hw2sol

hw2sol - ME 475 HOMEWORK #2 Solutions Spring 2011 PROBLEM...

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1 ME 475 HOMEWORK #2 Solutions Spring 2011 PROBLEM 1 : GIVEN : A rapid transit train car weighs 63000 lb. The combined effects of air resistance and wheel rolling resistance provide equivalent viscous damping of 147 lb/(ft/sec). The dc traction motors that propel the train car run on 1000 volts and provide an equivalent traction force of 17.3 lb/volt. FIND : (a) Provide a schematic to show how to set up this problem. Consider the velocity as the variable of interest. (b) Show that the governing equation of motion for this problem is given by: where v is the velocity and E is the applied motor voltage. (c) Using Laplace transform techniques, solve the equation of motion for v(t) given that E(t) is a step of 1000 volts. (d) Based on your solution of part (c), what is the top speed of this train (in miles per hour )? (e) Based on your solution of part (c), determine how long it will take for the train to reach a speed of 60 miles per hour. SOLUTION : (a) Schematic: (b) Equation of motion: where m = 63000/32.2 = 1956.5 slugs b = 147 lb/(ft/sec) and K = 17.3 lb/volt.
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hw2sol - ME 475 HOMEWORK #2 Solutions Spring 2011 PROBLEM...

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