Mechanics 2009 May

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Reg. No.:(c)http://www.reelxstudios.thrikkunnapuzha.com Name: (c)http://www.reelxstudios.thrikkunnapuzha.com Combined First and Second Semester B.Tech. Degree Examination, May 2009 (2008 Scheme) 08 -105 : ENGINEERING MECHANICS Time : 3 Hours

Max. Marks : 100

PART - A Answer all questions under Part A. Each carries 5 marks. 1. State the Varignon's principle and differentiate between moment of a force and a couple. 2. A simply supported beam AB is subjected to a distributed load increasing from 1500 N/m to 4500 N/m from end A to end B. Span AB = 6 m . Determine the support reactions. 3. Prove that the angle of friction is equal to the angle made by an inclined plane with the horizontal when a rigid body which is placed on the inclined plane is about to slide downwards. 4. Explain the theorems of Pappus - Guldinus. 5.Explain instantaneous centre of rotation. How can it be located for a body moving with combined motion of rotation ? 6. Prove that the lowest point in touch with the ground of a wheel rotating without slipping is the instantaneous centre of the motion of the wheel. 7. Explain D'Alembert's principle applicable to curvilinear motion. 8. Explain the terms angular momentum, angular impulse and torque. P.T.O.

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PART-B Answer any two questions from each Module. Each carries 10 marks. Module - 1 1. Two rollers weighing 6 kN and 3 kN supported on an inclined plane are connected by a string as shown in figure. Find the angle 0(theta) that makes with horizontal so that the system is in equilibrium.

2. a) Define cantilever and overhanging beam. b) A bar of 6 m length with negligible weight rest in a horizontal position on the smooth planes as shown in figure. Determine the load P and reactions at supports.

3. A wedge 'A' has to be driven for tightening a body B loaded with 2000 N weight as shown in figure. If the coefficient of friction for all surfaces is 0.25, find the force P which should be applied to the wedge.

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Module - II 1

a) Locate the centroid of a right angled triangular section with height 'h' and base ' b ' by method of integration.

b)Cross section of a culvert is shown in figure. Calculate the moment of inertia of shaded region about the horizontal axis AA. Qc*f>

2.A cylinder of radius 1 m rolls without slipping along a horizontal plane AB. Its ^ centre has uniform velocity of 25 m/s. Find the velocity at points C and D on the circumference of the cylinder is shown in figure.

3. Find : (i) Acceleration of the masses and (ii) tension in the strings acting on a system of weights shown in figure. Coefficient of friction for the contact surfaces of bodies A and B are 0.4.

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Module - III 1. A bullet of mass 40 gm moving with a velocity of 500 m/s is fired into a body of mass 10 kg which is suspended by a string of 1 m long. Due to the impact the body swings through an angle ' 9 '. i) Find the angle 9 ' through which the body swings when the bullet gets embedded in the body ii) the bullet instead of getting embedded into the body it escapes out from the body through the other end with a velocity of 98 m/s. Find the angle through which the body will swing. 2. A ball of mass 3 kg moving with a velocity of 25 m/s strikes on a ball of mass 3 kg moving with a velocity of 35 m/s. At the instant of impact the velocities of the balls are inclined at an angle of 30° and 60° to the line joining their centres. If the coefficient of restitution is 0.9, then find the magnitude and direction of first and second ball after impact. 3. A solid cylindrical pulley of mass 800 kg having 0.9 m radius of gyration and 2 m diameter is rotated by an electric motor which exerts a uniform torque of 65 kN-m. A body of mass 3t is to be lifted by a wire wrapped round the pulley. Find the acceleration of the body and tension in the rope. . (c)http://www.reelxstudios.thrikkunnapuzha.com