Code No: R05010302 Set No. 1 I B.Tech Supplimentary Examinations, February 2008 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. A mast AB supported by a spherical socket at A and horizontal guy wires BC and BD carries a vertical load P at B as shown in Figure 1. Find the axial force induced in each of the three members of this system. [16] Figure 1 2. (a) Find the least horizontal force P to start motion of any part of the system of three blocks resting upon one another as shown in figure2a. The weights of the blocks are A = 3000N, B = 1000N, C = 2000N. Between A and B µ= 0.3, between B and C, µ = 0.2 and between C and the ground µ = 0.1. Figure 2a (b) A block overlying a 10 0 wedge on a horizontal floor and leaning against a vertical wall and weighing 1500N is to be raised by applying a horizontal force to the wedge. Assuming the coefficient of friction to be 0.3, determine the minimum horizontal force to be applied to raise the block. As shown in the Figure2b. [8+8] 1 of 3
Code No: R05010302 Set No. 1 Figure 2b 3. (a) Distinguish between cone pulley and loose & fast pulley drive. (b) A shaft rotating at 200 r.p.m drives another shaft at 300 r.p.m and transmits 6KW through a belt, the belt is 100mm wide and 10mm thick. The distance between the shafts is 4000mm the smaller pulley is 500mm in diameter calculate the stress in, i. Open - belt and ii. Crossed belt. Take µ = 0.3. Neglect centrifugal tension. [6+10] 4. Determine the moment of inertia of a triangle about x x axis as shown in figure 4. [16] Figure 4 5. (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 MR 2. (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] 6. (a) A baloon is ascending with a velocity of 20 m/s above a lake. A stone is dropped to fall from the balloon and the sound of the splash is heard 6 seconds later. Find the height of the balloon when the stone was dropped. Velocity of sound is 340 m/s. (b) The acceleration of a particle in rectilinear motion is defined by the relation a = 25 4s 2 where a is expressed in m/sec 2 and s is position coordinate in metres. The particle starts with no initial velocity at the position s = 0. Determine 2 of 3
Code No: R05010302 Set No. 1 i. the velocity when s = 3metres ii. the position where the velocity is again zero iii. the position where the velocity is maximum. [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 surfaces of contact is 0.3, find the distance at which the block stop on the horizontal 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 weight of an empty railway wagon is 240 KN on loading it with goods weighing 320KN, its springs get compressed by 80mm. (a) calculate its natural period of vibration when i. empty and ii. loaded as above. (b) It is set into natural vibrations with amplitude of 100mm,when empty. Calculate the velocity when its displacement is 40mm from statical equilibrium position. [16] 3 of 3
Code No: R05010302 Set No. 2 I B.Tech Supplimentary Examinations, February 2008 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. (a) Two forces equal to 2P and P respectively act on a particle. If first be doubled and the second increased by 12N the direction of the resultant is unaltered, find the value of P? (b) A 675 N man stands on the middle rung of a 225 N ladder, as shown in Figure 1b. Assuming a smooth wall at B and a stop at A to prevent slipping, find the reactions at A and B. [8+8] Figure 1b 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. 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] 1 of 3
Code No: R05010302 Set No. 2 4. (a) Locate the centroid of given parabola bounded by x- axis the line x = a. {As shown in the Figure 4a} Figure 4a (b) Locate the centroid of the wire bent as shown in figure 4b. [8+8] Figure 4b 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/m 3 and density of aluminium =25.6kN/m 3. Determine the mass moment of inertia of the composite body about the vertical geometrical axis. [16] 6. (a) A train is uniformly accelerated and passes successive kilometer stones with velocities of 18 km/hr and 36 km/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) A weight P attached to the end of a flexible rope of diameter d=5mm, is raised vertically by winching the rope on a reel. The reel is turned uniformly at the rate of 2 revolutions per second. Find the tension in the rope. Neglect the inertia of the rope and the lateral motion of the weight P. As shown in the Figure 7a. 2 of 3
Code No: R05010302 Set No. 2 Figure 7a (b) A right circular cylinder of radius r and weight W is suspended by a cord that is wound around its surface. If the cylinder is allowed to fall, prove that the center of gravity C will follow a vertical rectilinear path and find the acceleration a c along this path. Determine also the tensile force S in the cord. As shown in the Figure 7b. [8+8] Figure 7b 8. A pendulum having a time period of 1 sec. is installed in a lift. Determine its time period when (a) the lift is moving upwards with an acceleration of g 10. (b) the lift is moving downwards with an acceleration of g 20. [16] 3 of 3
Code No: R05010302 Set No. 3 I B.Tech Supplimentary Examinations, February 2008 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. A strut AB attached to the face of a vertical wall at A by a spherical hinge stands perpendicular to the wall and is supported by two guy wires, as shown in figure 1. At B, in a plane parallel to the wall, two forces P and Q acts as shown, Q being horizontal and P vertical. Find the axial forces produced in the members if P = 500 N and Q = 1000 N. [16] Figure 1 2. (a) A 108 N block is held on a 40 0 incline by a bar attached to a 150 N block on a horizontal plane Figure 2a. The bar which is fastened by smooth pins at each end, is inclined 20 0 to the horizontal. The co-efficient of friction between each block and its plane is 0.325. For what horizontal force P, applied to 150 N block will motion to the right be impending? Figure 2a 1 of 3
Code No: R05010302 Set No. 3 (b) A block weighing 100 N is resting on a rough plane inclined 20 0 to the horizontal. It is acted upon by a force of 50N directed upward at angle of 14 0 above the plane. Determine the friction. If the block is about to move up the plane, determine the co-efficient of friction. [10+6] 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 170 0 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) Find the centroid of the Z section shown in Figure 4a. Figure 4a (b) Find the moment of inertia about the horizontal centroidal axis.shown in Figure 4b. [6+10] Figure 4b 5. Determine the mass moment of inertia of a thin equilateral triangular plate of mass m and thickness t about the axis perpendicular to the plane of the plate and passing through the mass center. Base width= b and height of vertex above base= h. Density of material is w. [16] 6. (a) A train is uniformly accelerated and passes successive kilometer stones with velocities of 18 km/hr and 36 km/hr respectively. Calculate the velocity when 2 of 3
Code No: R05010302 Set No. 3 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) A weight P attached to the end of a flexible rope of diameter d=5mm, is raised vertically by winching the rope on a reel. The reel is turned uniformly at the rate of 2 revolutions per second. Find the tension in the rope. Neglect the inertia of the rope and the lateral motion of the weight P. As shown in the Figure 7a. Figure 7a (b) A right circular cylinder of radius r and weight W is suspended by a cord that is wound around its surface. If the cylinder is allowed to fall, prove that the center of gravity C will follow a vertical rectilinear path and find the acceleration a c along this path. Determine also the tensile force S in the cord. As shown in the Figure 7b. [8+8] Figure 7b 8. A pendulum having a time period of 1 sec. is installed in a lift. Determine its time period when (a) the lift is moving upwards with an acceleration of g 10. (b) the lift is moving downwards with an acceleration of g 20. [16] 3 of 3
Code No: R05010302 Set No. 4 I B.Tech Supplimentary Examinations, February 2008 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. (a) A system of forces consists of i. Force P 1 = 3i + 5j 6k acting through point (2,1,-3) ii. Force P 2 = 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 1 st octant which makes angles of 65 0 and 75 0 with X and Y-axes respectively. (b) Write the Equilibrium equations for concurrent force system in space. [12+4] 2. (a) A 108 N block is held on a 40 0 incline by a bar attached to a 150 N block on a horizontal plane Figure 2a. The bar which is fastened by smooth pins at each end, is inclined 20 0 to the horizontal. The co-efficient of friction between each block and its plane is 0.325. For what horizontal force P, applied to 150 N block will motion to the right be impending? Figure 2a (b) A block weighing 100 N is resting on a rough plane inclined 20 0 to the horizontal. It is acted upon by a force of 50N directed upward at angle of 14 0 above the plane. Determine the friction. If the block is about to move up the plane, determine the co-efficient of friction. [10+6] 1 of 3
Code No: R05010302 Set No. 4 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 170 0 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) State and prove parallel axis theorem. (b) Find the moment of inertia about the horizontal centroidal axis of shaded portion for the Figure 4b. [6+10] Figure 4b 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. (a) With respect to the plane motion of rigid bodies, explain i. Instantaneous centre of rotation ii. Centrode iii. Absolute and relative velocity (b) A bomber flies along a horizontal line at an altitude of 1500m with a velocity of 400 km per hour i. Find at what horizontal distance before passing over a target on the ground, a bomb should be dropped so as to hit the target on the ground. ii. calculate the magnitude and direction of the velocity with which the bomb will hit the target. iii. Where will be the bomber when the bomb strikes the target? Take g = 9.81 m/sec 2. [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 surfaces of contact is 0.3, find the distance at which the block stop on the horizontal 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] 2 of 3
Code No: R05010302 Set No. 4 Figure 7b 8. A clock with a second s pendulum is running correct time at a place where the acceleration due to gravity is 9.81m/s 2. Find the length of the pendulum. This clock is taken at a place where the acceleration due to gravity is 9.80m/s 2. Find how much the clock will loose or gain in a day at this place? [16] 3 of 3