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Very simple kinematics problem, but possibly no solution? Maximum accel of object.

  1. May 12, 2012 #1
    1. The problem statement, all variables and given/known data
    This problem seems so simple yet I don't feel there is enough information to know what is the maximum acceleration the object can travel at without tipping over. I uploaded a picture of the object along with the variables.

    rope AB = 6 ft

    Angle of AB = 78 degrees

    Acceleration positive to the right.

    2. Relevant equations

    ∑F = m*a

    ∑M = I*α + r*m*a, where r is the distance between the center of mass and location at which the moments are being taken, and a is the acceleration at the center of mass of the object.

    3. The attempt at a solution

    Drawing the free body diagram of the entire cart, there is no normal force acting on the rear wheel, since this is the limiting condition for tipping over.

    I tried taking the cart apart at the point where the horizontal board meets the vertical board. I set reaction forces at the joint, a weight of m1g at the center of the board and the tension force Tab, along with unknown acceleration a.

    I was able to figure going this way that the minimum tension of the rope, using the sum of the moments at the joint, must be .5*m1g/sin(78) since:

    ∑ M(joint) = I*α + r*m*a

    but we want to avoid tipping, so alpha is zero. And the vector r is zero as well at the reaction points, so:
    ∑ M(joint) = 0, ccw positive.
    6*cos(78)/2 *m1g + 6*cos(78)*Tabsin(78) = 0

    Tab = .5m1g/sin(78). Anything larger for Tab than this will cause the object to rotate.

    That's as far as I got. I couldn't use the sum of the moments in the second body consisting of vertical board and block since there is a lack of dimensions.

    Maybe this is not the right way to approach this problem? It doesn't seem to make much sense because there is no external force acting on the body to make it accelerate in the first place. I'm so stuck. :(
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
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