Solve the following engineering problems by coding in python:
A super charged road racing automobile has an engine capable of giving
an output torque of 1 kN-m, this torque being reasonably constant over a speed range from
100 km/h to 275 km/h in top gear. The road wheels are of 0.9 m effective diameter, and the back axle
ratio is 3.3 to 1. When travelling at a steady speed of 170 km/h in top gear on a level road, the
power absorbed is 50 kW. The vehicle has a mass of 1000 kg, the four road wheels each has mass of
40 kg and a radius of gyration of 0.25 m. The moment of inertia of the engine and all parts forward
of the differential is 6 kg-m^2. Assuming that the resistance caused by windage and road drag varies as the square of the speed, determine the time taken for the speed to rise from 100 km/h to 275 km/h in top gear at full throttle on an upgrade of 1 in 30.
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
1. The power which the motor must develop to drive the machine at a uniform speed of 160 r.p.m.,
2. The time required for the speed of the machine to increase from zero to 60 r.p.m., when the
torque developed on the motor armature in starting from rest is 30 N-m, and
3. If the gear ratio were altered so as to give the machine the greatest possible angular
acceleration in starting from rest, what would then be the gear ratio ? The starting torque of the
motor is 30 N-m as before.