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Statics, determine the force required to rotate a body

  1. Mar 11, 2013 #1
    1. The problem statement, all variables and given/known data

    I´ll use a picture to show the problem:

    1zyh95e.jpg

    2. Relevant equations

    Sum forces=0

    Sum Moments=0


    3. The attempt at a solution

    Basically I´m not sure about the forces on the free body diagram and I´d like to talk about them.

    Assuming that P is not acting, and the body is masless these are the only three forces acting on it: Fb, reaction at O on the x axis Rox, and reaction at C on the x axis too Rcx, Am I right?

    I know that is not what the problem is asking, it´s only to make this clear, solving the equations it´s pretty easy:

    Sum Fy= there are not any forces on this axis

    Sum Fx=> Rcx + Nox =Fb

    Sum Mc= Fb*40=Nox*80----> Nox=1750*10/1000*2=17.5N

    Rcx=8.75N

    Is everything right until here?

    Now, assuming a force P must be acting on the body to start rotation, I´m a bit lost with forces, basically on the y axis.

    I thought that at the point C a force on the y axis cannot act, but then I thought that maybe it was possible. For example, if you push an object against a wall it doesn´t fall, you are applying a force on the x axis, there is a reaction force at that axis, but there must be a friction force on the y axis with the same modulus as the gravity, well I think that´s the only option to guarantee that the statics equations are correctly used.

    So, let´s suppose that we have a general force at the point C, and we don´t know its direction, we have three unknown quantities: P, Rcx, Rcy.

    Now If I look to point O, I think that due to Fk there must be a reaction on the x axis, but I´m not sure if there could be a reaction on the y axis.

    ANyway I have more unknown quantities Rox, Roy.

    I have a total of 5 unknown quantities and three equations, so I can´t solve the system, but the book gives me a numerical answer, so I think that I should make two assumtions, maybe that Rcy is 0, and Roy is 0 too, but in that case for the y axis I have:

    SUm Forces Y axis= P=0, which doesn´t make any sense.

    So, Is the system able to create reaction forces on the Y axis? At what point? Why?
     
  2. jcsd
  3. Mar 11, 2013 #2
    When "breaking contact at C", what is the reaction at C?
     
  4. Mar 11, 2013 #3
    Is cero and gives me these set of equations:

    x---> Rox=Fk=17,5 N

    y--> P=Roy

    Moments--> -Fk*40 + P*120=0---> P=5,83N

    Which is the correct answer.

    Thanks voko!!!
     
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