Moments Question 1

Question: a uniform metre rule is balanced on a pivot at its 50 cm mark. A 2.0 N weight hangs from the 10 cm mark. Where must a 5.0 N weight be hung to balance the rule?Step 1: identify the moments. The rule is uniform, so its centre of gravity is at the 50 cm mark, directly above the pivot. Its weight has no moment about the pivot and can be ignored.The 2.0 N weight is 50 - 10 = 40 cm = 0.40 m to the left of the pivot, so it gives an anticlockwise moment.Step 2: calculate the known moment.anticlockwise moment = 2.0 N × 0.40 m = 0.80 N mStep 3: apply the principle of moments. The rule is in equilibrium, so the sum of clockwise moments equals the sum of anticlockwise moments. The 5.0 N weight must hang to the right of the pivot, at a distance d.5.0 × d = 0.80d = 0.16 m = 16 cmAnswer: the 5.0 N weight hangs 16 cm to the right of the pivot, at the 66 cm mark.Check: the larger weight is closer to the pivot. This makes sense, because a larger force needs a smaller perpendicular distance to produce the same moment.Tips: convert distances to metres, measure every distance from the pivot (not from the end of the rule), and state whether each moment is clockwise or anticlockwise.