This light demonstrates static equilibrium. The combined tension in the two rods must be equal to the downward force of the lights and the wooden support. The resulting equation would look like:
T1sintheta+T2sintheta=mglight1+mglight2+mgwood
We can also know that because the light is at equilibrium, the net torque is 0. To find the net torque, we can use the equation Tccw (counter clockwise) -Tcw (clockwise)=T=0.
To solve the problem, you could use either end as the fulcrum. For instance, if the left side (when looking at the picture) was used as the fulcrum, than the equation would be:
T2y(r)=mglight1(r)+mglight2(r)+mgwood(r)
After finding T2y you could then find T1y.
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