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 27.0° above the horizontal. One child, with a mass of 38.0 kg, is hanging 1.00 m along the branch from the tree trunk. The other child, with a mass of 33.0 kg, is hanging 2.10 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

Answer 1

here,

theta = 27 degree

mass of child 1 , m1 = 38 kg

l1 = 1 m

mass of child 2 , m2 = 33 kg is at l2 = 2.1 m

the magnitude of net torque acting on the branch by the children , T = m1 * g * l1 * cos(theta) + m2 * g * l2 * cos(theta)

T = (38 * 1 + 33 * 2.1) * 9.81 * cos(27)

T = 937.9 N.m

the magnitude of net torque acting on the branch by the children is 937.9 N.m