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Assignment on Dynamics - 2007 - MIT
Typology: Exercises
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Turn in each problem on separate sheets so that grading can be done in parallel
Problem 1 (20 points)
Foam can’t hurt the Shuttle?
The space shuttle Columbia was damaged on liftoff when a piece of insulating foam from the bipod ramp that holds the shuttle to the external tank came loose, accelerated in the air flow and hit the leading edge of the wing. The wing span of the shuttle is 78 ft. Use 56 ft. as your estimate of the flight path length of the foam in the air stream (see figure).
The incident occurred at an altitude of 65600 ft where the atmospheric density is .000171 slugs/cu ft. The velocity of the shuttle was 2500 fps. The foam block had a cross sectional area of 1 sq ft and a weight of 2 lbs. Assume a drag coefficient CD=1.25.
Problem 2 (20 points)
The technique used to obtain an analytic solution to the governing equation of Problem 1 is not always possible. In this problem, determine the solution by a numerical ap proach to the solution of the ordinary differential equation using MATLAB. This will prepare you for our later uses of MATLAB both in the homework and in the extended labs. Use the parameters given in problem 1. run your numerical method and answer the questions posed in problem 1, parts 1.1, 1.2, and 1.7. Become familiar with the numerical approach, explore graphical presentations, have fun. Plot x(t) and v(t) vs. t for parts 1.2 and 1.7.
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16.07 Dynamics Fall 2009
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