8/6/2019 Nr10105 Engineering Mechanics Set1

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Code No: NR10105 NR

I B.Tech Semester Supplimentary Examinations, June 2009ENGINEERING MECHANICS

( Common to Civil Engineering, Mechanical Engineering, Mechatronics,Metallurgy & Material Technology, Production Engineering and

Aeronautical Engineering)Time: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

1. (a) State and prove Lames theorem.

(b) A prismatic bar AB of 7m long is hinged at A and supported at B as shownin Figure 1b. Neglecting friction, determine the reaction Rb produced at Bowing to the weight of the bar. q = 4000 N, Take = 250. [6+10]

Figure 1b

2. (a) Explain the principles of operation of a screw-jack with a neat sketch.

(b) Outside diameter of a square threaded spindle of a screw Jack is 40 mm. Thescrew pitch is 10 mm. If the coefficient of friction between the screw and thenut is 0.15, neglecting friction between the nut and collar, determine

i. Force required to be applied at the screw to raise a load of 2000N

ii. The efficiency of screw jack

iii. Force required to be applied at pitch radius to lower the same load of 2000

N andiv. Efficiency while lowering the load

v. What should be the pitch for the maximum efficiency of the screw? and

vi. what should be the value of the maximum efficiency? [6+10]

3. A leather belt is required to transmit 9kW from a pulley 1200 mm in diameterrunning at 200 r.p.m The angle embraced is 1650 and the coefficient of frictionbetween leather belt and pulley is 0.3. If the safe working stress for the leather beltis 1.4N/mm2 the weight of leather is 1000Kg/m3 and the thickness of the belt is10mm, determine the width of the belt taking the centrifugal tension in to account.

[16]

4. (a) Deduce an expression from first principle to determine the center of gravity ofa sight circular solid cone about its base.

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Code No: NR10105 NR

(b) Locate the centroid of the shaded area as shown in figure4b. [8+8]

Figure 4b

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 accelerationdue 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 ofinertia of this cone about a line which passes through the vertex of the coneand which is parallel to the base of the cone. [8+8]

6. (a) A train is uniformly accelerated and passes successive kilometer stones withvelocities of 18km/hr and 36km/hr respectively. Calculate the velocity whenit passes the third kilometer stone. Also find the time taken for each of the

two intervals of one kilometer.(b) A ball projected vertically upwards attains a maximum height of 400 metres.

Calculate the velocity of projection and compute the time of flight in air. Atwhat altitude will this ball meet a second ball projected vertically upwards 4seconds later with a speed of 120 metres per second? [8+8]

7. (a) A homogeneous solid cylinder of weight 100 N whose axis is horizontal rotatesabout its axis, in frictionless bearings under the action of the weight of a 10Nblock which is carried by a rope wrapped around the cylinder. What will beangular velocity of cylinder two seconds after the motion starts? Assume the

diameter of cylinder as 100cm.(b) A block of mass 5Kg resting on a 300 inclined plane is released. The block after

travelling a distance of 0.5m along the inclined plane hits a spring of stiffness15N/cm. Find the maximum compression of spring. Assume coefficient offriction between the block and the inclined plane is 0.2. As shown in theFigure 7b. [8+8]

Figure 7b

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Code No: NR10105 NR

8. (a) A homogeneous circular disk of radius r and weight W hangs in a verticalplane from a pin O at its circumference. Find the period for small anglesof swing in the plane of the disk

(b) A slender wire 0.90 m long is bent in the form of a equilateral triangle andhangs from a pin at O as shown in the figure8b. Determine the period forsmall amplitudes of swing in the plane of the figure. [16]

Figure 8b

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