# Applied Mechanics

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Code No: RR10105I B.Tech.

Set No.1Regular Examinations, January -2005 APPLIED MECHANICS (Civil Engineering) Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks

Time: 3 hours

1. (a) Three identical cylinders, each weighing W, are stacked as shown in gure1, on smooth inclined surfaces, each inclined at an angle with the horizontal. Determine the smallest angle to prevent stack from collapsing.

Figure 1: (b) The boom of a crane is shown in gure2, if the weight of the boom is negligible compared with the load W = 60 kN, nd the compression in the boom and also the limiting value of the tension T when the boom approaches the vertical position. 2. (a) A short semicircular right cylinder of radius r and weight w rests on a horizontal surface and is pulled at right angles to its geometric axis by a horizontal force applied at the middle B of the front edge gure. Find the angle that the at face will make with the horizontal plane just before sliding begins if the coecient of friction at the line of contact A is . The gravity force W must be considered as acting at the center of gravity C as shown is the gure3. (b) The mean diameter of the threads of a square threaded screw is 50 mm. The pitch of the thread is 6 mm. The coecient of friction = 0.15. What force must be applied at the end of a 600 mm lever, which is perpendicular to the longitudinal axis of the screw ( i ) to raise a load of 17.5 kN and ( i i ) t o lower the load. 3. (a) Derive an expression for length of an open belt in standard form.

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Code No: RR10105

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Figure 2:

Figure 3:

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(b) A belt is running over a pulley of diameter 1200 mm at 200 r.p.m. The angle of contact is 1650 and coecient of friction between the belt and pulley is 0.3 If the maximum tension in the belt is 3000N, nd the power transmitted by the belt. 4. (a) Find the centroid of the plain lamina shown Figure 4

Figure 4: (b) Find the moment of inertia about the horizontal centroidal axis and about the base A B {As shown in the Figure 5}

Figure 5: 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.

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Code No: RR10105

Set No.1

(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 6. (a) A train is traveling at a speed of 60km/hr. It has to slow down due to certain repair work on the track. Hence, it moves with a constant retardation of 1km/hrper second until its speed is reduced to 15km/hr. It then travels at a constant speed of for 0.25km/hr and accelerates at 0.5km/hr per second until its speed once more reaches 60km/hr. Find the delay caused. (b) The motion of a particle in rectilinear motion is dened 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. 7. (a) A body weighing 20N is projected up a 200 inclined plane with a velocity of 12m/s, coecient of friction is 0.15. Find i. The maximum distance S, that the body will move up the inclined plane ii. Velocity of the body when it returns to it original position. (b) Find the acceleration of the moving loads as shown in f i gure 6 . Take mass of P=120kg and that of Q=80Kg and coecient of friction between surfaces of contact is 0.3 .Also nd the tension in the connecting string.

Figure 6: 8. Two springs of stiness k1 and k2 are connected in series. Upper end of the compound spring is connected to a ceiling and lower end carries a load W. Find the equivalent spring stiness of the system. If the above two springs are connected in parallel then nd the equivalent spring stiness of the system also.

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Code No: RR10105 I B.Tech.

Set No.2Regular Examinations, January -2005 APPLIED MECHANICS (Civil Engineering) Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks

Time: 3 hours

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 Figure7. Find the axial force induced in each of the three members of this system.

Figure 7: 2. (a) Referring to gure8 the coecient of the friction is as follows: 0.25 at the oor, 0.30 at the wall, and 0.20 between blocks. Find the minimum value of a horizontal force P applied to the lower block that will hold the system in equilibrium.

Figure 8: (b) Two identical blocks A and B are connected by a rod and rest against vertical and horizontal planes respectively, as shown in gure9. If sliding impends when = 450 , determine the coecient of friction , assuming it to be the same at both oor and wall. 3. (a) Show that the maximum power can be transmitted at Tmax = 3 Tc

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Figure 9: (b) A belt embraces the shorter pulley by an angle of 1650 and runs at a speed of 1700m/min. Dimensions of the belt are width = 200mm and 8mm thickness. It weight 1000 kg/m3 . Determine the maximum power that can be transmitted at the above speed, if the maximum permissible stress in the belt is not to exceed 2.5N/mm2 and = 0.25. 4. (a) Dene the terms centroid, moment of inertia and radius of gyration. (b) Compute moment of inertia of hemisphere about its diametral base of radius R. 5. (a) Show that the moment of inertia of a homogenous triangular plate of weight W with respect to its base of width b is W b2 /6g where g is the acceleration due to gravity. (b) A right circular cone has the radius of base as 200mm and height 500mm. The mass density of the cone is 7800 kg/m3 . Find out the mass moment of inertia of this cone about a line which passes through the vertex of the cone and which is parallel to the base of the cone. 6. (a) Ram and Rahim are sitting in cars A and B respectively. The cars are 300m apart and at rest. Ram starts the car and moves towards B with an acceleration of 0.5m/s2 . After three seconds , Rahim starts his car towards A with an acceleration of 1m/s2 . Calculate the time and point at which two cars meet with respect to A. (b) A projectile is red at a speed of 800 m/s at an angle of elevation of 500 from the horizontal. Neglecting the resistance of air, calculate the distance of the point along the inclined surface at which the projectile will strike the inclined surface which makes an angle of 150 with the horizontal. 7. (a) A body weighing 20N is projected up a 200 inclined plane with a velocity of 12m/s, coecient of friction is 0.15. Find i. The maximum distance S, that the body will move up the inclined plane ii. Velocity of the body when it returns to it original position. (b) Find the acceleration of the moving loads as shown in gure10. Take mass of P=120kg and that of Q=80Kg and coecient of friction between surfaces of contact is 0.3 .Also nd the tension in the connecting string.

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Figure 10: 8. Determine the frequency of torsional vibrations of the disc shown in (gure11) below, if both the ends of the shaft are xed and diameter of the shaft is 40mm. The disc has a mass of 600Kg, and a radius of gyration of 0.4m.Taking modulus of rigidity for the shaft material as 85GN/m2 .l1 =1m, and l2 = 0.8m.

Figure 11:

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Code No: RR10105 I B.Tech.

Set No.3Regular Examinations, January -2005 APPLIED MECHANICS (Civil Engineering) Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks

Time: 3 hours

1. (a) Dene free body diagram, Transmissibility of a force and resultant of a force. (b) Two identical rollers, each of weight 100 N, are supported by an inclined plane and a vertical wall as shown in Figure12. Assuming smooth surfaces, nd the reactions induced at the points of support A, B and C.

Figure 12: 2. The two 50 wedges shown are used to adjust the position of the column under a vertical load of 5 kN. Determine the magnitude of the forces P required to raise the column if the coecient of friction for all surfaces is 0.40. {As shown in the Figure13}

Figure 13: 3. (a) Derive an expression for length of a crossed belt in standard form. (b) An engine drives a shaft by means of a belt. The driving pulley of the engine is 3 meters and that in the shaft 2 meters diameter. If the engine runs at 150.r.p.m. what will be the speed of the shaft when. 1 of 3

Code No: RR10105 i. there is no slip ii. there is a slip of 3% ? 4. (a) Find the centroid of the plain lamina shown Figure14

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Figure 14: (b) Find the moment of inertia about the horizontal centroidal axis and about the base A B {As shown in the Figure15}

Figure 15: 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 . 6. (a) An airplane is ying horizontally with a velocity of 450 km/hr at an altitude of 1960 m towards a target on the ground which is to be bombed. Estimate 2 of 3

Code No: RR10105

Set No.3

where the bomb must be released in order to hit the target and the time of travel of the bomb. What is the velocity with which the bomb will hit the target?. Also nd the angle made by the line of sight of the pilot when the bomb is released. (b) The acceleration of a particle is dened by the r