APPLIED MECHANICS, compilation of exams, Study notes of Mechanical Engineering

Download APPLIED MECHANICS, compilation of exams and more Study notes Mechanical Engineering in PDF only on Docsity! Code No: R07A10101 Set No. 1 I B.Tech Semester Regular Examinations, June 2009 APPLIED MECHANICS (Civil Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆ ⋆ ⋆ ⋆ ⋆ 1. (a) State polygon law of forces for resultant of several coplanar concurrent forces? (b) Four forces of magnitude 10 N, 20 N, 30 N and 40 N are acting respectively along the four sides of a square ABCD as shown in the figure 1b. Determine the resultant moment about the point A. Each side of the square is given as 2m. [4+12] Figure 1b 2. (a) A block weighing 50 N is resting on a horizontal plane. A horizontal force of 10 N is applied to start the sliding of the block. Find i. coefficient of friction ii. angle of friction iii. resultant force. (b) Find the force that should be applied upward at an angle 30o to the horizontal on the block of weight 100 N to cause impending sliding on a surface, the coefficient of friction between the surfaces being 0.3. [8+8] 3. (a) An open belt running over two pulleys 440 mm and 650 mm diameter connects two parallel shafts 6 metres apart and transmits 7 kW from the smaller pulley that rotates at 600 r.p.m. Coefficient of friction between the belt and the pulley is 0.34and the safe working tension is 20 N per mm width. Determine: i. minimum width of the belt 1 of 2 Code No: R07A10101 Set No. 1 ii. initial belt tension, and iii. length of the required. (b) Obtain an expression for the length of a cross belt drive. [12+4] 4. (a) Determine the product of inertia of a right angle triangle i. with respect to x and y axes. ii. with respect to x’ and y’ axes (x’ and y’ axes are passing through centroid and parallel to x and y axes). (b) State parallel axis theorem as applied to moment of inertia of plane areas. [12+4] 5. Calculate the mass moment of inertia of thin plate shown in figure 5. with respect to the axis X. Take mass of the plate as m. [16] Figure 5 6. A train starts from rest with uniform acceleration, it attains a speed of 90 km/h in 11/2 minutes, Find, (a) The acceleration, (b) The distance traveled in 11/2 minutes and (c) The time to reach a speed of 72 km/h. [16] 7. A 100 kg block rests on a horizontal plane. Find the magnitude of the force P required to give the block an acceleration of 2.5 m/sec2 to the right. The coefficient of kinetic friction between the block and the plane is µk = 0.25. [16] 8. A shaft 1.5 m long supported in flexible bearings at the ends carries two wheels each of 50 kg mass. One wheel is situated at the centre of the shaft and the other at a distance of 375 mm from the centre towards left. The shaft is hollow of external diameter 75 mm and the internal diameter 40 mm. The density of shaft material is 7700 kg/m3 and its modulus of elasticity is 200 GN/m2. Find the lowest whirling speed of the shaft, taking into account the mass of the shaft. [16] ⋆ ⋆ ⋆ ⋆ ⋆ 2 of 2 Code No: R07A10101 Set No. 3 I B.Tech Semester Regular Examinations, June 2009 APPLIED MECHANICS (Civil Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆ ⋆ ⋆ ⋆ ⋆ 1. (a) A body is subjected to the three forces as shown in the figure 1a. If possible de- termine the direction of the force F so that the resultant is in X direction, when Figure 1a i. F=5000 N ii. F=3000N. (b) Differentiate between scalar and vector quantities? (c) Define coplanar non-concurrent forces with suitable sketch. [8+4+4] 2. (a) Find the horizontal force P required to pull the block A of weight 230 N which carries block B of weight 1400 N as shown in figure 2a. Take angle of limiting friction between floor and block A as 14o and that between vertical wall and block B as 13o and Coefficient of limiting friction between the blocks as 0.3. Figure 2a 1 of 3 Code No: R07A10101 Set No. 3 (b) A wooden block rests on a horizontal plane. Determine the force required to pull it. Assume the mass m of the block to be 150 kg and the µ =0.19. [8+8] 3. (a) A flat belt, 6mm thick and 80 mm wide transmits power between two pulleys, running at 1200 m/min. The mass of the belt is 1.9 kg/m length. The angle of lap in the smaller pulley is 135o and the coefficient of Friction between the belt and pulley is 0.3. If the maximum Permissible stress in the belt is 3 MN/m2. Find i. maximum power Transmitted, and ii. initial tension in the belt. (b) Briefly explain the belt materials. [12+4] 4. (a) Determine the product of inertia of a right angle triangle i. with respect to x and y axes. ii. with respect to x’ and y’ axes (x’ and y’ axes are passing through centroid and parallel to x and y axes). (b) State parallel axis theorem as applied to moment of inertia of plane areas. [12+4] 5. Determine the mass moment of inertia of the homogeneous rectangular prism with respect to the Z-axis. [16] 6. A train starts from rest with uniform acceleration, it attains a speed of 90 km/h in 11/2 minutes, Find, (a) The acceleration, (b) The distance traveled in 11/2 minutes and (c) The time to reach a speed of 72 km/h. [16] 7. An elevator weighing 5000 N is ascending with an acceleration of 3 m/s2. During this ascent, its operator whose weight is 700 N is standing on the weighing pan placed on the floor. What is the weighing pan reading? What will be the total tension in the cables of elevator during this motion? [16] 8. A flywheel is mounted on vertical shaft as shown in figure 8. The both the ends of the shaft are fixed and its diameter is 50 mm. The flywheel has a mass of 500 kg. Find the natural frequencies of longitudinal and transverse vibrations. Take E = 200 GN/m2. [16] 2 of 3 Code No: R07A10101 Set No. 3 Figure 8 ⋆ ⋆ ⋆ ⋆ ⋆ 3 of 3