Two supports do not necessarily carry equal loads. Their forces depend on where the load acts. A moment equation supplies information that vertical force balance alone cannot provide.
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Define positions and assumptions
A light horizontal beam is supported at its ends, 1.0 m apart. A downward 20 N load acts 0.40 m from the left support. Neglect the beam's own weight and assume static equilibrium.
Let the upward reactions be L and R. Vertical balance gives L + R = 20 N. This is one equation for two unknowns.
Take moments about a convenient point
About the left support, L has zero lever arm. Balancing moments gives R(1.0) = 20(0.40), so R = 8 N. Therefore L = 12 N.
The nearer left support carries more. The lever arm is the perpendicular distance from the pivot to the force's line of action, not automatically any distance marked on a diagram.
Check with a different pivot
About the right support, L(1.0) = 20(0.60), again giving 12 N. Both equations agree. Include the beam's weight at its centre of mass if it is no longer negligible.
A load outside the support interval may require a different contact or attachment analysis; do not assume every calculated negative reaction is physically available. This original problem develops statics foundations rather than reproducing an official Olympiad question.
Continue reading: British Physics Olympiad Mechanics: Momentum vs Kinetic Energy.
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Official information and further reading: Source 1
