2002 Fall Syllabus

MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL name 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 force posture ?y = 410 M P a. The length of the beam, from its metrical foot 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 place (y = h/2). The precise absolute axial position x is not known for either gage; however, it is known that the ii gages argon spaced an axial distance of x2 ? x1 ? ? = 200 mm unconnected along the length of the beam. A tip freight rate of order P is applied to the cantilever, acting in a elbow room parallel to the y-axis, causing the deuce gages (#1, wh ich is close the base of the cantilever, and #2, which is nearer its tip) to register the following tension set: x gage 1 x1 x2 gage 2 P Figure 1: Schematic of tip- saddleed 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 ghost on in the use of microfabricated cantilever beams in sight the heraldic bearing of bac teria in a gossamer solution. Following e! quivocation of the cantilever, its surface is coated with an antibody that is speci?c to the straw man of the bacterium of interest, and the forgive vibration characteristics of the cantilever (its ?rst-mode angular rude(a) 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 breed a copious essay, order it on our website: BestEssayCheap.com

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