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At a construction site a box with a mass of 100 kg is to be moved vertically using an elevator.

At a construction site a box with a mass of 100 kg is to be moved vertically using an elevator. A motor, which
can supply a constant torque of 2 kN·m is directly attached to a gear with 53 teeth. The moment of inertia of all
parts keyed to the shaft attached to the motor is 43.5 kg·m
2
. A disk which is attached to a second shaft (shaft 2,
which is geared to the motor shaft) has a rope wrapped around it by which the box is to be pulled vertically
upward. The moment of inertia of all parts keyed to shaft 2 is 22.71 kg·m
2
. The diameter of the disk is 25 cm,
and the efficiency of the gear train is 72%. Select the number of teeth on the gear which is keyed to shaft 2
such that the acceleration of the box is a maximum. Determine the corresponding acceleration of the box.

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