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### C L A S S I C A L M E C H A N I C S J N T U M O D E L P A P E R{Www

1. 1. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 1 I B.Tech Regular Examinations, May/Jun 2008 CLASSICAL MECHANICS ( Common to Mechanical Engineering, Chemical Engineering, Mechatronics, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) The resultant of the two forces when they act at an angle of 650 is 20 N. If the same forces are acting at right angles their resultant is 16.5 N. Determine the magnitude of the two forces. (b) A force of 100N makes angles of 300, 600 and 1000 with x,y, z axes respectively. Find the components of the force along the x,y and z axes. [8+8] 2. Determine the resultant of the force system as shown in gure 2 graphically. [16] Figure 2 3. (a) Find the centroid of the inverted T section shown in Figure 3a.
2. 2. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 1 Figure 3a (b) Determine the centre of gravity of the composite bo dy consisting of a cylinder of radius ‘r’ attached to a hemisphere of raduis ‘r’ as shown in gure 3b.[8+8] Figure 3b 4. Find the moment of inertia of the plane area shown in gure 4 about X and Y axes through its centroid. [16] Figure 4
3. 3. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 1 gure 5. Show the values on a neat diagram of the truss. Mention clearly the nature of the forces (tension or compression) in each memeber. [16] Figure 5 6. Bars AB and BE, each of weight 3.2 kg are welded together and are pin-jointed to two links AC and BD. The assembly is released from rest in the position shown in gure 6 and Neglecting the masses of the links determine (a) the acceleration of the assembly (b) the forces in the links. [16] Figure 6 7. (a) What is the advantage of work-energy theorem? (b) A shaft of radius r rotates with constant angular speed in bearings for which are coe cient of friction is . Through what angle will it rotate after the driving force is removed? [4+12] 8. The central de ection of a simply supported beam with a central point load is given
4. 4. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 1 The beam is of uniform cross section with a static load “P”. Determine (a) equivalent spring constant of the beam (b) the frequency of vibration of a 60kg block attached to the centre of the beam. Neglect the mass of the beam and assume that the load remaining in contact with the beam. [16]
5. 5. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 2 I B.Tech Regular Examinations, May/Jun 2008 CLASSICAL MECHANICS ( Common to Mechanical Engineering, Chemical Engineering, Mechatronics, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. Determine and locate the resultant R of the forces and one couple acting on the beam as shown in gure 1. [16] Figure 1 2. In a shop-unloading operation, 1000 kg automobile is supported by a cable as shown in gure 2. A rope is tied to the cable at A and pulled in order to centre the automobile over its intended position. The angle between the cable AB and the vertical is 40, while the angle between the rope and the horizontal is 300. What is the tension in the rope AC? [16] Figure 2 3. Determine the centroid of the area shown in gure 3. [16]
6. 6. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 2 Figure 3 4. Determine the moment of inertia of the section shown in gure 4 about the cen- troidal axes. [16] Figure 4 5. Determine the forces in the truss shown in gure 5. [16] Figure 5
7. 7. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 2 6. Two cars A and B are traveling in adjacent highway lakes and at t = 0 have the positions and speeds shown in gure 6. The car A has a constant acceleration of 0.8m/sec2 and that B has a constant deceleration of 0.6 m/s2 determine (a) when and where A will overtake B (b) the speed of each car at that time. [16] Figure 6 7. (a) A body of mass 18 kg slides up an incline of 300 under the action of an applied force 300N along the incline and in the presence of friction, = 0.2. If the body moves from rest determine, after a period of 6 secs; i. Acceleration of the body ii. Distance traveled by the body iii. Kinetic energy of the body iv. Work done on the body. (b) A 2kg collar can slide without friction along a horizontal ro d as shown in gure 7b and is released from rest at A. The undeformed lengths of springs BA & CA are 30cm and 25cm respectively and the constant of each spring is 490KN/m. Determine the velocity of the collar when it has moved 3 cm to the right. [8+8]
8. 8. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 2 Figure 7b 8. The central de ection of a simply supported beam with a central point load is given by S = PL3 / 48EI. Where L = 5 M, E = 2 ×105 N/mm2, I = 1.73 × 10-5 m4. The beam is of uniform cross section with a static load “P”. Determine (a) equivalent spring constant of the beam (b) the frequency of vibration of a 60kg block attached to the centre of the beam. Neglect the mass of the beam and assume that the load remaining in contact with the beam. [16]
9. 9. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 3 I B.Tech Regular Examinations, May/Jun 2008 CLASSICAL MECHANICS ( Common to Mechanical Engineering, Chemical Engineering, Mechatronics, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. Three forces of magnitude 150 N, 300 N and 500 N are acting at the origin O(0,0,0) and are directed from the points A(3,2,4), B(3,-2,-4) and C(-1,-3,-4) respectively to the origin. Determine the magnitude of the resultant. [16] 2. A force F with a magnitude of 150 N is applied at the origin O of the axes x, y and z as shown in Figure 2. The line of action of F passes through a point A whose co-ordinates are 2 m, 4 m and 6 m. Determine (a) the x, y, and z scalar components of F (b) the pro jection of F on x-y plane, and (c) the pro jection of F along the line OB. [16] Figure 2 3. (a) Find the centroid of the area shown in gure 3a
10. 10. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 3 Figure 3a (b) Determine the co ordinates of the centroid of the quadrant PQ of the are of a circle of raduis ‘r’ showin gure 3b. [8+8] Figure 3b 4. Find the moment of inertia of the plane area shown in gure 4 about X and Y axes through its centroid. [16] Figure 4
11. 11. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 3 Figure 5 6. (a) The velo city of a particle is V = 0 1 - pt T. The particle starts from the origin with an initial velocity 0, determine i. its position and its acceleration at t = 4T, ii. its average velo city during the interval t = 0 to t = T. (b) The motion of a rotor is de ned by de relation = 8t3 - 6 (t - 2)2, where and t are expressed in radians and seconds, respectively. Determine i. When the angular acceleration is zero ii. The angular co ordinate and angular velocity at that time. [8+8] 7. (a) What is the energy of motion for a rigid body rotating about a xed axis? (b) A 70kg sprinter starts from rest and accelerate uniformly for 5.8s over a dis- tance of 34.5m. Neglecting air resistance, determine the average power devel- oped by the sprinter. [6+10] 8. (a) The amplitude and maximum velocity of a particle is 40 cm and 2m/sec. A particle moves in SHM. Determine the maximum acceleration of the particle and the period of its motion. (b) The particle which moves in SHM has maximum velocity of 100 mm/sec and maximum acceleration of 2 m / sec2. Determine the amplitude and frequency of the motion. [8+8]
12. 12. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 4 I B.Tech Regular Examinations, May/Jun 2008 CLASSICAL MECHANICS ( Common to Mechanical Engineering, Chemical Engineering, Mechatronics, Production Engineering and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. Replace the given system of forces acting on a bo dy as shown in gure 1 by a single force and couple acting at the point A. [16] Figure 1 2. Five strings are tied at a point and are pulled in all directions, equally spaced, from one another. If the magnitude of the pulls on three consecutive strings is 70 N, 40 N and 55 N respectively, nd graphically the magnitude of the pulls on two other strings, if the system is in equilibrium. [16] 3. Find the centroid of the area shown in gure 3. [16]
13. 13. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 4 4. Find the moment of inertia of the plane area shown in gure 4 about X and Y axes through its centroid. [16] Figure 4 5. Determine the forces in the trusses shown in gure 5. [16] Figure 5 6. (a) De ne Newton’s law of gravitation. (b) A 2 kg revolves in a horizontal circle as shown in gure 6b at a constant speed of 1.8 m /s. L = 600 mm determine i. The angle that the cord forms with the vertical ii. The tension in the cord. [4+12]
14. 14. www.studentyogi.com www.studentyogi.com Code No: 07A1EC03 Set No. 4 Figure 6b 7. A solid cylinder of weight W and radius ‘r’ rolls, down an inclined plane which makes angle with the horizontal axis. Determine the minimum coe cient of friction and the acceleration of the mass center for rolling, without slipping. [16] 8. The central de ection of a simply supported beam with a central point load is given by S = PL3 / 48EI. Where L = 5 M, E = 2 ×105 N/mm2, I = 1.73 × 10-5 m4. The beam is of uniform cross section with a static load “P”. Determine (a) equivalent spring constant of the beam (b) the frequency of vibration of a 60kg block attached to the centre of the beam. Neglect the mass of the beam and assume that the load remaining in contact with the beam. [16]