Two children hang by their hands from the same tree branch. The branch is straig

Question

Two children hang by their hands from the same tree branch. The branch is straight, and grows out from the tree at an angle of 27° above the horizontal. One child, with a mass of 53 kg, is 1.2 m along the branch from the tree trunk. The other child, with a mass of 52 kg, is 2.2 m along the branch 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.

Explanation / Answer

Torque = Force * perpendicular distance = m1 g * ( r1 cos theta ) + m2 g * ( r2 cos theta ) = 53 * 9.8 * 1.2 * cos 27 + 52 * 9.8 * 2.2 * cos 27 = 1554.3 N.m Note: Clockwise torque is considered to be negative, where as the counterclockwise torque is considered to be positive.

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