To build a wide fixed-free cantilever beam with a force constant of 10 N/m and a resonant frequency of 10 kHz out of single crystal silicon, find the desired length and thickness of the cantilever beam.The Young’s modulus of silicon is 120 GPa. The density of the silicon material is 2330 Kg/m3

4. A hollow shaft with outside diameter of 14 cm and wall thickness of 0.8 cm transmits 200 kW at 400 rpm. What must be the angular deflection (degrees) of the shaft If the length is 4 meters? The material of the shaft is C4140 steel.

5. Compare the formulation of wave propagation (one-dimensional) in elastic and viscoelastic environments and say that if the return time to equilibrium is zero, what will be the difference between the wave velocities in the two assumed environments? (

In the analysis of stress transfer along the length of the short fiber, it was assumed that the matrix is a perfectly plastic material for which the strength was T= Ty and the stress distribution was obtained as of= 2*Tyz'r where z is the distance from fiber end and 2r is the interface diameter of the fiber. Consider a linear variation of interface shear stress as T = Ty-kz, where k is a constant. Assuming this linear variation, derive an expression for the load transfer length in terms of maximum fiber stress (occurring at mid fiber length), fiber radius and the matrix shear stress Ty-

1. Arectangular plate 50 mm x 10 mm with a hole 10 mm diameter is subjected to an axial load of 10KN. Taking stress concentration into account, find the maximum stress induced. [Ans. 50 MPa]

find the deflection under the load f in the following sketch using the following two approaches: a. Assume the bar is rigid ( EI don't matter) using the Principe of Stationary Potentiel Energy. b. Assume the bar is flexible (EI matter) using the rayleigh-ritz method. hint: you can assume a polynomial displacement field with two d.o.f. c. How do the answers from parts (a) and (b) compare if, in part (b), you also assume that ei = kl3? in this case, you should be able to write your displacement for part (b) again in terms of only f, k, and maybe l.

At room temperature (20°C) the electrical conductivity of Gallium phosphide (GaP) is 63 (2.m)–1, whereas the electron and hole mobility are 0.24 and 0.057 m²/V-s, respectively. a) Compute the intrinsic carrier concentration for GaP at room temperature, (q=1.6 x 10 -19 c). b) If the energy gap of GaP is 0.92 eV, calculate its conductivity at 70°C (k= 8.62 x 10 eV/K). -5

An optical fiber for telecommunication is made of SiO2 glass (density = 2.20 Mg/m'). How many Si atoms and how many O atoms are present per millimeter of length (L=1 mm) of a fiber 10 um in diameter (d=10 mm)? Given: M(Si)=28.09 g/mole M(O)=16 g/mole Avogadro's Number: AN = 0.6203 (10)24

From the matrix can you show me how the value stiffness (k) calculated?

A 0 degree lamina of glass fiber-epoxy 3501 composite with fiber arranged withmax. volume fraction of fiber in a square array is subjected to a stress σx = 50MPa at theta =20 degrees. What are the resulting lamina strains [ε]xy and strains[ε]12? (Apply the Halpin-Tsai correction to transverse moduli and shear moduli)