A uniform 40-N board supports two children weighing 500 N and 350 N. If the support is at the center of the board and the 500-N child is 1.5 m from its center, how far is the 350-N child from the center?
A) 2.1 m
B) 1.1 m
C) 2.7 m
D) 1.5 m

Question

A uniform  40-N board supports two children weighing  500 N and  350 N. If the support is at the center of the board and the  500-N child is  1.5 m from its center, how far is the  350-N child from the center?
A)  2.1 m
B)  1.1 m
C)  2.7 m
D)  1.5 m

Quizplus · Accepted Answer

To balance the board, the moments (torques) around the pivot (the center of the board) must be equal. The moment is calculated as the force times the distance from the pivot. Let $x$ be the distance of the 350-N child from the center. The moment due to the 500-N child is $500 \times 1.5$. To balance this, the moment due to the 350-N child must be equal, so $350 \times x = 500 \times 1.5$. Solving for $x$ gives $x = \frac{500 \times 1.5}{350} = 2.14$ m, which rounds to 2.1 m, option A.

A Uniform 40-N Board Supports Two Children Weighing