greenrichy
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- 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?
Is it possible to solve this with the given information?