Tension in Strings Holding Up Shelf

[ARL91]

1. A 50.0 cm, uniform, 57.0 N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (the figure ). A very small 26.0 N tool is placed on the shelf midway between the points where the wires are attached to it.
http://session.masteringphysics.com/problemAsset/1260552/1/YF-11-23.jpg
2. All I know is that The downward force which is 83 N (26 N+ 57 N) and upward force must be equal to zero because this is an equilibrium problem.
3. I have tried to find the center of gravity:
x=(m1x1+m2x2)/(m1+m2)--> 185.2040Kgcm/8.469 Kg = 21.867 cm from the left, after this I am unsure how to proceed.

 

[gneill]

1. A 50.0 cm, uniform, 57.0 N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (the figure ). A very small 26.0 N tool is placed on the shelf midway between the points where the wires are attached to it.
http://session.masteringphysics.com/problemAsset/1260552/1/YF-11-23.jpg



2. All I know is that The downward force which is 83 N (26 N+ 57 N) and upward force must be equal to zero because this is an equilibrium problem.



3. I have tried to find the center of gravity:
x=(m1x1+m2x2)/(m1+m2)--> 185.2040Kgcm/8.469 Kg = 21.867 cm from the left, after this I am unsure how to proceed.

You can proceed by taking moments about the points where the shelf is supported.

Suppose you start with the leftmost support point. Assuming that all the mass of the shelf and tool are concentrated at their center of mass, what torque does this weight produce about the left hand suspension point? Then, if the torque caused by the tension in the right hand suspension wire must exactly counteract this (sum of the torques must be zero for a static system), what must the tension be?

 

[ARL91]

Thank you so much! Turns out I was using the wrong distance from the left wire.