A branch of a tree grows out from the trunk at an angle of 29.0° above the horiz

Question

A branch of a tree grows out from the trunk at an angle of 29.0° above the horizontal. Two children hang by their hands from the branch of the tree. The first child has a mass of 46.0 kg and hangs 1.45 m from the tree trunk, as measured along the length of the branch. The second child, with a mass of 31.0 kg, hangs 2.10 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. N m

Explanation / Answer

tree branches are of angle 29 degrees

child 1 mass m1 = 46 kg , l1 = 1.45 m

child 2 mass m2 = 31 kg , l2 = 2.10 m

let the torque about the trunk is  

Tx = m1*l1 cos theta + m2*l2 cos theta

Tx = 46*1.45 cos 29 + 31*2.10 cos29

and the Tx = 58.34 + 57 Nm = 115.34 N.m

so the net torque exerted on the branch is 115.34 N.m

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