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.