3. A branch of a tree grows out from the trunk at an angle of 26.5° above the ho

Question

3. A branch of a tree grows out from the trunk at an angle of 26.5° above the horizontal. Two children hang by their hands from the branch of the tree. The first child has a mass of 46.5 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 36.0 kg, hangs 1.90 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

here,

for the tree branch

theta = 26.5 Kg

m1 = 46.5 Kg , d1 = 1.15 m

m2 = 36 Kg , d2 = 1.90 m

Now ,

magnitude of net torque acting on the branch = m1 * g * d1 * cos(theta) + m2 * g * d2 * cos(theta)

magnitude of net torque acting on the branch = 46.5 * 9.8 * 1.15 * cos(26.5) + 36 * 1.90 * 9.8 * cos(26.5)

solving

magnitude of net torque acting on the branch = 1068.9 N.m

the magnitude of net torque acting on the branch is 1068.9 N.m

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