R5100305-engineering-mechanics

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1

Code No: R5100305

Time: 3 hours

I B.Tech (R05) Supplementary Examinations, June 2009 ENGINEERING MECHANICS (Mechanical Engineering) Answer any FIVE Questions All Questions carry equal marks ?????

Max Marks: 80

1. (a) Explain the types of friction with examples. (b) Two equal bodies A and B of weight ‘W’ each are placed on a rough inclined plane. The bodies are connected by a light string. If µA = 1/2 and µB = 1/3, show that the bodies will be both on the point of motion when the plane is inclined at tan−1 (5/12). [6+10] 2. 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] 3. (a) Define the terms pertaining to belt drives : Creep, Slip and initial tension. (b) A shaft which rotates at a constant speed of 150 r.p.m is connected by belting to a parallel shaft 720mm apart which has to run at 60,80 and 100 r.p.m. The smallest pulley on the driver shafts is 40mm in radius. Determine the remaining radii of the two stepped pulleys for i. A crossed belt and ii. An open belt. [6+10] 4. A cylinder of diameter 500 mm and height 1200 mm has mass density of 8000 kg/m3 . Find out the mass moment of inertia of the cylinder (a) with respect to the axis of the cylinder and (b) about a line which coincides with an end face of the cylinder and passing through the centre of this face. [16] 5. A Cube of side 400 mm has mass density of 2000kg/m3 . Find out the mass moment of inertia of the cube about one of its edges and also about its centroidal axis parallel to one of its sides. [16] 6. (a) The distance covered by a freely falling body in the last one second of its motion and that covered in the last but one second are in the ratio 5:4. Calculate the height from which the body was dropped and the velocity with which it strikes the ground. (b) A stationary car attains a maximum permissible speed of 80 km/hour in a distance of 40metres. It continues at this speed for a distance of 200 metres and then a uniform retardation brings it to a stop in 10 seconds. How far does the car travel from the starting point and what is the total elapsed time? [8+8] 7. If Wa :Wb :Wc is in the ratio of 3:2:1 , find the accelerations of the blocks A, B, and C. Assume that the pulleys are weightless. {As shown in the Figure1}. [16]

Figure 1: 8. A vertical shaft 100mm in diameter and 1m in length has its end fixed to the ceiling. At the other end, it carries a disc of mass 500kg having a radius of gyration of 450mm. The modulus of rigidity for the material of shaft is 80Gpa. Determine the frequency of torsional vibrations. [16] ?????

2

Code No: R5100305

Time: 3 hours

I B.Tech (R05) Supplementary Examinations, June 2009 ENGINEERING MECHANICS (Mechanical Engineering) Answer any FIVE Questions All Questions carry equal marks ?????

Max Marks: 80

1. (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 figure1. 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 1: 2. An open belt running over two pulleys 1500 mm and 1000 mm diameters connects two parallel shafts 48000 mm apart. The initial tension in the belt when stationary is 3000N. If the smaller pulley is rotating at 600 r.p.m and coefficient of friction between the belt and pulley is 0.3. Determine the power transmitted taking centrifugal tension into account. The mass of belt is given as 0.6703 kg/m length. [16] 3. (a) Deduce an expression for centrifugal tension of belt drive. (b) The maximum allowed tension in a belt is 1500 N. The angle of lap is 1700 and coefficient of friction between the belt and material of the pulley is 0.27. Neglecting the effect of centrifugal tension, calculate the net driving tension and power transmitted if the belt speed is 2 m/s. [6+10] 4. (a) From the first principles determine product of inertia for right angle triangle of base ‘ b’ and altitude ‘ h’. (b) State and prove transfer formula for product of inertia. [8+8] 5. A square prism of cross section 200mm × 200mm and height 400mm stands vertically and centrally over a cylinder of diameter 300mm and height 500mm. Calculate the mass moment of inertia of the composite solids about the vertical axis of symmetry if the mass density of the material is 2000kg/m3 . [16] 6. (a) A particle moves along straight line. Its motion in represented by the equation S = 16t + 4t2 − 3t3 where S is in metres and t in seconds. Determine i. displacement, velocity and acceleration 2 seconds after start. ii. displacement and acceleration when velocity is zero and iii. displacement and acceleration when acceleration is zero. (b) A projectile is aimed at a target on the horizontal plane and falls 12m short when the angle of projection is 150 while it overshoots by 24m when the angle is 450 . Find the angle of projection to hit the target. [8+8] 7. A weight of 10N attached to a spring oscillates at a frequency of 60 oscillations per minute. If the maximum amplitude is 30mm, find the tension induced in the spring. Also find the spring constant and the maximum velocity in the spring. [16] 8. A gun is so designed that on firing, the barrel recoils against a spring. A dashpot, at the end of the recoil, allows the barrel to come back to its initial position within the minimum time without any oscillation. A gun barrel has a mass of 500kg and a recoil spring of 300 N/mm. The barrel recoils 1m on firing. Determine (a) the initial recoil velocity of the gun barrel and (b) the critical damping coefficient of the dashpot engaged at the end of the recoil strike. ?????

[16]

3

Code No: R5100305 I B.Tech (R05) Supplementary Examinations, June 2009 ENGINEERING MECHANICS (Mechanical Engineering) Time: 3 hours

Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

1. (a) A system of forces consists of i. Force P1 = 3i + 5j – 6k acting through point (2,1,-3) ii. Force P2 = 5i – 4j + 3k acting through point (1,4,2) and a moment M = 20i – 35j + 60k. The forces are in Newton (N) units, distances in ‘m’ units and the moment in ‘N-m’ units. Calculate i. The component of the resultant forces and its magnitude ii. The total moment of the system about the origin ‘O’. iii. The moment of the system about the line through ‘O’ drawn in the 1st octant which makes angles of 650 and 750 with X and Y axes respectively. (b) Write the Equilibrium equations for concurrent force system in space. [12+4] 2. (a) Explain the principles of operation of a screw-jack with a neat sketch. (b) Outside diameter of a square threaded spindle of a screw Jack is 40 mm. The screw pitch is 10 mm. If the coefficient of friction between the screw and the nut is 0.15, neglecting friction between the nut and collar, determine i. Force required to be applied at the screw to raise a load of 2000N ii. The efficiency of screw jack iii. Force required to be applied at pitch radius to lower the same load of 2000 N and iv. Efficiency while lowering the load v. What should be the pitch for the maximum efficiency of the screw? and vi. what should be the value of the maximum efficiency? [6+10] 3. (a) Distinguish between quarter turn and compound belt drives. (b) Determine the maximum power that can transmitted using a belt of 100 mm × 10 mm with an angle of lap of 1600 . The density of belt is 1000kg/m3 and coefficient of friction may be taken as 0.25. The tension in the belt should not exceed 1.5N/mm2 . [6+10] 4. (a) Define the terms centroid, moment of inertia and radius of gyration. (b) Compute moment of inertia of hemisphere about its diametral base of radius ‘R’.

[6+10]

5. A brass cone with base diameter of 400 mm and height of 225 mm is placed on a vertical aluminum cylinder of height 300 mm and diameter 400 mm. Density of brass = 85kN/m3 and density of aluminium =25.6kN/m3 . Determine the mass moment of inertia of the composite body about the vertical geometrical axis. [16] 6. An enemy ship was located at a distance of 25km in north-west direction by a warship. If the enemy ship is moving with a velocity of 18kmph N300 E, in which direction the warship must move with a velocity of 36 kmph, to strike at its earliest. Assume the fire range of warship is 5km. When is the shell to be fired? [16] 7. A clock with a second’s pendulum is running correct time at a place where the acceleration due to gravity is 9.81m/s2 . Find the length of the pendulum. This clock is taken at a place where the acceleration due to gravity is 9.80m/s2 . Find how much the clock will loose or gain in a day at this place? [16] 8. A homogeneous rectangular plate is free to rotate with respect to a fixed axis AB coinciding with one of its edges, along the side of length b=1.25m and inclined to the vertical by an angle α = 200 . Determine the period of small rotational oscillations if the length of the other side a=0.90m. [16] ?????

4

Code No: R5100305

Time: 3 hours

I B.Tech (R05) Supplementary Examinations, June 2009 ENGINEERING MECHANICS (Mechanical Engineering) Answer any FIVE Questions All Questions carry equal marks ?????

Max Marks: 80

1. A bar AB hinged to the foundation at A and supported by a strut CD is subjected to a horizontal 50 kN load at B, as shown in Figure1. Determine the nature and magnitude of the force in the strut and also the reaction at A. [16]

Figure 1: 2. (a) Obtain the conditions for the maximum power transmitted by a belt from one pulley to another. (b) A shaft running at 100 r.p.m drives another shaft at 200 r.p.m and transmits 12 kW. The belt is 100 mm wide and 12 mm thick and µ = 0.25. The distance between the shafts is 2.5 meters and the diameter of the smaller pulley is 500 mm. Calculate the stress in i. An open belt ii. A crossed belt, connecting the two pulleys. [6+10] 3. (a) The maximum allowable tension in a flat belt is 1500N. The angle of lap is 1700 and coefficient of friction between the belt and material of the pulley is 0.27. Neglecting the effect of centrifugal tension. Calculate the net driving tension and power transmitted if the belt speed is 2 m/s. (b) Two pulley on parallel shafts are connected by a crossed belt. The diameters of the pulleys are 450 mm and 200 mm. The shafts are 1950 mm apart. Find the length of the belt required and angle of contact between the belt and each pulley. [8+8] 4. (a) Show that the moment of inertia of a thin circular ring of mass ‘M’ and mean radius ‘R’ with respect to its geometric axis is M R2 . (b) Find out the mass moment of inertia of a right circular cone of base radius ‘R’ and mass ‘M’ about the axis of the cone. [8+8] 5. A flywheel consist of a 1m diameter plate 100mm thick with four holes. Each 200mm in diameter cut at a pitch circle diameter of 400mm symmetrically. Compute the mass moments of inertia of the flywheel about the axis of rotation. The material of the flywheel is cast iron with specific gravity 7.5. [16] 6. (a) A train is uniformly accelerated and passes successive kilometer stones with velocities of 18km/hr and 36km/hr respectively. Calculate the velocity when it passes the third kilometer stone. Also find the time taken for each of the two intervals of one kilometer. (b) A ball projected vertically upwards attains a maximum height of 400 metres. Calculate the velocity of projection and compute the time of flight in air. At what altitude will this ball meet a second ball projected vertically upwards 4 seconds later with a speed of 120 metres per second? [8+8] 7. A centrifugal pump rotating at 400 rpm is driven by an elastic motor at 1200 rpm through a single stage reduction gearing. The moment of inertia of the pump impeller at the motor are 1500 kg.m2 and 450 kg.m2 respectively. The lengths of the pump shaft and the motor shaft are 500 and 200 mm, and their diameters are 100 and 50 mm respectively. Neglecting the inertia of the gears, find the frequency of torsional oscillations of the system. G = 85 GN/m2 . [16] 8. (a) Explain how a simple pendulum differ from a compound pendulum briefly with the help of differential mathematical equations. (b) Determine the stiffness in N/cm of a vertical spring to which a weight of 50 N is attached and is set vibrating vertically. The weight makes 4 oscillations per second. [8+8] ?????