Two childred hang by their hands from the same tree branch. The branch is straig

Question

Two childred hang by their hands from the same tree branch. The branch is straight, and grows out from the tree trunk at anangle of 27.0o above the horizontal. One child,with a mass of 44.0 kg, is hanging 1.30 m along the branch from thetree trunk. The other child, with a mass of 35 kg, is hanging2.10 m from the tree trunk. What is the magnitude of the nettorque exerted on the branch by the childred? Assume that theaxis is located where the branch joins the tree trunk and isperpenedicular to the plane formed by the branch and the trunk.

Explanation / Answer

   Given that the mass of each child is m1 = 44 kg and m2= 35 kg    angle above horizontal is = 27o separation between the trunk and first child isL1 = 1.30m separation between the trunk and 2ndchild is L2 = 2.10m -------------------------------------------------------------------- Torque is = force *perpendicular distance between the forceand axis of rotation Then the torque about the trunk is                    = m1*g *L1*cos +m2*g*L2*cos                     = 499.5 N.m + 641.8 N.m                     = 1141.3 N.m

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