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6 problems on Engineering Mechanics I
Typology: Exercises
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Due: Wednesday ƱSeptember 12, 2007 (In Class)
MIT Ʊ1.050 (Engineering Mechanics I) Fall 2007 Instructor: Markus J. BUEHLER
This subject, 1.050 Engineering Mechanics I, builds upon what you have learned in your physics and mathematics courses, in particular at MIT, 8.01 and 18.01. The following exercises, which are inspired from problem sets in 8.01 and 18.01, are designed for you to refresh your memory after the long summer. They are also important for us to get a good feel on what we can build together Ʊnow that we start to explore the world of Engineering Mechanics. In all these exercises, specify your assumptions, and feel free to add any physics quantity you may need to provide an engineering answer. Furthermore, specify all the resources you use for your solution.
Team Building and Team Work We strongly encourage you to form Homework teams of three students. Each team only submits one solution for correction. We expect true team work, i.e. one where everybody contributes equally to the result. This is testiĆed by the team members signing at the end of the team copy a written declaration that Ƭthe undersigned have equally contributed to the homeworkĆ®. Ideally, each student will work Ćrst individually through the homework set. The team then meets and discusses questions, diĀ¢ culties and solutions, and eventually, meet with TA or instructor. This Ćrst assignment is a good occasion for team building.
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Figure by MIT OpenCourseWare.
(a) When Alberto placed an egg in a container full of water, he noticed that it sank. Why was that so? Explain the phenomenon. (b) Someone told Alberto a trick to make the egg Ɣoat: add some salt to the water, mix thoroughly, and surely enough, the egg Ɣoated! If the container Alberto used had 1 liter of water, how much salt did he add to make the egg Ɣoat? Make any assumptions you think appropriate, just make sure to justify your procedure. Use the handout from the CRC Handbook of Chemistry and Physics posted in the for data on concentration of salt and mass per unit weight of water.
class website
(a) Set up the di§erential equation, and solve for the position of the ball as a function of time, z (t). Use the appropriate boundary conditions. (b) Calculate the terminal velocity for the motion of the ball. Assume that the height of the building and the time to reach the Ôoor are large enough to allow the ball to reach the terminal velocity. (c) Numerical application: Using a drag coe¢ cient c = 0: 1 s ^1 , plot the velocity of the ball as a function of time v (t) for three di§erent initial velocities: V 0 = 10; 100 ; 200 m/s. For this numerical application, use MATLAB to construct the plot. Inter- pret your results.
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(a) Find the optimal dimensions l and for the channel displayed in the Ćgure. (b) A colleague of yours in the company proposes the use of a semi-circular shape for the same size of cross-section area obtained in part (a). Would this be advan- tageous? Explain your answer in terms of other engineering aspects involved in optimization problems (e.g. material cost, labor).
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