Engineering Mechanics (EM) - Dec 2013
First Year Engineering (Semester 2)
TOTAL MARKS: 50
TOTAL TIME: 2 HOURS
(1) Solve Q.1 or Q.2, Q.3 or Q.4, Q.5 or Q.6, Q.7 or Q.8
(2) Assume suitable data, if necessary.
Answer any one question from Q1 & Q2
1 (a) The resultant of two forces P and Q is 1200 N horizontally leftward. Determine the force Q and corresponding angle ? for the system of force s as shown in Fig. 1a.
(4 marks)
1 (b) The tanker is pulled with constant acceleration of 0.001 m/s2 using cable that makes an angle of 10° with the horizontal as shown in Fig. 1b. If the force in the cable is 45.694 KN, determine the mass of tanker using Newton's 2nd law of motion.
(4 marks)
1 (c) An outdoor track is 126 m in diameter. A runner increases her speed at a constant rate from 4.2 to 7.2 m/s over a distance of 28.5 m. Determine the total acceleration of the runner 2 s after she begins to increase her speed.(4 marks)
1 (d) A 2 kg stone is dropped from a height h and strike the ground with a velocity of 24 m/s. Find the kinetic energy of the stone as it strikes the ground and the height h from which it was dropped using work energy method.(4 marks)
2 (a) Determine the y coordinate of centroid of the shaded area as shown in Fig. 2a.
(4 marks)
2 (b) A sphere is fired into a medium with a initial speed of 27 m/s. If it experience a deceleration a=(-6t) m/s2, where t is in seconds, determine the distance traveled before it stop.(4 marks)
2 (c) The small 0.6 kg block slides on a smooth circular path of radius 3 m in the vertical plane. If the speed of the block is 5 m/s as it passes point A and 4 m/s as it passes point B, determine the normal force exerted on the block by the surface at each of these location. Refer Fig. 2 c.
(4 marks)
2 (d) A railroad car having a mass of 15 Mg is coasting at 1.5 m/s on a horizontal track. At the same time another car having a mass of 12 Mg is coasting at 0.75 m/s in the opposite direction. If the car meet and couple together, determine the speed of both cars just after the coupling.(4 marks)
Answer any one question from Q3 & Q4
3 (a) Determine the magnitude of F1 and F2 so that the particle is in equilibrium. Refer Fig. 3a.
(6 marks)
3 (b) Determine the reactions at support for the beam loaded and supported as shown in Fig. 3b.
(5 marks)
3 (c) A concrete foundation mat of 5 m radius supports four equally spaced columns, each of which is located 4 m from the centre of the mat. Determine the magnitude and point of application of the resultant of the four loads as shown in Fig. 3 c.
(6 marks)
4 (a) A 300 mm wooden beam weighing 540N is supported by a pin and bracket at A and by cable BC. Find the reaction at A and tension in cable BC. Refer Fig. 4 a.
(6 marks)
4 (b) A rectangular plate is supported by three cables at A as shown in Fig. 4 b. Knowing that the tension in cable AD is 120 N, determine the weight of the plate.
(6 marks)
4 (c) State and explain Two Force and Three Force Principle for equilibrium with sketches.(5 marks)
Answer any one question from Q5 & Q6
5 (a) Determine the magnitude and nature of forces in the members AB, AH and GC of the truss loaded and supported as shown in Fig. 5 a.
(6 marks)
5 (b) The 15 m ladder has a uniform weight of 80 N and rest against the smooth wall at B as shown in Fig. 5 b. If the coefficient of static friction between ladder and floor is ?s=0.4, determine the smallest angle ? at which the ladder will not slip.
(6 marks)
5 (c) Define angle of repose, angle of friction, coefficient of friction and cone of friction with sketches.(5 marks)
6 (a) Determine the forces in number of HG, HC and BC in the truss as shown in Fig. 5a. Use method of section.(6 marks)
6 (b) Determine the horizontal force P needed to just moving the 300 N block up the plane. Take ?s=0.3 and refer Fig. 6b.
(5 marks)
6 (c) Two loads are suspended as shown in Fig. 6C from cable ABCD. Knowing the dc=0.75 m and db=1.125 m, determine the component of reaction at A and maximum tension in the cable.
(6 marks)
