
    Therefore, r = v^2/g tan theta
    = (62.5)^2/(9.8)(tan15)
    = 1487.6 m

    b) Calculate the centripetal acceleration of the car.

    a(c) = v^2/r
    = (62.5)^2/1487.6
    = 2.6 m/s^2

    *Thus far, I feel pretty good about my solutions but here's where my confidence is quickly stripped from me.

    c) If the car maintains a circular track around the curve (does not move up or down the bank), what is the magnitude of the force of static friction?

    For y:

    F(y) = F(n) - F(gy) = 0
    F(n) - F(g)cos15 = 0
    F(n) = mgcos15
    F(n) = 13725.8 N = 1.4*10^4 N

    For x:

    F(x) = F(f) - F(gx) = 0
    F(f) - F(g)sin15 = 0
    F(f) = mgsin15
    F(f) = 3677.8 N = 3.7*10^3 N

    Therefore, the magnitude of the force of static friction is 3.7*10^3.

    d) What is the coefficient of static friction necessary to ensure the safety of this turn?

    u(s) = F(s)/F(n)
    = 3.7*10^3/1.4*10^4
    = 0.26

    Sorry about the size of the question, hoping someone can catch any errors and help to guide me to the correct solution before I send this in. I'm asking alot, any input is much appreciated.
     
  2. jcsd
  3. Aug 14, 2006 #2
    Seems correct to me.
     
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