A branch of a tree grows out from the trunk at an angle of 25.5° above the horiz

Question

A branch of a tree grows out from the trunk at an angle of 25.5° above the horizontal. Two children hang by their hands from the branch of the tree. The first child has a mass of 47.0 kg and hangs 1.15 m from the tree trunk, as measured along the length of the branch. The second child, with a mass of 34.5 kg, hangs 2.15 m from the tree trunk, also measured along the branch. Determine the magnitude of the net torque exerted on the branch by the children, about an axis located where the branch joins the tree trunk and is perpendicular to the plane formed by the branch and the trunk.
Ans)_______N · m

Explanation / Answer

theta=25.5 degrees

mass, m1=47 kg at r1=1.15 m

mass, m2=34.5 kg at r2=2.15 m

net torque=F1*r1*cos(theta1) + F2*r2*cos(theta2)

net torque=m1*g*cos(theta1)+m2*g*r2*cos(theta2)

=47*9.8*1.15*cos(25.5)+34.5*9.8*2.15*cos(25.5)

=1134.2 Nm

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