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Homework Statement
A uniform solid cube, of edge 1m and weight 200N, rests on a rough horizontal plane. A light rod AB
of length 1.2m is smoothly hinged at A to a point of the plane and B is in contact with a smooth face
of the cube. The rod lies in a vertical plane perpendicular to this face and passing through the centre
of mass of the cube. The rod makes an angle of 30◦ with the horizontal (see diagram). A gradually
increasing force of magnitude PN is applied vertically downwards at the mid-point of AB until the
cube is on the point of turning about the edge through D. By considering the forces acting on the cube
at this instant, find the normal contact force at B.
Homework Equations
sum of Forces and the sum of torque about a point are always zero if the system is in equilibrium.
The Attempt at a Solution
I don't understand the question at all. My first query : Is this system in equilibrium ?
Can i equate the Torques about "any" point to be equal to zero (specifically talking about the cube) ?
Secondly : The one thing i think would help me get started is the Free Body Diagram for this particular set up. I noticed that there is no friction between the (mass less rod) and the cube.
The first attachment was the QUESTION , as given in the book.
The second attachment is my (flawed) Free body diagram.
About my diagram :
I am not sure about whether the forced shown in green should exist or not. Theoretically speaking, they should not ! But if i think it intuitively, the only way a force "P" acting on the rod can cause the cube to reach the point of turning over (toppling over) is that there is friction (shown in green) that would cause torque. (Am i correct) ?
Next, i am unsure where exactly would the Normal Reaction force due to the horizontal plane act ? At D or at the mid point of CD ?
I am completely confused , any help is appreciated .