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- A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance measured along the beam; [x]=[L] y = displacement of the beam; [y]=[L] = circular frequency of vibration; []=[T1] = mass of the beam per unit length; []=[ML1] D = bending rigidity of beam; [D]=[FL2] Show that the equation is dimensionally homogeneous. Note that [F]=[MLT2] see Eq. (1.21:)..Find Momer 160 N 200 N 30- 100 200 min 30 150 N AFind the displacement, velocity, kinetic energy, potential energy and momentum of an objęct, taking www. wwwww wwww www. mon mmwm w into account that F = ma and F = -kx. wwww w
- Find the displacement if work done 2.1 J and force applied 3 NQ1: 1. 3. Find the relative velocity of car A relative to в. Choose the correct answer 20 m/s 50 m/s A car is moving on a concave road as shown [30 m/s Find the reaction between the car and road mass of car = 900 kg and R = 50 m ( assume g = 10 m/s ) ( a =v/r) Select one: Select one: a. 50 m/s angle 45 a. 18000 kg b. 58.3 angle 30.9 b. 1800 kg c. 50 m/s angle 36.87 c. 18000 N d. 40 m/s angle 30 d. 16200 N 2. 4. A car initial velocity is 12 m/s moves with accn 3 Find the accn of the frictionless system shown. m/s Assume the pulleys are light and have no friction Assume g = 10 m/s" Find the its velocity after it moves a distance of 4kg 120 m 8 kg { laws you may use are 2 V,- V, = at , v. - v, = 2zas , s = v, t• 0.5 at } D1kg 5 kg Choose the correct answer Select one: a. 29.4 m/s Select one: b. 29.4 mm a. 1.579 m/s c. 23 m/s b. 2.22 m/s d. 21.9 m/s C. 2 m/s O d. 3 m/s1- Calculate the piston travel, velocity, and acceleration for an engine with R= 50 mm and lo=170 mm using the equation and graphical representation and compare the results (take 45° increment ,N= 3000 r.p.m).
- Q2/ A force of 100 N applied on a mass of body 25 kg moves at a constant acceleration, if the displacement function of the body is X = 2t + t2 , find th ce following: 1- the acceleration of body 2- The force of friction 3- The velocity of it at 5 second1. The density of an oil is 850 kg/m3. Find its relative density (or specific gravity) and Kinematic viscosity if the dynamic viscosity is 5 x 10-3 kg/ms. 2. If the viscosity of water at 70 °C is 0.00402 poise and its specific gravity is 0.978 determine its absolute viscosity in Pa-s and its kinematic viscosity in m²/s and in stokes 3. Calculate the Reynolds number, Re for water flow in a circular pipe. The diameter of the pipe is 50 mm, the density of water is 998 kg/m³, the volumetric oil flowrate is 720 L/min, and the dynamic viscosity of water is 1.2 centipoisevalg, (21535mm 1.15 The pressure difference, Ap, across a partial blockage in an artery (called a stenosis) is approximated by the equation μV Ap - K. 4 + K.(A-1) pv² = K₂ A s.r to zogy nish190 32\V as bonb dignol a 3 basiy noft where V is the blood velocity, u the blood viscosity (FL-2T), p the blood density (ML), D the artery diameter, Ao the area of the unobstructed artery, and A, the area of the stenosis. Determine the dimensions of the constants K, and K. Would this equation be valid in any system of units?
- The dynamic coefficient of viscosity m (viscosity of a fluid) is from, where v= velocity, d = distance, F = Force and A = area. Find the dimensions of m.A particle P of mass m = 6 kg is travel- ing at vp = -8i m/s and has a net force F = -5i N acting on it. At a certain instant, 0 = 25° and the distance from O and Hp, at this instant. P.2) %3D to P is L = 3 m. Calculate HP. %3D j L.The acceleration due to gravity at sea level is gR81 m/sland is decreased 000S ft/s per 1000 ft of elevation. Find the height (miles) above sea level for which the weight of a 75 kgi decreased by 10 101.3 miles O 326.85 miles O 203.14 miles O 110.3 miles Neit