Answer to Question #90931 in Mechanics | Relativity for sara

Question

Weights of 10 N, 16 N, and 30 N are placed on a meterstick at 21 cm, 40 cm, and 61 cm respectively. The meterstick is
balanced by a single support at its midpoint. At what point may a 9 N be attached to produce equilibrium?

Answer 1

Principle of Moments: for equilibrium the sum of the clockwise moments about a point = sum of the anticlockwise moments about that point.

If these weights are on one side of the center, then for equilibrium it is necessary to place on the other side at a distance x cm weight 9 N so that

$$10 \cdot 21 + 16 \cdot 40 + 30 \cdot 61 = 9 x.$$

Thus

$$x = \frac{2680}{9} \approx 297.8.$$

Answer: 2680/9 cm.