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Circular motion of a subway train

  1. May 22, 2008 #1
    1. The problem statement, all variables and given/known data
    A subway train rounds an unbanked curve at 67 km/h. An unused strap makes an angle of 15 degrees to the vertical. What is the radius of the turn. The book answer is 132 m.


    2. Relevant equations
    F = ma = mv^2/r


    3. The attempt at a solution
    A free-body diagram shows a normal force pointing up 75 degrees from the horizontal axis. An mg force points down along the y axis.

    Along the x axis N sin 15 degrees = mv^2/r.

    r = mv^2/N sin 15 degrees.

    Along the y axis N = mg cos 15 degrees.

    Substituting, r = mv^2/mg sin 15 degrees/cos 15 degrees = v^2 / g tan 15 degrees

    r = (67)^2 km^2/ H^2 / 9.8 m/s^2 / 3600 s^2/ h^2 * 1000 m/km / .268 = 475 m
     
  2. jcsd
  3. May 22, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Good.

    You mean: N cos 15 degrees = mg

    Good.

    First convert 67 km/h to m/s.
     
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