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 28.1° above the horizontal. One child, with a mass of 46.0 kg, is hanging 1.40 m along the branch from the tree trunk. The other child, with a mass of 34.5 kg, is hanging 2.11 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.

Explanation / Answer

torque is given by multiplication of force with perpendicular distance from the point of application of force.

so torque exerted by first child=weight of the child*distnace along the branch*cos(28.1)=46*9.8*0.8821*1.4=556.71N.m

so torque exerted bysecond child=weight of the child*distance along the branch*cos(28.1)=34.5*9.8*0.8821*2.11=629.282 N.m

net torque=1185.992 N.m ,anticlockwise direction

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