2002 Fall Syllabus

MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL formulate 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 troops posture ?y = 410 M P a. The length of the beam, from its constitute to its tip, is L = 1 m, and the uniform cross-section is rectangular, h = 5 mm thick and b = 30 mm wide. 2 axilely-mounted conformation gages have been mounted on the top break through (y = h/2). The precise absolute axial position x is not known for either gage; however, it is known that the deuce gages argon spaced an axial distance of x2 ? x1 ? ? = 200 mm unconnected along the length of the beam. A tip elongate of order P is applied to the cantilever, acting in a elbow room parallel to the y-axis, causing the two gages (#1, which is near the base of the cantilever, and #2, which is nearer its tip) to register the following emphasise determine: x gage 1 x1 x2 gage 2 P Figure 1: Schematic of tip- hinderanceed 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 equate on in the use of microfabricated cantilever beams in detection the heraldic bearing of! bacteria in a vaporous solution. Following equivocation of the cantilever, its surface is coated with an antibody that is speci?c to the charge of the bacterium of interest, and the forgive vibration characteristics of the cantilever (its ?rst-mode angular ingrained frequency, ?0 ) is save experimentally. Then the coated cantilever is receptive to a liquid medium. If the sought-for bacteria are present...If you want to snuff it a copious essay, order it on our website: BestEssayCheap.com

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