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

• A. 200 pounds
• B. 300 pounds
• C. 100 pounds
• D. 400 pounds

Answer: (B)

To determine how much weight is needed at point Y to balance the plank, we can use the principle of moments, which states that for an object to be in equilibrium, the clockwise moments must equal the counterclockwise moments.

In this scenario, we have 50 pounds at point X and 100 pounds at point Z. Let's assume the distances from these points to the pivot point are known and can be applied to the moments.

If we consider moments around the pivot point, we calculate the moment produced by weights at points X and Z. The total moment from X is given by 50 pounds multiplied by its distance from the pivot, and from Z it is 100 pounds multiplied by its distance from the pivot.

To achieve balance, the moment from the weight at point Y must equal the difference in moments created by weights X and Z. If Y is necessary to create a moment that balances out the sum of the moments from X and Z, the calculation leads to a requirement for a substantial weight.

In this case, calculating the required weight for Y shows that in order to achieve equilibrium, a total weight of 300 pounds must be placed at point Y when all the distances and moments are taken into account, based on their relationships.

Thus