If a weight of 50 pounds is located at point X and 100 pounds at point Z, how much weight must be located at point Y to balance the plank?

To determine how much weight must be located at point Y to balance the plank, we need to apply the principle of moments, which states that for an object to be in equilibrium (balanced), the counterclockwise moments about any point must equal the clockwise moments.

Assuming point X and point Z are positioned at known distances from point Y (which we can denote as dX for point X and dZ for point Z), the torque due to the weight at point X would be calculated as the product of the weight and its distance from point Y (Torque_X = Weight_X * dX). Similarly, the torque for the weight at point Z would be represented as Torque_Z = Weight_Z * dZ.

We aim for the moments to balance, leading to the equation:

Torque_X + Torque_Y = Torque_Z.

This arrangement means we can calculate the required weight at point Y knowing the positions of points X and Z and the weights present.

Given the weights involved – 50 pounds at point X and 100 pounds at point Z – we can set up the equation depending on their respective distances from point Y. If solved correctly, the resultant equation demonstrating how much weight at Y would be needed to create a torque that counterbalances the tor