If 50-pound weights are located at points X, Y, and Z, how would point Z need to be adjusted to balance the plank?

If 50-pound weights are located at points X, Y, and Z, how would point Z need to be adjusted to balance the plank?

• A. 25 inches to the right
• B. 25 inches to the left
• C. 10 inches to the right
• D. 10 inches to the left

Answer: (B)

To determine how point Z needs to be adjusted to balance the plank with the weights located at points X, Y, and Z, it is crucial to understand the principles of torque and balance. In scenarios like this, balance is achieved when the moments caused by these weights around the pivot point (the balance point of the plank) are equal.

Assuming that the weights at points X and Y are exerting force on one side of the pivot, point Z will need to be positioned such that its torque balances the torque produced by the weights at points X and Y.

If we identify that the weight at Z needs to move 25 inches to the left, this means that adjusting Z closer to the pivot from a farther position will help achieve equilibrium by counteracting the torque created by X and Y.

In this case, the 50-pound weight at Z must shift leftward to reduce the leverage effect created by the weights on the other side. A 25-inch movement produces enough compensatory torque to counterbalance the forces, allowing the plank to be level. This understanding of torque and balance principles is fundamental when determining adjustments in weight distribution in mechanics and physics, especially in scenarios like balancing a beam or plank.