Question

Concept Simulation 9.1 illustrates how the forces can vary in problems of this type. A hiker, who weighs 603 N, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs 4020 N, and rests on two concrete supports, one on each end. He stops 1/5 of the way along the bridge. What is the magnitude of the force that a concrete support exerts on the bridge (a) at the near end and (b) at the far end?

Answer 1

here,

weight of bridge , W1 = 4020 N

weight of hiker , W2 = 603 N

r1 = l/5

let the magnitude of the force exerted by the far end be F2

taking moment of force about the near end

W1 * l/2 + W2 * r1 - F2 * l = 0

W1 * l/2 + W2 * l/5 - F2 * l = 0

4020 * (1/2) + 603 * (1/5) = F2

F2 = 2130.6 N

a)

the magnitude of force exerted on the near end , F1 = (W1 + W2) - F2

F1 = ( 4020 + 603) - 2130.6 N = 2492.4 N

b)

the magnitude of force exerted on the far end is 2130.6 N