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Acceleration of a rolling sphere up a ramp

  1. Mar 4, 2008 #1
    1. The problem statement, all variables and given/known data
    "A bowling ball rolls without slipping up a ramp that sloped upward at an angle B to the horizontal. Treat the ball as a uniform, sold spehere, ignoring the finger holes. a) explain why the friction force must be directed uphill. b) what is the acceleration of the center of mass of the ball? c) what minimum coefficient of static friction is needed to prevent slipping?


    2. Relevant equations
    I=2/5mr^2
    F=ma, torque=fr=I alpha, a=r alpha
    f=mu n


    3. The attempt at a solution

    b) f-mgsinB=ma
    fR=Iaplhpa
    fR=I(a/r)
    f=2/5ma
    2/5ma-mgsinB=ma
    a=-5/3gsinB

    c)f=2/5m(-5/3gsinB)
    f= -2/3mgsinB
    f/n=mu
    mu>-2/3tanB
    ???????
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 4, 2008 #2

    Doc Al

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    Staff: Mentor

    Careful with signs: The acceleration is down the incline.
     
  4. Mar 4, 2008 #3
    so a = 5/7gsinB
    is that the same as it the ball was moving down the ramp?
     
  5. Mar 4, 2008 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Yep.
     
  6. Mar 4, 2008 #5
    thanks
     
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