Solve Falling Plank Problem: Acceleration & Angle of Separation

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Homework Help Overview

The problem involves a uniform plank of mass M and length 2L, which is leaning against a frictionless wall and resting on a frictionless floor. The task is to determine the acceleration of the upper end of the plank immediately after a supporting string is cut, as well as the angle at which the upper end first separates from the wall. The context includes dynamics and rotational motion principles.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to apply Newton's second law and consider the forces acting on the plank. There is mention of drawing a free body diagram to visualize the forces and applying equations related to the motion of the center of mass and angular motion.

Discussion Status

Some participants have shared diagrams to illustrate their understanding, although there are issues with visibility. There is an ongoing exploration of the relevant equations and the dynamics of the situation, but no consensus has been reached yet.

Contextual Notes

Participants note that the original poster's professor suggested a specific height at which the plank would separate from the floor, which may influence their reasoning. The discussion is still in the early stages, with participants seeking clarification and guidance on the problem setup.

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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!:smile:
 
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ViolinIsLife said:
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!:smile:
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.
 
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.
 

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ViolinIsLife said:
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?
 

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