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Problem 2 (40 points): PMDC motor If a manufacturer's specifications for a PM DC motor shows that it has the following parameters: Parameter Value 1.7 Unit Nm/A Torque constant k Electrical constant ku 9 V/1000 RPM S2 Armature resistance R 1.2 1) For an input voltage Vin- 24, a. Find the starting torque T, in N.m. [3 points] b. Find the motor's no-load speed @max [5 points] c. Find the stall current I, in A. [3 points] 2) Plot the Torque - Speed and the Current - Speed curves on the same graph using different ordinate axis. Show co is in rad/s and rpm on the abscissa axis. [3 points] 3) Find the equation of torque T(co) in N.m and the equation of current I(o) in A when o is in rad/s. [5 points] 4) Find the equation of Mechanical Power Pm (o), Electrical Power Pe (o) in watts and the motor efficiency n (). [5 points] 5) Find (* where Pm (o) is maximum. Deduce Pm (*) Show all the steps in the uploaded document and fill the final answers below. [4 points] 6) Taking 10 steps in the abscissa axis from zero to Oma Plot the three curves Pm (o). Pe (c) and n (co) on the same graph above. Deduce the torque, the speed and the current of the operational point where the motor is running with a maximum efficiency. Show this point on the graph. [3 points] 7) We are using the PMDC studied above to lift up vertically the mass in the Mass-Pulley system shown below with an acceleration a = 0.34 m/s², where the m = 0.8 kg and the pulley radius r= 6 cm and polar mass moment of inertia J-0.003 kg.m². Neglect the motor shaft mass moment of inertia and any dissipative force. a. Find am on the motor shaft. [1 point] b. Find the Je of the system pulley-mass. [3 points] c. Find the torque required by the motor to lift the mass and accelerate. [3 points] d. Is the motor that we have capable of doing the work? why? if not, what is your suggestion to fix the problem without changing it? [2 points]