5 A young man of mass 60 kg swings on a trapeze. A simple model of this situation is as follows.
The trapeze is a light seat suspended from a fixed point by a light inextensible rope. The man's centre of mass, G , moves on an arc of a circle of radius 9 m with centre O , as shown in Fig. 5. The point C is 9 m vertically below O . B is a point on the arc where angle COB is \(45 ^ { \circ }\).
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\caption{Fig. 5}
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- Calculate the gravitational potential energy lost by the man if he swings from B to C .
In this model it is also assumed that there is no resistance to the man's motion and he starts at rest from B.
- Using an energy method, find the man's speed at C .
A new model is proposed which also takes into account resistance to the man's motion.
- State whether you would expect any such model to give a larger, smaller or the same value for the man's speed at C . Give a reason for your answer.
A particular model takes account of the resistance by assuming that there is a force of constant magnitude 15 N always acting in the direction opposing the man's motion. This new model also takes account of the man 'pushing off' along the arc from B to C with a speed of \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Using an energy method, find the man's speed at C .