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## 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/s^{2} 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 2^{nd} law of motion.

**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/s

^{2}, 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 F_{1} and F_{2} 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.

**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 d

_{c}=0.75 m and d

_{b}=1.125 m, determine the component of reaction at A and maximum tension in the cable.

(6 marks)