4-APRIL 2011

THE INSTITUTION OF ENGINEERS, BANGLADESH

AMIE SECTION “A” EXAMINATION, APRIL 2011 SUBJECT: ENGINEERING MECHANICS

Full Marks: 100 Time: 3 Hours [N.B: The figures in the margin indicate full marks. There are SEVEN questions in this paper. Answer any FIVE]

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1. (a) Replace the three forces which act on the bent bar by a force-couple system at the support point A, as shown in Figure 1(a). (b) One end of rod AB rests in the corner A and the other is attached to the cord BD, as shown in Figure 1(b). if the rod supports a 150 N-load at its midpoint C, find the reaction at A and the tension in the cord.

2. (a) Determine the x and y coordinates of the centroid of the shaded area, as shown in Figure 2(a) .

(b) Determine the x and y coordinates of the centroid of the shaded area, as shown in Figure 2(b).

3. (a) Determine the force in each member of the loaded truss, as shown in Figure 3(a).

(b) Determine the reaction at the roller F for the frame loaded as shown in Figure 3(b).




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4. (a) The horizontal position of the 500 kg rectangular block of concrete is adjusted by the ퟓ° wedge under the action of the force P, as shown in Figure 4(a). if the coefficient of static friction for both pairs of wedge surface is 0.30 and if the coefficient of static friction between the clock and the horizontal surface is 0.60, determine the least force P required to move the block. (b) Calculate the moment of inertia about the x axis for the shaded area, as shown in Figure 4(b).

5. (a) Calculate the vertical acceleration “a” of the 150-kg cylinder for each of the two cases, as shown in Figure

5(a). Neglect friction and mass of the pulleys. (b) The system, as shown in Figure 5(b), is released from rest with the cable taut. For the friction co-efficient 흁풔 = ퟎ.ퟐퟎ and 흁풌 = ퟎ.ퟐퟎ, calculate the acceleration of each body and the tension T in the cable. Neglect the small mass and friction of the pulleys.

6. (a) Two blocks A and B, of mass 8 kg and 12 kg, respectively from a cable which passes over a pulley of negligible

mass, as shown in Figure 6(a). Knowing that blocks are released from the rest and that the energy dissipated by the axle friction in the pulley is 10 J, determine (i) the velocity of block B as it strikes the ground (ii)the force exerted by the cable on each of the two blocks during the motion.




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(b) The 0.6 kg slider, as shown in Figure 6(b), is released from rest at A and slides down the smooth parabolic guide (which lies in a vertical plane) under the influence of its own weight and of the spring of constant 120 N/m. Determine speed of the slider as it passes point B and the corresponding normal force exerted on it by the guide. The unstretched length of the spring is 200 mm.

7. (a) A 50-Mg railroad car moving with a velocity of 3 km/h is to be coupled to a 30-Mg car which is at rest, as shown in Figure 7(a). Determine (i) the final velocity of the coupled car. (ii) the average impulsive force acting on each car if the coupling is completed in 0.4 s.

(b) Horizontal motion of the piston rod of the hydraulic cylinder controls the rotation of link OB about O as shown in Figure 7(b). For the instant represented, 푽푨 = ퟐ풎/풔 and OB is horizontal. Determine the angular velocity 흎 of OB for this instant.

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4-APRIL 2011