An elastic bar of length L spins with angular velocity ω about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = ω 2 x. Due to this radial acceleration, the bar stretches along x with displacement function u(x). The displacement u(x) is governed by the following equations: ( d dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (1) where σ(x) is the axial stress in the rod, ρ is the mass density, and E is the (constant) Young’s modulus. The bar is pinned on the rotation axis at x = 0, and it is free at x = L.   Determine:1. Appropriate BCs for this physical problem.2. The displacement function u(x).3. The stress function σ(x).

With reference to the given figure: a) Draw a free-body diagram of the structure supporting the pulley. b) Draw shear and bending moment diagrams for both the vertical and horizontal portions of the structure. 48 in. 100 lb 12 in. Cable 27 in. 12-in. pulley radius 100 lb Cable

Consider a standard piston engine . Draw a free body diagram of the piston. Then:a) For an A  SI engine with a 100 mm bore at an instantaneous cylinder pressure of 42 bar i. Calculate the level of the combustion gas loading force on the wrist pin in kN. b)  Repeat this calculationfor a forced-induction Diesel engine with a 145 mm boreat a cylinder pressure of 115 bar

Figure 1 shows a half-wave controlled rectifier which is supplied by a Vin = 120 Vrms voltage source. Assume that the load resistance is R = 10 2. Determine: a) The firing angle a of the thyristor to produce an average output voltage 50Vdc. Vin=Vmsinoot b) The average power Po absorbed by the load R. Figure 1 R = 1092

For each set of measurements below, calculate the Grubbs statistic, G, look up the appropriate critical value of G from Table 4.6, and determine whether the Grubbs test supports discarding the first value in the list at the 95% level of confidence. a) 106.0, 165.0, 167.5, 170.5, 163.5, 170.7 (Geale -2.028; Gerit 1.822; yes, the Grubbs test supports discarding 106.0) b) 214.8, 263.0, 229.9, 236.9, 221.8, 230.8, 241.1 c) 357.0, 309.3, 304.9, 314.8, 305.8, 295.3, 284.7, 299.5 TABLE 4-6 Critical values of G for rejection of outlier Number of observations otsulsve os Tenos nagsibarito G to buboxy (95% confidence) 456 1.463 1.672 1.822 7 1.938 8 upa 2.032 9 2.110 10 2.176 - 1 12 15 20 11 2.234 2.285 2.409 2.557

6.6 Consider a one-dimensional hole flux as shown in Figure 6.4. If the generation rate of holes in this differential volume is gp = 100 cm³-s¹ and the recombination rate is 2 × 1019 cm³-s, what must be the gradient in the particle current density to maintain a steady-state hole concentration?

6.4 (a) A sample of semiconductor has a cross-sectional area of 1 cm² and a thickness of 0.1 cm. Determine the number of electron-hole pairs that are generated per unit volume per unit time by the uniform absorption of 1 watt of light at a wavelength of 6300 Å. Assume each photon creates one electron-hole pair. (b) If the excess minority carrier lifetime is 10 μs, what is the steady-state excess carrier concentration?

6.1 Consider silicon at 7 = 300 K that is doped with donor impurity atoms to a concentra- tion of Na = 5 x 105 cm³. The excess carrier lifetime is 2 x 10-'s. (a) Determine the thermal equilibrium recombination rate of holes. (b) Excess carriers are generated such that Sn = p = 104 cm³. What is the recombination rate of holes for this condition?

A punch press with flywheel adequate to minimize speed fluctuation produces 120 punching strokes per minute, each providing an average force of 2000 N over a stroke of 50 mm. The press is driven through a gear reducer by a shaft rotating 200 rpm. Overall efficiency is 80%. a) What power (W) is transmitted through the shaft? b) What average torque is applied to the shaft?