Solve Falling Plank Problem: Acceleration & Angle of Separation

[ViolinIsLife]

Could someone help me with this problem? I appreciate it!

A uniform plank of mass M and length 2L is resting on a frictionless floor and leaning against a frictionless vertical wall. It is held steady by a massless string connecting the lower end of the plank to the base of the wall. The angle between the floor and the plank is theta. Calculate the acceleration of the upper end of the plank immediately after the string is cut, and the angle theta at which the upper end of the plank first separates from the wall.

My prof. said that the plank would separate from the floor at about 2/3 of the original height where the plank was leaning against the wall.

Thank you very much in advance!

 

[OlderDan]

Could someone help me with this problem? I appreciate it!

A uniform plank of mass M and length 2L is resting on a frictionless floor and leaning against a frictionless vertical wall. It is held steady by a massless string connecting the lower end of the plank to the base of the wall. The angle between the floor and the plank is theta. Calculate the acceleration of the upper end of the plank immediately after the string is cut, and the angle theta at which the upper end of the plank first separates from the wall.

My prof. said that the plank would separate from the floor at about 2/3 of the original height where the plank was leaning against the wall.

Thank you very much in advance!

Please post your attempt at solving this problem. Draw a free body diagram with the forces acting and apply Newton's second law to the motion of the center of mass and its rotational analog to the angular motion.

 

[ViolinIsLife]

I have attached a diagram for this problem. Sorry, don't know why the jpg file doesn't show the forces that I have drawn with MS Paint on the diagram.

 

[OlderDan]

I have attached a diagram for this problem. Sorry, don't know why the jpg file doesn't show the forces that I have drawn with MS Paint on the diagram.

We cannot yet see the diagram, and probably do not need it to see if you are on the right track. Do you have the equations related to the diagram?