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 40.0 kg, is hanging 1.80 m along the branch from the tree trunk. The other child, with a mass of 29.0 kg, is hanging 2.00 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

Answer:1135.13 N-m

Step-by-step explanation:

Given

inclination of tree from horizontal $\theta =27^{\circ}$

mass of first child $m_1=40 kg$

distance of first child $r_1=1.8 m$

mass of first child $m_2=29 kg$

distance of first child $r_2=2.0 m$

Torque exerted by first child

$T_1=m_1g\cos \theta \times r_1$

$T_1=40\times 9.8\cos 27\times 1.8=628.69 N-m$

Torque exerted by second child

$T_2=m_2g\cos \theta \times r_2$

$T_2=29\times 9.8\cos 27\times 2=506.44 N-m$

Both torques are in same sense therefore

$T_{net}=T_1+T_2$

$T_{net}=628.69+506.44$

$T_{net}=1135.13 N-m$