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Homework Help: Equilibrium Ball attached to wall problem

  1. Jan 6, 2008 #1
    1. The problem statement, all variables and given/known data
    A uniform sphere of mass m and radius r is held in place by a massless rope attached to a frictionless wall a distance L above the center of the sphere. Find (a) the tension in the rope and (b) the force on the sphere from the wall.


    2. Relevant equations
    net torque = 0
    net force = 0
    t=force of tension
    F=force of wall
    mg=gravitational force on ball
    3. The attempt at a solution
    well, strangely enough I am able to solve for part B. choosing the point where the string is attached to the wall as my origin. I am able to determine the torque caused by tension to be 0 as the tension force runs 180 parallel the string. Using motion arm times force = torque, I can find the remaining torques so that:
    -mgr+t*0+L*F=0
    which yields
    F=mgr/L
    which is the correct answer to part B. However, I have no clue how to solve part A. I have already used my torque, so I tried setting the force equations for the x and y axis to 0.
    T*cos(x)-mg=0
    F-T*sin(x)=0
    but that doesn't get me anything close to the correct answer of
    T=(mg/L)*sqrt(L^2+r^2)

    help please
     
  2. jcsd
  3. Jan 6, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Either one of those force equations will get you the answer. Hint: Evaluate sin(x)--or cos(x)--in terms of the lengths given.
     
  4. Jan 6, 2008 #3
    oh, thanks!...so

    t*cosx-mg
    t*cosx=mg
    replace L/a for cosx
    t*(L/a)=mg
    t=mg/L*a
    by pyth. theorem a = sqrt(r^2+L^2)
    t=(mg/L)sqrt(r^2+L^2)

    THANK YOU SO MUCH! It feels so good to get that problem done. For awhile I thought that there would be something way complex to do that would take a lot of work...and I was intimidated to go any further. Thanks again.
     
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