## Engineering Mechanics - Dec 2013

### First Year Engineering (Semester 2)

TOTAL MARKS:

TOTAL TIME: HOURS

**1** Explain the principle of transmissibility.(2 marks)
**10** What is general plane motion?(2 marks)
**11 (a)** Determine the magnitude and direction of force F shown in fig. 1 so that particle 'A' is in equilibrium.

(8 marks)
**11 (b)** Three cables are used to support the 10 kg cylinder show in Fig. 2. Determine the force developed in each cable for equilibrium.

(8 marks)
**12 (a)** Determine the reaction at the pin at A and in the cable shown in Fig. 3 required to support the 300 kg crate. Neglect the weight of the connecting rod AB.

(8 marks)
**12 (b)** Compute the moment of the force P=1500 N and of the force Q=1200 N shown in Fig. 4 about points A,B and C

(8 marks)
**13 (a)** Determine the polar moment of inertia of the section shown in Fig. 5

(8 marks)
**13 (b)** Determine the principal moment of inertia of the section shown in Fig 6.

(8 marks)
**14 (a)** The 50 kg block shown in Fig 7 rests on a horizontal plane for which the coefficient of kinetic friction is 0.3. If the block is pulled by a 350 N force as shown, determine the velocity of the block after it has moved 65 m starting from rest. Use the principle of work and energy.

(8 marks)
**14 (b)** The 50 kg block shown in Fig 8 is originally at rest on the smooth horizontal surface. Determine the time needed for the block to attain a velocity of 30 m/s if a force of 300 (N) is acting on the block as shown. Use principle of impulse and momentum.

(8 marks)
**15 (a)** Calculate the static coefficient of friction ?_{s} between the block shown in Fig. 9 having a mass of 75 kg and the surface. Also find the magnitude and direction of the friction force if the force P applied is inclined at 45° to the horizontal and ?_{s}=0.30

(8 marks)
**15 (b)** A body rotates according to the relation ?=at^{4} + bt^{2}+ ct where a,b and c are constants. Determine the value of the constants a, b and c if the angular coordinate is 20 rad, angular velocity is 20 rad/s and angular acceleration is 16 rad/s^{2} at time t=2s.(8 marks)
**2** State the necessary and sufficient conditions for equilibrium of a particle in two dimensions.(2 marks)
**3** State Varignon's theorem of moments.(2 marks)
**4** What is meant by a force-couple system?(2 marks)
**5** Define centroid and centre of gravity of an area.(2 marks)
**6** What do you mean by polar moment of inertia?(2 marks)
**7** Write the working energy equation of particles.(2 marks)
**8** State impulse momentum principle(2 marks)
**9** Give the causes of rolling resistance.(2 marks)