College Physics

posted by .

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 -

    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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics

    A child's swing is held up by two ropes ties to a tree branch that hangs 13.0 degrees from the vertical. If the tension in each rope is 2.28 N, what is the combined forece (magnitude and direction) of the two ropes on the swing?
  2. physics

    a child's swing is held up by two ropes tied to a tree branch that hangs 13.0 from the vertical. if the tension in each rope is 2.28N, what is the combined force(magnitude and direction) of the two ropes on the swing?
  3. Physics

    1000 N man walks across an 8 meter plank that is suspended from two ropes(one on each side of the plank) that can only support 400N where will the man be when the plank breaks?
  4. Physics

    An insulating sphere of mass m and positive charge q is attached to a spring with length h and spring constant ks and is at equilibrium as shown below: An infinitely long wire with positive linear charge density λ is placed a …
  5. physics

    Two children hang by their hands from the same tree branch. The branch is straight, and grows out from the tree at an angle of 26° above the horizontal. One child, with a mass of 38 kg, is 1.1 m along the branch from the tree trunk. …
  6. physics

    Two children hang by their hands from the same tree branch. The branch is straight, and grows out from the tree at an angle of 26° above the horizontal. One child, with a mass of 38 kg, is 1.1 m along the branch from the tree trunk. …
  7. physics

    Two children hang by their hands from the same tree branch. The branch is straight, and grows out from the tree at an angle of 23° above the horizontal. One child, with a mass of 59 kg, is 1.8 m along the branch from the tree trunk. …
  8. Physics

    A wooden bridge crossing a canyon consists of a plank with length density λ = 2 kg/m suspended at h = 10.0 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 …
  9. physics

    a 200 N wooden platform is suspended from the roof of the house by ropes attached to it's ends. it has a total length of 4.2 meters. a painter weighing 650 N stands from the left end of the platform. find the tension in each end of …
  10. physics101

    a 200 N wooden platform is suspended from the roof of the house by ropes attached to it's ends. it has a total length of 4.2 meters. a painter weighing 650 N stands from the left end of the platform. find the tension in each end of …

More Similar Questions