Moments Question 2

Question: a uniform plank of length 4.0 m and weight 200 N rests horizontally on two supports, A at the left end and B at the right end. A person of weight 600 N stands 1.0 m from A. Calculate the upward forces R_A and R_B from the supports.Step 1: find the centre of gravity. The plank is uniform, so its 200 N weight acts at its midpoint, 2.0 m from A.Step 2: take moments about A. Choosing A as the pivot removes the unknown R_A, because a force has no moment about the point where it acts.Clockwise moments about A = (600 × 1.0) + (200 × 2.0) = 600 + 400 = 1000 N mAnticlockwise moment about A = R_B × 4.0R_B × 4.0 = 1000, so R_B = 250 NStep 3: balance the vertical forces. The plank is in equilibrium, so total upward force = total downward force.R_A + R_B = 600 + 200 = 800 NR_A = 800 - 250 = 550 NCheck: taking moments about B gives R_A × 4.0 = (600 × 3.0) + (200 × 2.0) = 2200 N m, so R_A = 550 N, as before.The support nearer the person carries more of the load, as expected. Remember to include the weight of the beam itself: forgetting it is the most common mistake in this type of question.