MIT2_007s09_sol_exam02A

MIT2_007s09_sol_exam02A - MIT OpenCourseWare...

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MIT OpenCourseWare http://ocw.mit.edu 2.007 Design and Manufacturing I Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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Page 1 of 13 2.007 – Design and Manufacturing I Draft Exam on Gears, Springs, Mechanisms, and Drawing This is a practice exam. On the real exam, you’ll have 1.5 hours to answer about 7 questions. This exam is somewhat longer and would take about 2.5 hours by my reckoning. Point allocations (out of 100 total) are listed for each question based on what they’d be worth on the real exam. So, this practice exam adds up to about 160 points. 1. (10 points) Define the term “hysteresis . Explain its significance for sensors and for energy storage elements (e.g. rubber bands). The wikipedia entry for hysteresis inluded the following material I find both accurate and relevant to the course: “a syst em with hysteresis exhibits path- dependence” “A simple way to understand it is in terms of a rubber band with weights attached to it. If the top of a rubber band is hung on a hook and small weights are attached to the bottom of the band one at a time, it will get longer. As more weights are loaded onto it, the band will continue to extend because the force the weights are exerting on the band is increasing. When each weight is taken off, or unloaded , it will get shorter as the force is reduced. As the weights are taken off, each weight that produced a specific length as it was loaded etch . ing onto the band now produces a slightly longer length as it is unloaded. … In one sense the rubber band was harder to str when it was being loaded than when it was being unloaded …In another sense more energy was required during the loading than the unloading; that energy must have gone somewhere, it was dissipated or "lost" as heat. Elastic hysteresis is more pronounced when the loading and unload is done quickly than w hen it's done slowly… The Flexiforce sensors available to you in the contest “kit” exhibit a modest degree of hysteresis http://www.tekscan.com/pdfs/FlexiforceUserManual.pdf: Figure by MIT OpenCourseWare. Please also see http://upload.wikimedia.org/wikipedia/commons/d/df/Elastic_Hysteresis.jpg
Page 2 of 13 2. (10 points) You fill a one liter container with air at 60 psi gauge pressure and plan to use it as a source of power for a machine. The air in the bottle is at thermal equilibrium with the air in the room at 20 degree Centigrade. Estimate the force applied if a valve is opened connecting the reservoir of air to a piston with a three inch internal diameter and a four inch throw. First, consider the case that the air flow is minimal, for example if the actuator is used to apply a force at the beginning of its throw. If we assume the volume of the pneumatic lines is small compared to the one liter reservir, then 60 psi is applied to the face of the piston. The piston has a three inch diameter, about 7 square inches of area, and therefore 7in^2*60psi=420 pounds of force would be applied.

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MIT2_007s09_sol_exam02A - MIT OpenCourseWare...

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