Chapter 7, Problem 97P

In MATLAB write out a program to integrate the equations of motion of a rigid body. The inertia matrix is given by I = [125 0 0; 0 100 0; 0 0 75] which is a diagonal, where diag operator provides a matrix with given elements placed on its diagonal. Consider three cases where the body rotates 1 rad/sec about each principal axis. Integrate the resulting motion and study the angular rates and the resulting attitude (use any attitude coordinates). For each principal axis case, assume first that a pure spin about the principal axis is performed, and then repeat the simulation where a small 0.1 rad/sec motion is present about another principal axis. Discuss the stability of each motion. The code should produce a total of 6 simulations results when it is ran.

Q. A strain gauge rosette that is attached to the surface of a stressed component C). If the strain gauge rosette is of the D° gives 3 readings (a = A, b = B, &c = type (indicating the angle between each of the gauges), construct a Mohr's Strain Circle overleaf. You should assume that gauge A is aligned along the x-axis. Using the Mohr's Strain Circle calculate the: [10 marks] 100 918 ucy evods gringiz ya mwo quoy al etsede 39 926919 (i) principal strains (1, 2)? (au) oniona [5 marks] (ii) principal angles (1, 2)? You should measure these anticlockwise from the y-axis. 20 [5 marks] (iii) maximum shear strain in the plane (ymax)? Ex = Ea Ey = εc [5 marks] (epol) (apob) é Ea = A = -210 2 B=E₁ = -50 E₁ = C = 340 D = 45° bril elled ✓A bedivordan nemigas olloho shot on no eonsoup Imeneo alubom shine sail-no viss ieqse sidetiva bnat sabied 2

1) Solve and show which is converage or diyverage a = 2+(0.1)" 3 16) a = n 1-2n 2) a = In n 1+2n 17) a = n 1-5n4 3) an = n* +8n³ 18) a =√4"n n² -2n+1 n! 20) a = 4) a₁ = 10 n-1 (Ina) 5) a=1+(-1)" 21) a= 6) a 7) an = * = (12+) (1-1) 2n (-1)+1 2n-1 3n+1 22) a= 3n-1 x" 23) a= .x>0 2n+1 2n 3"x6" 8) a = 24) a = n+1 π 9) a = sin 2 sin n 10) an = n + 2 x n! 25) a = tanh(n) n² 1 26) a = -sin- 2n-1 27) a = tan(n) n n 11) a = 2" 12) a = n 13) a = 8/ +=(1+2)" 14) a = 15) a = √10n In(n+1) 29) a = n 30) an-√n²-1 1 28) a = + √2" (In n)200 n 31) a=- = 1 dx nix

HW12 A multiple-disc clutch has five plates having four pairs of active friction surfaces. If the intensity of pressure is not to exceed 0.127 N/mm², find the power transmitted at 500 r.p.m. The outer and inner radii of friction surfaces are 125 mm and 75 mm respectively. Assume uniform wear and take the coefficient of friction = 0.3.

The sketch below gives some details of the human heart at rest. What is the total power requirement (work/time) for an artificial heart pump if we use a safety factor of 5 to allow for inefficiencies, the need to operate the heart under stress, etc.? Assume blood has the properties of water. p pressure above atmosphere blood going to the lungs for a fresh charge of oxygen p = 2.9 kPa 25v pulmonary artery d = 25mm fresh oxygenated blood from the lungs p = 1.0 kPa vena cava d=30mm right auricle pulmonary vein, d = 28mm aorta, d=20mm spent blood returning from left auricle the body p = 0.66 kPa right left ventricle ventricle blood to feed the body, p 13 kPa normal blood flow = 90 ml/s

4- A horizontal Venturi meter is used to measure the flow rate of water through the piping system of 20 cm I.D, where the diameter of throat in the meter is d₂ = 10 cm. The pressure at inlet is 17.658 N/cm2 gauge and the vacuum pressure of 35 cm Hg at throat. Find the discharge of water. Take Cd = 0.98.

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