A cat burglar is planning a daring heist. He will lower himself from a beam as shown in the figure on the left. The burglar weighs 150 lbs. He plans to use a long rope that can withstand a tension of 100 lbs to suspend himself from a shorter rope, reasoning that each segment of the longer rope will only need to support half his weight. (The short rope segment is Kevlar and can easily support the burglar's full weight.)
(a) Despite your moral outrage, you decide to set the burglar straight. Compute the tensions T1, T2, and T3 and explain why the plan will not work.
(b) As a strictly intellectual exercise, you design an alternative arrangement of ropes that will support the burglar's weight using the same long rope from part (a). In the configuration on the right, what is the maximum angle f
that will result in a tension of less than 100 lbs in each segment of rope?
You may ignore the mass of the rope in parts (a) and (b).
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