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Sem - II Jun 2008 Pattern Eng. Mechanics (II)

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Total No. of Questions : 6] [Total No. of Printed Pages : 4 [3761]-118 F. E. (Semester - II) Examination - 2010 ENGINEERING MECHANICS (June 2008 Pattern) Time : 2 Hours] [Max. Marks : 50 Instructions : (1) (2) (3) (4) (5) (6) Attempt Q. 1 or Q. 2, Q. 3 or Q. 4 and Q. 5 or Q. 6. Answer should be written in one answer book. Figures to the right indicate full marks. Neat diagram must be drawn wherever necessary. Use of cell phone is prohibited in the examination hall. Use of electronic non-programmable pocket calculator is allowed. (7) Assume suitable data, if necessary. Q.1) (A) Three forces of magnitude 100N each are acting along the sides of an equilateral triangle as shown in Fig. 1(A). Determine resultant in magnitude and direction with reference to point A. [06] (B) A sphere is fired into a medium with an initial velocity of 27 m/s. If it experiences a deceleration a = ( 6t) m/s2, where t is in second, determine distance travelled before it stops. [06] 100N C B A 100N [3761]-118 100N Fig. 1(A) 3m OR 1 P.T.O. Q.2) (A) (B) Determine position of the centroid C of the shaded area which is part of the circle having a radius r. Refer Fig. 2(A). [06] Block A of weight 100N is resting on block B of weight 150N. The coefficients of static and kinetic frictions at all contact surfaces are s = 0.4 and k = 0.3 respectively. Determine acceleration of each block, if block A is pushed horizontally with a force : (a) F = 30N, (b) F = 250N. [06] y m 0m 15 r O = 30o C Block A F x 30o Block B Fig. 2(A) Q.3) (A) (B) Fig. 2(B) s = 0.4, k = 0.3 If rope BC fails when the tension becomes 50 kN, determine greatest vertical load F that can be applied to the beam AB. Also determine reaction components at A. Refer Fig. 3(A). [06] The uniform concrete slab has a weight of 5500N. Determine tension in each of the three parallel supporting cables when the slab is held in horizontal plane as shown in Fig. 3(B). [07] z 26 kN A 60o 2m 4m B TA C F A 0.6 x Fig. 3(A) Q.4) (A) [3761]-118 TC C 30o y B m 0.3 (C) TB m 0.3 0. 6m m Fig. 3(B) A particle moves along the path r = {(8 t2)i + (t3 + 5)j } m, where t is in seconds. Determine magnitudes of particle velocity and acceleration when t = 3s. [06] OR The maximum allowable value of each of the reactions is 360N neglecting the weight of the beam; determine range of values of distance d for which the beam is safe. Refer Fig. 4(A). [07] 2 Contd. (B) The cable exerts forces FAB = 100N and FAC = 120N on the ring at A as shown in Fig. 4(B). Determine magnitude of the resultant force acting at A. [06] z A FAB A y 4m B d 900mm B 900mm C 2m x Fig. 4(A) (C) 4m FAC 300N 200N 100N Fig. 4(B) The bob of a 2m pendulum describes an arch of a circle in a vertical plane. If the tension in the cord is 2.5 times the weight of the bob for the position shown in Fig. 4(C), find velocity and acceleration of the bob in that position. [06] O 2m 30 o Bob of mass m Q.5) (A) (B) Identify zero force members and determine forces in the members of the truss as shown in Fig. 5(A). [07] A cord having weight of 0.5 N/m and a total length of 10m is supported over a peg P as shown in Fig. 5(B). If the coefficient of static friction between the peg and cord is s = 0.5, determine longest length h which one side of the suspended cord can have without causing motion. Neglect size of peg and length of cord draped over it. [06] 10kN D E P 10kN 2m A B 2m [3761]-118 Fig. 4(C) h C 2m Fig. 5(A) 3 Fig. 5(B) P.T.O. (C) Block A has a weight of 300N and block B has a weight of 50N. Determine distance block A must descend from rest before it obtains a speed of 2.5 m/s. Neglect mass of pulleys and cord. [06] Block B Block A Fig. 5(C) OR Q.6) (A) Determine components of reaction at pin C for the pin jointed frame loaded and supported as shown in Fig. 6(A). [06] (B) A block of mass 150 kg is resting on a plane inclined at 30o with horizontal as shown in Fig. 6(B). Determine range of an external force P to maintain equilibrium. Assume s = 0.25. [07] (C) Disk A has a mass of 250 g and is sliding on a smooth horizontal surface with an initial velocity of 2 m/s. It makes a direct collision with disk B, which has a mass of 175 g and is originally at rest. If both the disks are of the same size and the collision is perfectly elastic, determine velocity of each block just after collision. [06] E 10kN 10kN 2m D C 2m A 2m B 2m k Bloc g k 150 30o s = 0.25 Fig. 6(B) Fig. 6(A) [3761]-118/4 P

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