Question

A hiker, who weighs 649 N, is strolling through the woods and crosses a small horizontal bridge. The bridge is uniform, weighs 3220 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

Take summation of moments about the support that is farthest from the hiker:

649(4L/5) + 3220(L/2) = F1(L)

where

L = length of the bridge
F1 = force exerted by the support near the hiker

Since "L" appears on both sides of the equation, it will simply cancel out and solving for F1,

F1 = 2129.2 N

b)

Take summation of forces on the acting on the bridge.

F1 + F2 = 649 + 3220 = 3869

where

F1 = 2555.25 (as determined above)
F2 = force exerted by the support farthest from the hiker

Solving for "F2"

F2 = 3869 - 2129.2

F2 = 1739.8 N