Statics problem -- Rectangular plate lying on two inclined surfaces

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Mzaa
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Homework Statement


https://www.img.in.th/image/VNaqVa
https://www.img.in.th/image/VNa3k9
Text problem: a thin uniform rectangular plate of width L (L = AB) rests on two inclined surfaces with angles alpha and beta, followed by multiple-choice parts (1) to (3) about static balance conditions.


Fig. 3-1: diagram of a horizontal line with two inclined lines meeting it at one point, labeled A and B on the upper ends, with angles α and β marked at the base.


This is my home work.

Homework Equations

The Attempt at a Solution


I have a problem with the force at A and B. I don't know how to use NA NB in the term of α and β to use moment calculation. I got that In x-axis NAsin∝=NBsinβ, but in the y-axis it still confuse.
 
Attachments
  • Fig. 3-1: diagram of a horizontal line with two inclined lines meeting it at one point, labeled A and B on the upper ends, with angles α and β marked at the base.
    upload_2018-5-12_11-36-38.png
    7 KB · Views: 836
  • Text problem: a thin uniform rectangular plate of width L (L = AB) rests on two inclined surfaces with angles alpha and beta, followed by multiple-choice parts (1) to (3) about static balance conditions.
    upload_2018-5-12_11-36-12.png
    66.4 KB · Views: 793
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Mzaa said:

Homework Statement


https://www.img.in.th/image/VNaqVa
https://www.img.in.th/image/VNa3k9
This is my home work.

Homework Equations

The Attempt at a Solution


I have a problem with the force at A and B. I don't know how to use NA NB in the term of α and β to use moment calculation. I got that In x-axis NAsinα=NBsinβ, but in the y-axis it still confuse.
How many forces act on the plate?
With that many forces acting on a body in equilibrium, what can you say about the lines of action of the forces?
 
I recently searched for definition of "line of action of force",but I still confuse.Are they the line passing through A and B and they're pararelled?
 
Mzaa said:
Are they the line passing through A and B
Yes. The normal force at A passes through point A. This is important for finding the torque that a force exerts about a given axis.
Here you have three forces acting on the plate. The lines of action of the two normal forces intersect at some point, P. If we take moments about that point, what torque do those two forces exert about P?
The third force is gravity.
If the system is in equilibrium, what does that tell you about the torque the gravitational force exerts about P?
 

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