Mathematics: 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

Step-by-step explanation:57,200...

Two children hang by their hands from the same tree

meganenaranjo

09.01.2022

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

$T_{net}=T_1+T_2$

$T_{net}=628.69+506.44$

$T_{net}=1135.13 N-m$

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