I am trying to figure out how to calculate the force created by an offset torque. The theoretical scenario is a 2x4 piece of lumber mounted by a hinge on the wall at exactly 90°. The weight of the 2x4 creates torque on the hinge, making the hinge want to swing down, but there is a wall in the way preventing the hinge from swinging: the wall receives force created by the torque, in this case offset by 4 inches (assume a 2x4 is literally 2"x4").
I think I can calculate the torque (measured at the hinge) correctly using
torque = force * distance, because the force is the weight of the lumber in foot-pounds, and the distance is x/2 (since the weight is distributed evenly over the whole length x, we can pretend all of the weight is halfway).
w = weight in foot-pounds
x = length in feet the equation is:
torque = w * x/2
But how do you translate that torque into the force that is applied at the bottom of the 2x4?
Warning: I'm about to try it below, but if you already know the correct way to do it, feel free to skip the rest of this and just provide the correct answer!
force = torque / distance so if
d = distance from hinge to pressure point in feet
For a 6' board, the force would be 6 times the weight.
For an 8' board, the force would be 12 times the weight.
For a 20' board, the force would be 30 times the weight.
Is this the right approach?