# An electric motor drives a machine through a speed reducing gear of ratio 9:1. The motor armature, with its shaft and gear wheel, has moment of inertia 0.6 kg-m^2. The rotating part of the driven machine has moment of inertia 45 kg-m^2. The driven machine has resisting torque of 100 N-m and the efficiency of reduction gear is 95%. Find the power which the motor must develop to drive the machine at a uniform speed of 160 r.p.m.

+1 vote
An electric motor drives a machine through a speed reducing gear of ratio 9:1. The motor armature, with its shaft and gear wheel, has moment of inertia 0.6 kg-m^2. The rotating part of the driven machine has moment of inertia 45 kg-m^2. The driven machine has resisting torque of 100 N-m and the efficiency of reduction gear is 95%. Find the power which the motor must develop to drive the machine at a uniform speed of 160 r.p.m.

(a) 1764 W

(b) 2764 W

(c) 3764 W

(d) 4764 W

This question was addressed to me during a job interview.

Enquiry is from Numericals On Kinetics Of Motion and Loss of Kinetic Energy in chapter Kinematics & Kinetics of Motion of Machine Kinematics

by (45.7k points)
Right choice is (a) 1764 W

To explain I would say: Given : G = 9; IA = 0.6 kg-m^2 ; IB = 45 kg-m^2;

TB = 100 N-m; η = 95% = 0.95;

N = 160 r.p.m. ; N1 = 0 ; N2 = 60 r.p.m.  TA = 30 N-m

We know that the power which the motor must develop,

P = 2πN TB/60× η

= 2π × 160 × 100/60 x 0.95

= 1764 W