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Minimum coefficient of friction to prevent slipping - torque

  1. Apr 11, 2007 #1
    A hollow, spherical shell with mass 1.95 rolls without slipping down a slope angled at 30.0. Find the minimum coefficient of friction needed to prevent slipping.

    I have already calculated the acceleration of the sphere and the magnitude of the friction force on the sphere in previous parts. I used torque and newton's laws to find the acceleration and friction. They are:
    a = 2.94 m/s^2
    f = 3.82 N

    I used the following equation for the sum of forces in the x-direction, which I oriented along the slope of the incline, with the positive direction down the incline. I didn't think I needed to use torque here, because I got the same answer that way as well.

    (sum)Fx = mgsin(theta) - f = ma
    = mgsin(theta) - (mu)mgsin(theta) = ma
    mu = [a - gsin(theta)] / [-gsin(theta)]
    mu = (-1.96 m/s^2) / (-4.9 m/s^2)
    = 0.4

    This coefficient of friction isn't right, but I'm sure I included all of the forces. Anyone know where I messed up? Thanks.
     
  2. jcsd
  3. Apr 11, 2007 #2

    AlephZero

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    The friction force is mu times the normal force on the plane

    f = (mu)mg COS(theta).

    You don't need the rest of your equation. You already found f = 3.82N so just plug the numbers into that equation.
     
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