RR
Code No: RR100305 I B.Tech (RR) Supplementary Examinations, June 2009 ENGINEERING MECHANICS (Mechanical Engineering) Time: 3 hours
Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
1. Determine the resultant of the four forces and one couple that act on the plate shown in Figure 1.
[16]
Figure 1: 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 cross belt drive is to transmit 7.5 KW at 1000 r.p.m of the smaller pulley. The diameter of the smallest pulley is 250mm and velocity ratio is 2. The centre distance between the pulley is 1250mm. A flat belt of thickness 6 mm and of coefficient friction 0.3 is used over the pulleys. Determine the necessary width of the belt if the maximum allowable stress in the belt is 1.75N/mm2 and density of the belt is 1000Kg/m3 . [16] 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. Derive the expression for the moment of inertia of a cylinder length ‘l’, radius ‘r’ and density ‘w’ about longitudinal centroidal axis and about the centroidal transverse 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) A particle is projected with a velocity of 10m/s at an angle of elevation of 600 . Find i. The equation of the path of motion. ii. The length of latus rectum of the path of motion iii. Time required to cover the range. iv. The length of range. (b) An electric train which starts from one station is uniformly accelerated for the first 10 seconds, during which period it covers 150 metres. It then runs with constant speed until it is finally retarded uniformly in the last 40 metres. Calculate the maximum speed and the time taken over the journey to the next stopping station which is 600m form the previous station. [8+8] 8. 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] ?????