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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 Spring '09
 inverse laplace

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