Estimate power of the motor:

A punching machine punches 6 holes per minute. The diameter of each of the hole is 4 cm and thickness of the plate is measured as 3 cm. The stroke of the punch is as 10 cm. The work done per square cm of sheared area is equal to 600 J. The maximum speed of the flywheel at its radius of gyration is equal to28 m/s. Estimate mass of the flywheel needed so that its speed at its radius gyration does not fall below 26 m/s. Estimate power of the motor needed.

Solution

The sheared area of the hole = Circumference × depth

                                                    =π × 4 × 3 = 12π = 37.68 cm²

Energy needed per hole E = 37.68 × 600 = 22608 J

Number of holes per minute = 6

∴          Energy needed per minute = 6 × 22608

∴          Energy needed per second = (6 × 22608)/60 = 2260.8

∴          Power of motor needed = 2260.8/1000 = 2.2608 kW = 2.26 kW

The fluctuation of energy

                  = 22608 (1 - 0.15)

                  = 22608 × 0.85 = 19216.8 J

∴          19216.8 = M² (28²  - 26² ) = 108 M = 54 M

 or,       M = 355.87 kg.