Tarzan plans to cross a gorge by swinging in an arc from a hanging vine. if his arms are capable of exerting a force of 1420 n on the rope, what is the maximum speed he can tolerate at the lowest point of his swing? his mass is 81.9 kg and the vine is 5.2 m long.

Angular velocity:

Linear velocity:

Explanation:

When he swings he es ina a circular movement with radius 5.2m. To maintain this circular movement at any time there must be total force on Tarzan equal to the centripetal force:

where m is his mass, r the radius and w the angular velocity. At the lowest point on Tarzan there are two forces acting, gravity and the rope tension, this rope tension equals the force on Tarzan arms:

Where T is the tension on his arms, and W the weigth calculated as:

Where g is the acceleration of gravity. replacing this and remembering that the total force must equal the centripetal force:

Solving for w:

To get the linear velocity at this point:

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where is the circuit diagram ?