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
Answer This Question
Related Questions
 Physics  A wooden bridge crossing a canyon consists of a plank with length ...
 Physics  1000 N man walks across an 8 meter plank that is suspended from two ...
 physics  a 200 N wooden platform is suspended from the roof of the house by ...
 physics101  a 200 N wooden platform is suspended from the roof of the house by ...
 Physics  An insulating sphere of mass m and positive charge q is attached to a ...
 physics  a child's swing is held up by two ropes tied to a tree branch that ...
 physics  A child's swing is held up by two ropes ties to a tree branch that ...
 physics  a boy of mass 'm' stands on one end of a wooden plank of length L and ...
 physics  Two children hang by their hands from the same tree branch. The branch...
 physics  Two children hang by their hands from the same tree branch. The branch...
More Related Questions