R07a1ec09-engineering-mechanics

Set No. 1

Code No: R07A1EC09

I B.Tech Supplimentary Examinations, Aug/Sep 2008 ENGINEERING MECHANICS ( Common to Metallurgy & Material Technology and Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. Determine the reactions of the beam shown in figure 1.

[16]

Figure 1 2. A square threaded screw-jack has a mean diameter of 50 mm and pitch 10 mm. If µ = 0.2, what force at the end of the lever will lift a load of 2000 N? State the reasons whether the screw is self-locking or not. Length of the lever = 450 mm. [16] 3. (a) Find the power required to run the pulley belt drive if i. The differential tension is 2 kN. ii. The maximum tension is 8 kN. (b) What is meant by cross belt drive? Find the length of belt in a cross belt drive. [8+8] 4. (a) Find the centroid of the area shown in figure 4a.

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Set No. 1

Code No: R07A1EC09

Figure 4a (b) Find the centroid of the area shown in figure 4b. All dimensions are in cm. [8+8]

Figure 4b 5. (a) Starting from the first principles determine the moment of inertia of a triangle with respect to its base. (b) Determine the radius of gyration for rectangle i. about x axis and ii. about its base.

[8+8]

6. A bus starts from rest at point A and accelerates at the rate of 0.9 m/s2 until is reaches a speed of 7.2 m/s. It then proceeds with the same speed until the brakes are applied. It comes to rest, at point B, 18 m beyond the point where the brakes are applied. Assuming uniform acceleration, determine the time required for the bus to travel from A to B. Distance AB = 90 m. [16] 7. Two blocks are joined by an inextensible cable as shown in figure 7. If the system is released from rest, determine the velocity of block A after it has moved 2 m. Assume that µ equals to 0.25 between block A and the plane and that the pulley is weightless and frictionless. [16]

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Set No. 1

Code No: R07A1EC09

Figure 7 8. Determine the natural frequency of the free longitudinal vibrations of cantilever beam by equilibrium method and Rayleigh’s method. [16] ⋆⋆⋆⋆⋆

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Set No. 2

Code No: R07A1EC09

I B.Tech Supplimentary Examinations, Aug/Sep 2008 ENGINEERING MECHANICS ( Common to Metallurgy & Material Technology and Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Determine the magnitudes of F1 and F2 for the following system of forces which are in equilibrium as shown in figure 1a.

Figure 1a (b) Find the magnitude of 2 forces such that if they act at right √ angles, their √ o [8+8] resultant is 10 N, but if they act at 60 , their resultant is 13 N. 2. A person of mass 90 kg is standing on a ladder at point C, shown in figure 2. The ladder rests on a rough horizontal floor at A and against a smooth vertical wall at B. If the ladder is just on the point of slipping find the coefficient of friction between the ladder and the floor. Neglect the weight of the ladder. Also find the reactions at A and B. [16]

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Set No. 2

Code No: R07A1EC09

Figure 2 3. (a) Find the power required to run the pulley belt drive if i. The differential tension is 2 kN. ii. The maximum tension is 8 kN. (b) What is meant by cross belt drive? Find the length of belt in a cross belt drive. [8+8] 4. (a) From the first principle find the centroid of a right angle triangle of height h and breadth b. (b) Find the centroid of the area shown in figure 4b. All dimensions are in cm. [8+8]

Figure 4b 5. Calculate the mass moment of inertia of thin plate shown in figure 5 with respect to the axis X-X. Take mass of the plate as m. [16]

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Set No. 2

Code No: R07A1EC09

Figure 5 6. (a) The motion of a particle is defined by the relation x = t3 − 12t2 + 36t + 30 where x is expressed in meters and t is in sec. Determine the time, position, and acceleration; when v = 0. (b) A stone is thrown upwards from the top of a tower 70 m high with a velocity of 19.2 m/s. Determine its position and velocity when t = 6 secs. [8+8] 7. A 2000 kg automobile is driven down a 50 incline at a speed of 90 km/hr. When the brakes are applied, causing a constant total braking force (applied by the road on the types) of 7.5 KN, Determine the distance traveled by the automobile as it comes to stop. Use work-energy method. [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] ⋆⋆⋆⋆⋆

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Set No. 3

Code No: R07A1EC09

I B.Tech Supplimentary Examinations, Aug/Sep 2008 ENGINEERING MECHANICS ( Common to Metallurgy & Material Technology and Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Determine the magnitudes of F1 and F2 for the following system of forces which are in equilibrium as shown in figure 1a.

Figure 1a (b) Find the magnitude of 2 forces such that if they act at right √ angles, their √ o [8+8] resultant is 10 N, but if they act at 60 , their resultant is 13 N. 2. (a) A wooden block weighing 30 N is placed on a horizontal plane. A horizontal force of 12 N is applied and the block is on the point of moving. Find i. Coefficient of friction ii. Angle of friction and iii. The resultant reaction. (b) A block of weight 80 N is placed on a horizontal plane where the coefficient of friction is 0.25. Find the force that should be applied to the block at an angle of 300 with the horizontal to attain the condition of limiting equilibrium.[8+8] 3. A shaft which rotates at a constant speed of 160 r.p.m. is connected by belting to a parallel shaft 720 mm apart, which has to run at 60, 80 and 100 r.p.m. The smallest pulley on the driving shaft is 40 mm in radius. Determine the remaining radii of the two stepped pulleys for an open belt. Neglect belt thickness and slip. [16] 1 of 3

Set No. 3

Code No: R07A1EC09

4. (a) From the first principle find the centroid of a right angle triangle of height h and breadth b. (b) Find the centroid of the area shown in figure 4b. All dimensions are in cm. [8+8]

Figure 4b 5. A sheet metal is cut and bent as shown in figure 5. Determine the mass moment of inertia about x axis, if the density of material is 16 kg/m3 . [16]

Figure 5 6. (a) The motion of a particle is defined by the relation x = t3 − 12t2 + 36t + 30 where x is expressed in meters and t is in sec. Determine the time, position, and acceleration; when v = 0. (b) A stone is thrown upwards from the top of a tower 70 m high with a velocity of 19.2 m/s. Determine its position and velocity when t = 6 secs. [8+8] 7. For the system of connected bodies shown in figure 7, determine the acceleration of each block and the tension in the rope. Coefficient of friction between block A

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Set No. 3

Code No: R07A1EC09

and horizontal surface is 0.3. Block A and B weigh 100 N and 200 N respectively. Hence find the velocity of each block after 5 sec. [16]

Figure 7 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] ⋆⋆⋆⋆⋆

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Set No. 4

Code No: R07A1EC09

I B.Tech Supplimentary Examinations, Aug/Sep 2008 ENGINEERING MECHANICS ( Common to Metallurgy & Material Technology and Aeronautical Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. A rigid bar is subjected to a system of parallel forces as shown in Figure 1. Reduce this system to.

Figure 1 (a) A single force (b) A single force-moment system at A. (c) A single force-moment system at B.

[16]

2. A person of mass 90 kg is standing on a ladder at point C, shown in figure 2. The ladder rests on a rough horizontal floor at A and against a smooth vertical wall at B. If the ladder is just on the point of slipping find the coefficient of friction between the ladder and the floor. Neglect the weight of the ladder. Also find the reactions at A and B. [16]

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Set No. 4

Code No: R07A1EC09

Figure 2 3. Determine the width of a 9.75 mm thick leather belt required to transmit 15 kW from a motor running at 900 r.p.m. The diameter of the driving pulley of the motor is 300 mm. The driven pulley runs at 300 r.p.m. and the distance between the centre of two pulleys is 3 meters. The density of leather is 1000 kg/m3 . The maximum allowable stress in the leather is 2.5 MPa. The coefficient of friction between the leather and pulley is 0.3. Assume open belt drive and neglect the sag and slip of the belt. [16] 4. (a) From the first principle find the centroid of a right angle triangle of height h and breadth b. (b) Find the centroid of the area shown in figure 4b. All dimensions are in cm. [8+8]

Figure 4b 5. (a) Starting from the first principles determine the moment of inertia of a triangle with respect to its base. (b) Determine the radius of gyration for rectangle i. about x axis and ii. about its base.

[8+8]

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Set No. 4

Code No: R07A1EC09

6. (a) The motion of a particle is defined by the relation x = t3 − 12t2 + 36t + 30 where x is expressed in meters and t is in sec. Determine the time, position, and acceleration; when v = 0. (b) A stone is thrown upwards from the top of a tower 70 m high with a velocity of 19.2 m/s. Determine its position and velocity when t = 6 secs. [8+8] 7. Two blocks are joined by an inextensible cable as shown in figure 7. If the system is released from rest, determine the velocity of block A after it has moved 2 m. Assume that µ equals to 0.25 between block A and the plane and that the pulley is weightless and frictionless. [16]

Figure 7 8. A shaft 1.5 m long is supported in flexible bearings at the ends and carries two wheels each of 50 kg mass. One wheel is situated at the center of the shaft and the other at the distance of 0.4 m from the towards right. The shaft is hollow of external diameter 75 mm and inner diameter 37.5 mm. The density of the shaft material is 8000 kg/m3 . The Young’s modulus for the shaft material is 200 GN/m2 . Find the frequency of transverse vibration. [16] ⋆⋆⋆⋆⋆

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