Two children hang by their hands from the same tree branch. Thebranch is straigh

Question

Two children hang by their hands from the same tree branch. Thebranch is straight, and grows out from the tree trunk at an angleof 28.7° above the horizontal. Onechild, with a mass of 47.6 kg, is hanging1.31 m along the branch from the treetrunk. The other child, with a mass of 33.3 kg, is hanging 2.19 mfrom the tree trunk. What is the magnitude of the net torqueexerted on the branch by the children? Assume that the axis islocated where the branch joins the tree trunk and is perpendicularto the plane formed by the branch and the trunk.
1                N · m

Explanation / Answer

    Angle made by the branch with horizontal, = 28.7o     Mass of first child, M1 = 47.6 kg     Distance of first child from the trunk, d1 =1.31 m     Mass of second child, M2 = 33.3 kg     Distance of second child from the trunk, d2 =2.19 m .     Torque, = Force * Perpendiculardistance     Net torque, = ( M1 g * d1 * cos )+ ( M2 g * d2 * cos )                         = ( 47.6 * 9.8 * 1.31 * cos 28.7o ) + ( 33.3 * 9.8 *2.19 * cos 28.7o )                         = 536 + 626.9                         = 1162.9 N ( Clockwise )

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