Engineering Mechanics (EM) - Dec 2014

First Year Engg (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 and Q2

1 (a) Determine the magnitude of force P so that the resultant of the force system as shown in Fig. 1a is vertical and hence find magnitude of resultant force. (4 marks) 1 (b) The small collar of mass 0.5 kg is released from rest at A and strikes the base B with velocity 4.7 m/s as shown in Fig. 1 b, determine the work done by frictional force using work energy principle. (4 marks) 1 (c) During a break test, the car of mass 1500 kg is stop from an initial speed of 100 kmph in a distance of 50 m. Determine the breaking force assuming uniform deceleration.(4 marks) 1 (d) A particle moves in a circular path of radius 0.4m. Calculate magnitude of acceleration a of the particle if its speed is 0.6 m/s but it increasing at the rate of 1.2 m/s each second.(4 marks) 2 (a) The pendulum bob has a mass m and is released from rest when θ= 0°. Determine the tension in the cord as a function of the angle of decent θ. Neglect the size of bob. (4 marks) 2 (b) Determine the coordinate of centroid of the shaded area as shown in Fig, 2b. (4 marks) 2 (c) A ball is projected vertically upward with a velocity of 9.81 m/s. Determine the maximum height travel by the ball, the velocity at which it strikes the ground and total time of journey.(4 marks) 2 (d) One of the requirement for tennis balls to be used in official competition is that, when dropped onto a rigid surface from a height of 2540 mm, the height of the first bounce of the ball must be in the range of 1346 mm ≤ h ≥ 1473 mm. Determine the range of the coefficient of restitution of the tennis balls satisfying this requirement.(4 marks)

Answer any one question from Q3 and Q4

3 (a) A cylinder of weight 1000 N is rest on the stair as shown in Fig, 3 a. Determine the minimum magnitude of force P to raise the cylinder over the steps. (6 marks) 3 (b) The ball is suspended from the horizontal ring using three spring each having a stiffness of k = 50 N/m and an unstretched length of 1.5 m. If h = 2 m, determine the weight of ball. Refer Fig. 3 b (6 marks) 3 (c) Determine the length a of overhang so that the reaction at B is twice of the reaction at A for the beam loaded and supported as shown in Fig. 3 c. (5 marks) 4 (a) Three parallel bolting forces act on the rim of the circular cover plate as shown in Fig. 4 a. Determine the magnitude, direction and locate point of application of the resultant force on the cover plate. (6 marks) 4 (b) Determine the magnitude and direction θ of force F so that the particle is in equilibrium. Refer Fig. 4 b. (5 marks) 4 (c) A force of 150 N acts on the end of beam ABD as shown in Fig. 4 c. Determine the magnitude of tension in cable BC to maintain equilibrium. (6 marks)

Answer any one question from Q5 and Q6

5 (a) A block of mass m rest on a frictional plane which makes an angle α with the horizontal as shown in Fig. 5 a. If the coefficient of friction between the block and the frictional plane is 0.2, determine the angle α for limiting condition. (5 marks) 5 (b) Determine the forces in each member of the plane truss as shown in Fig. 5 b in teRMS of the external loading and state if the members are in tension or compression. Use θ = 30°, L = 2 m and P = 100 N. (6 marks) 5 (c) Determine the range of P for the equilibrium of block of weight W as shown in Fig. 5 c. The coefficient of friction between rope and pulley is 0.2. (6 marks) 6 (a) Determine the components of reaction at C for the frame loaded and supported as shown in Fig. 6 a. (6 marks) 6 (b) Determine the range of P for the limiting equilibrium of block B of mass 150 kg rest on an inclined plane as shown in Fig. 6 b. (6 marks) 6 (c) State the assumption for the analysis of cable and laws of static friction.(5 marks)