# A branch of a tree grows out from the trunk at an angle of 26.0° above the horizontal. Two children hang by their hands from the branch of the tree. The first child has a mass of 43.0 kg and hangs 1.40 m from the tree trunk, as measured along the length of the branch. The second child, with a mass of 34.5 kg, hangs 1.95 m from the tree trunk, also measured along the branch. Determine the magnitude (in N · m) 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.

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A branch of a tree grows out from the trunk at an angle of 26.0° above the horizontal. Two children hang by their hands from the branch of the tree. The first child has a mass of 43.0 kg and hangs 1.40 m from the tree trunk, as measured along the length of the branch. The second child, with a mass of 34.5 kg, hangs 1.95 m from the tree trunk, also measured along the branch. Determine the magnitude (in N · m) 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.
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Step 1

Given,

Mass of 1st child, m1 = 43.0 kg

Mass of 2nd child, m2 = 34.5 kg

Distance of 1st child from trunk, d1 = 1.40 m

Distance of 2nd child from trunk, d2 = 1.95 m

Angle of branch from trunk, α = 26.0o

Step 2

Formula used:

Weight = Force (F) = mass x acc. due to gravity = mg

Torque (T) = Force x perpendicular distance = F x d

Free body diagram of branch is below

Step 3

Net torque exerted on the branch by ...

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