Question

A branch of a tree grows out from the trunk at an angle of 28.0�� above the horizontal. Two children hang by their hands from the branch of the tree. The first child has a mass of 43.5 kg and hangs 1.25 m from the tree trunk, as measured along the length of the branch. The second child, with a mass of 32.0 kg, hangs 1.80 m from the tree trunk, also measured along the branch. Determine the magnitude (in N �� m) of the net torque exerted on the branch by the children, about an axis located where the branch joins the tree trunk and is perpendicular to the plane formed by the branch and the trunk?

Answer 1

To determine the magnitude of the net torque exerted on the branch by the children, calculate the torque contributed by each child and add them together. The torque can be calculated using the formula: torque = force * distance.

Step-by-step explanation:

To determine the magnitude of the net torque exerted on the branch by the children, we need to calculate the torque contributed by each child and then add them together.

The torque contributed by the first child can be calculated using the formula: torque = force * distance.

The force exerted by the first child is equal to the weight of the child, which can be calculated as: force = mass * gravity. The distance is the perpendicular distance between the child and the axis of rotation, which is given as 1.25 m.

Similarly, we can calculate the torque contributed by the second child.

The net torque is the sum of the torques contributed by both children.

Using the given values, the torque exerted on the branch by the children is 192.4 N · m.