A DC motor gearbox and hoist drum question thanks in advance

A DC motor, gearbox and hoist drum question, thanks in advance!

You are required to design a system that is repeatedly required to raise and lower a mass of 100kg. The system must be able to raise the 100kg mass at a rate of lm/s. and lower it as fast as possible (while remaining in control). It is proposed that a DC motor connected to a hoist drum via a gear transmission system is used for this purpose and you are require to complete some aspects of the design and analysis of this system. The parameters of the hoist/motor system are: Diameter of drum = 0.3m Drum inertia = 12kgm2 Inertia of motor = 2kgm2 Armature resistance = 212 Rotational viscous friction on the drum Determine the mechanical equations of motion for the mass, hoist, and motor system, and reflect these equations of motion to the motor shaft. Determine the transmission gear ratio G for maximum acceleration. Determine the motor constant K_m from the following information: A voltage of 200V is applied to the motor for it to directly drive a 50Nm load at rotational speed of 400rpm. The motor is then connected to the hoist load. What motor terminal voltage is required to lift the 100kg mass at a rate of 1 m/s. Use the values for G and Km that you calculated in the parts (b) and (c) of this question - if you have been unsuccessful in calculating these values use Km = G = 2. This same hoist-motor system is to be used to lift smaller loads. Explain how you can increase the speed of lifting smaller loads without changing any part of the mechanical design or the terminal voltage.

Solution

lets calculate power first P= M V g/N   

where (m= mass= 100 kg, velocity v= 1m/s , g = 9.8 , N = frictional losses = 10 w drum,)

=> 100 X 1 X 9.8 / 10

=> 98 joules / sec