Statics, determine the force required to rotate a body

[jonjacson]

Homework Statement

I´ll use a picture to show the problem:

Homework Equations

Sum forces=0

Sum Moments=0

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?

 

[voko]

When "breaking contact at C", what is the reaction at C?

 

[jonjacson]

When "breaking contact at C", what is the reaction at C?

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!