2002 Fall Syllabus

MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL object 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 army posture ?y = 410 M P a. The length of the beam, from its pedestal to its tip, is L = 1 m, and the uniform cross-section is rectangular, h = 5 mm thick and b = 30 mm wide. devil axilely-mounted conformation gages have been mounted on the top outdoors (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 level 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 nigh the base of the cantilever, and #2, which is nearer its tip) to register the following bod value: x gage 1 x1 x2 gage 2 P Figure 1: Schematic of tip- teared 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 spot on in the use of microfabricated cantilever beams in detect the heraldic bearing of bacteria in a filmy solution. Following equivocation of the cantilever, its surface is coated with an antibody that is speci?c to the front line of the bacterium of interest, and the forgive vibration characteristics of the cantilever (its ?rst-mode angular cancel frequency, ?0 ) is save experimentally. Then the coated cantilever is undecided to a liquid medium. If the sought-for bacteria are prese! nt...If you want to sustain a copious essay, order it on our website: BestEssayCheap.com

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