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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II .B.TECH – I SEM SUPPLEMENTARY EXAMINATIONS JUNE- 2010 ENGINEERING MECHANICS (CHEMICAL ENGINEERING) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks --1.a) A system of forces consists of i) Force P1 = 3i + 5j - 6k acting through point (2,1,-3) ii) Force P2 = 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’. st iii) The moment of the system about the line through ‘O’ drawn in the 1 octant which makes angles of 650 and 750 with X and Y axes respectively. b) Write the Equilibrium equations for concurrent force system in space. [12+4]

Explain the types of friction with examples. Two equal bodies A and B of weight ‘W’ each are placed on a rough inclined plane. The bodies are connected by a light string. If µA = 1/2 and µB = 1/3, show that the bodies will be both on the point of motion when the plane is inclined at tan-1(5/12). [6+10]

3.a) b)

Derive an expression for ratio of tensions of a belt in standard form. The centre of two pulleys of diameter 120 mm and 240 mm are 300 mm apart. They are connected by an open belt. If the coefficient of friction for the larger pulley be 0.28, what would be its value for the smaller pulleys simultaneously? [6+10]

4.a)

Derive an expression to determine the moment of inertia of a semi circle about its diametric base. Find the moment of inertia of the shaded area, as shown in figure about its centroidal axes parallel to x-axis. [8+8]

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5.a)

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Define mass moment of inertia and explain Transfer formula for mass moment of inertia. Derive the expression for the moment of inertia of a homogeneous sphere of radius ‘r’ and mass density ‘w’ with reference to its diameter. [8+8]

6.a)

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The shaft shown in figure carries two masses. The mass A is 300Kg with radius of gyration of 0.75 m and the mass B is 500 Kg with radius of gyration of 0.9 m. Determine the frequency of torsional vibrations. It is desired to have the node at the mid-section of the shaft of 120 mm diameter by changing the diameter of the section having a 90 mm diameter. What will be the new diameter? [16]

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The motion of a disk rotating about a fixed point is given by the relation -3t θ = 2(1 + e ) where θ is in radians and ‘t’ is in seconds. Determine the angular coordinates, velocity and acceleration of the disk when i) t = 0 and ii) t = 2secs. A projectile is aimed at a mark on the horizontal plane through the point of projection and falls 12m short when the angle of projection is 150 while it overshoots the mark by 24m when the angle of projection is 450. Find the angle of projection to hit the mark neglecting the resistance of air. Take g = 9.81 m/s2. [8+8] If Wa:Wb:Wc is in the ratio of 3:2:1 , find the accelerations of the blocks A, B, and C. Assume that the pulleys are weightless. {As shown in the Figure} [16]

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