Posted by **Kimmy** on Sunday, November 10, 2013 at 11:50pm.

A wooden bridge crossing a canyon consists of a plank with length density λ = 2.25 kg/m suspended at h = 10.89 m below a tree branch by two ropes of length L = 2h and with a maximum rated tension of 2000 N, which are attached to the ends of the plank, as shown in the figure. A hiker steps onto the bridge from the left side, causing the bridge to tip to an angle of 22.3° with respect to the horizontal. What is the mass of the hiker?

- College Physics -
**Damon**, Monday, November 11, 2013 at 12:17am
If the two lines are attached at the same point on the branch so a triangle is formed, then the center of gravity of the plank, hiker system must be directly below the attachment point.

mass of plank = 2.25 * length

for length (.5L)^2 = 21.78^2 - 10.89^2

(.5 L)^2 = 474.4 - 118.6

.5 L = 18.9

L = 37.7 meters long

so mass of plank = 2.25*37.7 = 84.9 kg

now balance

how far is G from center of plank?

tan(22.3) = x/10.89

x = 4.47

so how far is left end from G?

18.9 - 4.47 = 14.4

so m(14.4) = 84.9(4.47)

m = 26.4 kg

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