A non uniform beam of weight 120 N pivoted at one end is shown in the diagram below. Calculate the value of F to keep the beam in equilibrium.
Topic: Principle of moments and equilibrium
Answer
From the diagram, the beam is pivoted at O. The weight of 120 N acts at 0.20 m from the pivot, and the force F acts at 0.80 m from the pivot on the other side.
By the principle of moments, for equilibrium: clockwise moment = anticlockwise moment F × 0.80 = 120 × 0.20 0.80 F = 24 F = 24 ÷ 0.80 F = 30 N
Value of F to keep the beam in equilibrium = 30 N
Moment = force × perpendicular distance FROM THE PIVOT. Measure both distances from O, not from the ends of the beam.
The beam is described as NON-uniform, which matters: you cannot assume its weight acts at the middle. The diagram shows you where the 120 N acts, and that is the only place it may be taken from.
Sanity check the answer: F acts four times further from the pivot than the weight does, so it needs only a quarter of the force — 120 ÷ 4 = 30 N ✓. That is the whole point of a lever, and it is a fast way to confirm the arithmetic.