# Find the stretch of a steel wire in a static equilibrium problem.

Homework Statement:
A large wooden plank with p=471 kg/m^3 and dimensions of 20 cm by 35 cm by 10 m is attached to a wall so that the left side of the plank is connected to the wall with a single pin. Using a 2.83 m long steel wire with a diameter of 3 mm, the plank is also attached to the ceiling with the wire, so the wire is oriented vertically from the ceiling to the plank while the plank is oriented horizontally. A heavy object is also sitting, stationary atop the plank, precisely 3.1 m from the right end of the level plank.

- Given that the steel wire is attached to the plank 2 m away from the pin and that the plank has a uniform density, determine the final length of the wire (Young's modulus for the steel wire = 200 GN/m^2).
Relevant Equations:
∑ τ = 0
If I can determine the weight of that heavy object placed on the plank, I will be able to determine the stretch of that wire. But, when using the second condition for static equilibrium (torques of the system equal to 0), I always end up with two unknowns, no matter what point of rotation I choose. For example, if I choose the pin to be the axis of rotation, I will eliminate the force that the pin exerts on the plank but will end up with two unknown forces: the tension in the wire and the weight of the object at the end of the plank.

Is it possible to solve this with the given information?