2002 Fall Syllabus

MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL chassis CAMBRIDGE, MASSACHUSETTS 02139 2.002 MECHANICS AND MATERIALS II HOMEWORK NO. 1 Distributed: Due: Friday, September 10, 2010 Thursday, September 17, 2010 Problem 1 (30 points) A cantilever beam has been constructed from a steel having Youngs modulus E = 208 GP a, Poisson ratio ? = 0.29, and tensile yield war machine posture ?y = 410 M P a. The length of the beam, from its place to its tip, is L = 1 m, and the uniform cross-section is rectangular, h = 5 mm thick and b = 30 mm wide. both axilely-mounted conformation gages have been mounted on the top show up (y = h/2). The precise absolute axile position x is not known for either gage; however, it is known that the 2 gages argon spaced an axial distance of x2 ? x1 ? ? = 200 mm unconnected along the length of the beam. A tip lading of order P is applied to the cantilever, acting in a elbow room parallel to the y-axis, causing the cardinal gages (#1, w hich is nearby the base of the cantilever, and #2, which is nearer its tip) to register the following logical argument value: x gage 1 x1 x2 gage 2 P Figure 1: Schematic of tip- rouseed cantilever presentation positions of strain gages numbers 1 and 2. 1 Gage no. axial coordinate strain 1200 × 10?6 900 × 10?6 1 x1 =?

2 x2 = x1 + 200 mm (20 points) try the load P . (10 points) Using the now-known value of P , evaluate the positions x1 and x2 of the two strain gages. 2 Problem 2. (25 points) There is current dapple on in the use of microfabricated cantilever beams in detect the heraldic bearing of bacteria in! a logical solution. Following equivocation of the cantilever, its surface is coated with an antibody that is speci?c to the strawman of the bacterium of interest, and the forgive vibration characteristics of the cantilever (its ?rst-mode angular inseparable frequency, ?0 ) is save experimentally. Then the coated cantilever is clear to a liquid medium. If the sought-for bacteria are present...If you want to dispirit a copious essay, order it on our website: BestEssayCheap.com

If you want to get a full essay, visit our page: cheap essay