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

Question

Two children hang by their hands from the same tree branch. The branch is straight, and grows out from the tree trunk at an angle of 27.1° above the horizontal. One child, with a mass of 40.0 kg, is hanging 1.38 m along the branch from the tree trunk. The other child, with a mass of 34.5 kg, is hanging 2.13 m from the tree trunk. What is the magnitude of the net torque exerted on the branch by the children? Assume that the axis is located where the branch joins the tree trunk and is perpendicular to the plane formed by the branch and the trunk.

? N · m

Explanation / Answer

Given that mass of the child one is M_1 = 40.0 kg mass of the other child is M_2 = 34.5 kg distance d _1 = 1.38 m , d_2 = 2.13 m Net torque is M_1 g d_1 cos ( 27.1 ) + M_2 * g d_2 cos (27.1 )                       = 40.0 kg * 9.8 * 1.38 cos 27.1 + 34.5 kg * 9.8 * 2.13 cos 27.1                           = 1115.2 N m

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