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Homework Help: Drawing Free Body Diagrams with torque

  1. May 4, 2010 #1
    1. The problem statement, all variables and given/known data
    This is a review problem i was given for my final exam tommorow, I am stuck on 1 problem, even with the answer key im not understanding it.(also sorry but the picture wont copy from MSword, but its a cylinder rolling up a hill)

    (B) When the lander hits the surface, it eventually stops bouncing and finds itself rolling up the side of a crater wall inclined at an angle of theta, still wrapped in its airbags.

    To a good first approximation, the lander is a uniform cylinder of mass M and radius R. The airbags can be thought of as forming a thin shelled sphere of radius r and mass m around the lander. Assume that the lander is rolling up the steepest incline possible without slipping. It terms of the given quantities, show a good step-by-step method to find out what the acceleration of the lander will be. Use g of Mars for the acceleration due to gravity on the surface of Mars.

    Draw FBD
    ∑F ⃗ =ma ⃗

    Direction of acceleration is down along the incline (+), direction of alpha=out of page
    ∑τ ⃗ =Iα ⃗

    Forces parallel to the incline: +mg∙sin(theta)−fs=ma
    Forces perpendicular to incline: +FN − mg∙cos=0
    Torques about center of mass: fs∙r = I*alpha
    Moment of Inertia I = ½ MR2 + (2/3)∙mr2
    Rolling condition: a = r*alpha

    Substitute and solve for a: a=(mg∙sinθ)/((I/r^2 +m))



    2. Relevant equations

    given above

    3. The attempt at a solution

    The part that i dont understand is how they are going from a = r*alpha to a=(mg∙sinθ)/((I/r^2 +m)), i am not seeing what they could be doing to get that answer. Any help is GREATLY appreciated, thanks.
     
  2. jcsd
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