A punching machine has to carry out piercing operations at the rate of 12 holes per minute. The amount of work to be done in cutting 30mm diameter holes in 15mm thick plate is 8J/mm2 of the sheared area. The actual piercing operation takes 2s. The total frictional losses over a cycle are equivalent to one sixth of the work done during a single piercing operation. The machine shaft is driven by a constant power electric motor. The maximum fluctuation of the speed of the machine shaft is between 190 rev/min and 210 rev/min.
(a) Find the minimum required motor power to drive the piercing machine

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