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Posted By: India Member Level: Diamond Posted Date: 19 Jan 2008
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2007 Jawaharlal Nehru Technological University B.Tech I Year Engineering Mechanics (RR-Set 2 - Aug / Sep'2007- Sup) Question paper
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Code No: RR10302 Set No. 2 I B.Tech Supplimentary Examinations, Aug/Sep 2007 ENGINEERING MECHANICS ( Common to Mechanical Engineering, Mechatronics, Metallurgy & Material Technology, Production Engineering, Aeronautical Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. The uniform 30kg bar with end rollers is supported by the horizontal and vertical surfaces and by the wire AC. Calculate the tension (T) in the wire and the reactions against the rollers at A and at B, as shown in Figure 1. [16] Figure 1 2. (a) A screw jack has a pitch of 6 mm. The mean radius of the threads is 60 mm. The mean diameter of the bearing surface under the cap is 80 mm. The coefficient of friction for all surfaces is 0.06. What turning moment is necessary to raise a load of 7 kN. (b) Determine the magnitude and direction of the friction force acting on the 1000N block shown in figure2b. If, first P = 500 N and second P = 100 N. The coefficient of static friction is 0.2, and the coefficient of kinetic friction is 0.17. The forces are applied with the block initially at rest. [6+10] Figure 2b 3. An open belt drive connects two pulleys 1200mm and 500mm diameter on parallel shafts 4000mm apart. The belt weigh 9N/m length and maximum tension in it is not to exceed 2000N. The coefficient of friction is 0.3. The 1200mm pulley, which is the driver runs at 200r.p.m Due to belt slip on one of the pulleys, the velocity of the driven shafts is only 450 r.p.m Calculate the torque on each of the two shafts, the power transmitted and power lost in friction. What is the efficiency of the drive. [16] 4. (a) State and prove parallel axis theorem. (b) Find the centroid of the shaded lamina shown in Figure4b. [6+10] Figure 4b 5. (a) Prove that the mass moment of inertia of a right circular cone of base radius ‘R’ and height ‘h’, with respect to a diameter of the base is M(3R2 +2h2)/20 where M is the mass of the cone. (b) Calculate the mass moment of inertia of a circular cone of base radius 300mm and height 600mm about a line which passes through the mass centre of the cone and which is parallel to the base of the cone. The mass density of the cone is 2500 kg/m3. [8+8] 6. (a) A train is traveling at a speed of 60 km/hr. It has to slow down due to certain repair work on the track. Hence, it moves with a constant retardation of 1 km/hrper second until its speed is reduced to 15 km/hr. It then travels at a constant speed of for 0.25 km/hr and accelerates at 0.5 km/hr per second until its speed once more reaches 60 km/hr. Find the delay caused. (b) The motion of a particle in rectilinear motion is defined by the relation s = 2t3 -9t2 +12t-10 where s is expressed in metres and t in seconds. Find i. the acceleration of the particle when the velocity is zero ii. the position and the total distance traveled when the acceleration is zero. [8+8] 7. (a) A homogeneous sphere of radius of a=100 mm and weight W=100 N can rotate freely about a diameter. If it starts from rest and gains, with constant angular acceleration, an angular speed n=180rpm, in 12 revolutions, find the acting moment. . (b) A block starts from rest from‘A’. If the coefficient of friction between all sur- faces of contact is 0.3, find the distance at which the block stop on the hori- zontal plane. Assume the magnitude of velocity at the end of slope is same as that at the beginning of the horizontal plane. As shown in the Figure7b. [8+8] Figure 7b 8. The circular disc shown in the figure8 has a radius r=150 mm and weight of 225 N. The observed frequency of torsional vibration is 1 oscillation/sec. When another body is attached to the same shaft the observed frequency of torsional vibration is 1.2 oscillations/sec. Find the moment of inertia of the second body with respect to the axis of the shaft. [16] Figure 8
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