What is the magnitude of the net torque exerted on the branch by the children?

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 26.3° above the horizontal. One child, with a mass of 46.0 kg, is hanging 1.36 m along the branch from the tree trunk. The other child, with a mass of 34.2 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.

I would really appreciate your help! Thank you :)

Answer 1

First find the horizontal distances each child is from the trunk (axis).

1.36m = (cos 26.3) x 1.36, = 1.22 metres.

2.11m = (cos 26.3) x 2.11, = 1.89 metres.

(46kg x 1.22m) = 56.12kg/m.

(34.2kg x 1.89m) = 64.64kg/m.

Total torque = 120.76kg/m. around axis.

Answer 2

net torque=[(46.0kg)*(9.8m/s^2)*(1.36m)*(Cos 26.3° ) + (34.2kg)*(9.8m/s^2)*(2.11m)*(Cos 26.3° )]Nm

=((46×9.8×1.36)+(34.2×9.8×2.11))×cos(26.3) = 1183.61Nm

Answer 3

it should be kg * m not kg/m