Engineering Mechanics - May 2014

First Year Engineering (Semester 2)

TOTAL MARKS:
TOTAL TIME: HOURS

1 Resolve the 100 N force acting 30° to horizontal into component one along horizontal and other along 120° to horizontal.(2 marks) 10 What is general plane motion?(2 marks) 11 (a) Two cylinders, having weight W_A=200 N abd W_B=1000 N are resting on smooth inclined planes having inclination 60° and 45° with the horizontal respectively as shown in Fig. 3. They are connected by a weighless bar AB with hinge connections. The bar AB makes 15° angle with the horizontal. Find the magnitude of the force P required to hold the system in equilibrium.
(8 marks) 11 (b) Block P=5 kg and block Q of mass m kg is suspended through the chord is in the equilibrium position as shown in Fig. 4. Determine the mass of block Q.
(8 marks) 12 (a) Determine the tension in cable BC as shown in Fig. 5. Neglect the self-weight of AB.
(8 marks) 12 (b) Find the resultant of the force system shown in Fig. 6. Radius=2.5 m.
(8 marks) 13 (a) Find the centroid of the shaded area OPQ, shown in Fig. 7. The curve OQ is parabolic.
(8 marks) 13 (b) Find the moment of inertia of shaded area shown in Fig. 8 about I_x-x axis and I_y-y axis
(8 marks) 14 (a) A body A projected vertically upwards from the top of a tower with a velocity of 40 m/s, the tower being 180 m high. After t sec, another body B is allowed to fall from the same point. Both the bodies reach the ground simultaneously. Calculate t and the velocities of A and B on reaching the ground.(8 marks) 14 (b) Two smooth spheres 1 and 2 having a mass of 2 kg and 4 kg respectively colide with initial velocities as shown in Fig. 9. If the coefficient of restitution for the spheres is e=0.8, determine the velocities of each sphere after collision.
(8 marks) 15 (a) Two block A and B are placed on inclined planes as shown in Fig. 10. The block A weighs 1000 N. Determine minimum weight of the block B for maintaining the equlibrium of the system. Assume that the blocks are conneced by an inextensible string passing over a frictionless pulley. Coefficient of friction ?_A between the block A and the plane is 0.25. Assume the same value for ?_s.
(8 marks) 15 (b) Two bodies of 9 kg and 13.5 kg are suspended on two ends of a string passing over a pulley of radius 275 mm and moment of ineria= 16.5 km² as shown in Fig. 11. Determine the tesions in the strings and the angular acceleration of the pulley.
(8 marks) 2 Two forces of 400 N and 600 N act at an angle 60° to each other. Determine the resultant in magnitude and direction.(2 marks) 3 Replace the force 600 N from A as show Fig. 1 by equivalent force and couple at B.
(2 marks) 4 Find the resultant of the force system shown in Fig. 2
(2 marks) 5 Define centroid.(2 marks) 6 Define polar moment of inertia.(2 marks) 7 A motorist is travelling at 90 kmph, when he observes a traffic light 250 m ahead of him turns red. The traffic light is timed to stay red for 12 sec. If the motorist wishes to pass the light without stopping, just as it turns green, determine
a) the required uniform deceleration of the motor and
b) the speed of the motor as it passes the traffic light.(2 marks) 8 Define Work Energy Principle.(2 marks) 9 Define angle of friction.(2 marks)