Question

A stuntman whose mass is 76 kg swings from the end of a 3.5-m-long rope along the arc of a vertical circle. Assuming that he starts from rest when the rope is horizontal, find the magnitudes of the tensions in the rope that are required to make him follow his circular path at each of the following points.

(a) at the beginning of his motion

(b) at a height of 1.5 m above the bottom of the circular arc

(c) at the bottom of the arc

Answer 1

The three situations can be visualized by

PART A:

At the beginning of the motion, the stuntman is at the position A.

At this position, the centripetal force for the circular motion is provided by the tension in the string alone and we know that the centripetal force is given by

The speed at position A is zero as the stuntman starts from rest. So, the tension is given by

So, the tension in the rope when the stuntman is at point A is 0 N.

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PART B:

At position B the speed of the stuntman can be calculated using conservation of energy. i.e

The centripetal force at this point is given by

From the diagram

From the diagram

That gives us

So, the tension in the rope when the stuntman is at point B is 1276.8 N.

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PART C:

At point C, the conservation of energy gives us

The centripetal force at this point is given by

From the diagram

So, the tension in the rope when the stuntman is at point C is 2234.4 N.