r050210804 Engineering Mechanics

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Code No: R050210804 Set No. 1

II B.Tech I Semester Supplementary Examinations, February 2007ENGINEERING MECHANICS

(Chemical Engineering)Time: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

1. A strut AB attached to the face of a vertical wall at A by a spherical hinge standsperpendicular to the wall and is supported by two guy wires, as shown in Figure1.At B, in a plane parallel to the wall, two forces P and Q acts as shown, Q being

horizontal and P, vertical. Find the axial forces produced in the members if P =500 N and Q = 1000 N.

Figure 1:

2. (a) A screw jack has a pitch of 6 mm. The mean radius of the threads is 60mm. The mean diameter of the bearing surface under the cap is 80 mm.The coefficient of friction for all surfaces is 0.06. What turning moment isnecessary to raise 680 Kg.

(b) Determine the magnitude and direction of the friction force acting on the1000N block shown in figure2. If, first P = 500 N and second P = 100 N. Thecoefficient of static friction is 0.2, and the coefficient of kinetic friction is 0.17.The forces are applied with the block initially at rest.

3. An open flat belt drive connects two parallel shafts 1200mm apart. The drivingand driven shafts rotate at 350 r.p.m and 140 r.p.m respectively and the drivenpulley is 400 mm in diameter. The belt is 5mm thick and 80mm wide. Coefficientof friction between belt and pulley is 0.3 and maximum permissible tension in thebelting is 1.4N/mm2. Determine.

(a) Diameter of driving pulley.(b) Maximum power that may be transmitted by the belting and

(c) Required initial tension in the belt. Neglect centrifugal tension.

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Figure 2:

4. (a) Differentiate between centroid and center of gravity.

(b) Determine the product of inertia of shaded area as shown about the indicatex-y axis.{As shown in the Figure3}

Figure 3:

5. (a) Prove that the mass moment of inertia of a right circular cone of base radiusR and height h, with respect to a diameter of the base is M(3R2 + 2h2)/20

where M is the mass of the cone.

(b) Calculate the mass moment of inertia of a circular cone of base radius 300mmand height 600mm about a line which passes through the mass centre of thecone and which is parallel to the base of the cone. The mass density of thecone is 2500 kg/m3 [8+8]

6. (a) Maximum range of a field gun is 2000m. If a target at a distance of 1200m isto be hit, what should be the angle of projection.

(b) A stone dropped into a well is heard to strike the water in 3.5 seconds. Findthe depth of the well assuming the velocity of sound is 335 m/sec.

7. (a) A body weighing 20N is projected up a 200 inclined plane with a velocity of12m/s, coefficient of friction is 0.15. Find

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i. The maximum distance S, that the body will move up the inclined plane

ii. Velocity of the body when it returns to it original position.(b) Find the acceleration of the moving loads as shown in figure4. Take mass of

P=120kg and that of Q=80Kg and coefficient of friction between surfaces ofcontact is 0.3 .Also find the tension in the connecting string.

Figure 4:

8. A vertical U-tube manometer contains a liquid of mass density as shown in the(figure5). A sudden increase of pressure on one column forces the level of the liquiddown, When the pressure is released, the liquid column start vibrating. Neglectingthe frictional damping, determine the period of vibration. Comment if the periodis affected by changing the liquid, diameter of the tube or length l of the liquidcolumn.

Figure 5:

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1. (a) Two forces equal to ZP and P respectively act on a particle. If first be doubledand the second increased by 12N the direction of the resultant is unaltered,find the value of P?

(b) A 675 N man stands on the middle rung of a 225 N ladder, as shown in Figure1.Assuming a smooth wall at B and a stop at A to prevent slipping, find thereactions at A and B.

Figure 1:

2. The vertical position of the 100-kg block is adjusted by the screw-activated wedge.Calculate the moment M which must be applied to the handle of the screw to raisethe block. The single-threaded screw has square threads with a mean diameter of30 mm and advances 10 mm for each complete turn. The coefficient of friction for

the screw threads is 0.25, and the coefficient of friction for all mating surfaces ofthe block and wedge is 0.40. Neglect friction at the ball joint A.{As shown in the Figure2}

3. An open belt running over two pulleys 1500 mm and 1000 mm diameters connectstwo parallel shafts 48000 mm apart. The initial tension in the belt when stationaryis 3000N. If the smaller pulley is rotating at 600 r.p.m and coefficient of frictionbetween the belt and pulley is 0.3. Determine the power transmitted taking cen-trifugal tension into account. The mass of belt is given as 0.6703 kg/meter length.

4. (a) From first principles deduce an expression to determine the centroid of a tri-

angle of base b and height h(b) Determine the centroidal co-ordinates of the shaded area as shown in figure3.

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Figure 2:

Figure 3:

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5. (a) Show that the moment of inertia of a homogenous triangular plate of weightW 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.

6. (a) A car starts from the rest on a straight road and travels with uniform acceler-ation of 0.8m/s2 for the first 10sec and then travels with uniform velocity forthe next 30 sec. It then decelerates at the rate of 0.5m/s2 and comes to rest.Determine

i. Total time taken to complete the trip

ii. Total distance travelled and

(b) A fighter plane is directly over an antiaircraft gun at time t=0 and at analtitude of 1800m. The plane is moving with a speed of 600 km/hour. A shellis fired at time t=0 in an attempt to hit the plane. If the muzzle velocity is1000m/sec, find out the angle at which the gun should be held.

7. (a) A homogeneous sphere of radius of a=100mm and weight W=100N can rotatefreely about a diameter. If it starts from rest and gains, with constant angularacceleration, an angular speed n=180rpm, in 12 revolutions, find the acting

moment. .(b) A block starts from rest fromA . If the coefficient of friction between all

surfaces of contact is 0.3, find the distance at which the block stop on thehorizontal plane. Assume the magnitude of velocity at the end of slope issame as that at the beginning of the horizontal plane.{As shown in the Figure4}

Figure 4:

8. Two springs of stiffness 200N/m are attached to a ball of weight 5N as shown inthe (figure5). If the ball is initially displaced by 2.5cm to the left and released, findthe period of oscillation of the ball. Find also the velocity of the ball when it passesthrough the middle position.

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Figure 5:

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1. (a) Three identical cylinders, each weighing W, are stacked as shown in figure1,on smooth inclined surfaces, each inclined at an angle with the horizontal.Determine the smallest angle to prevent stack from collapsing.

Figure 1:

(b) The boom of a crane is shown in figure2, if the weight of the boom is negligiblecompared with the load W = 60 kN, find the compression in the boom and alsothe limiting value of the tension T when the boom approaches the verticalposition.

2. (a) A short right circular cylinder of weight W rests in a horizontal V-notch having

the angle 2 as shown in figure3. If the coefficient of friction is , find thehorizontal force P necessary to cause slipping to impend.

(b) A 150 wedge of negligible weight is to be driven to tighten a body B whichis supporting a vertical load of 1000N. If the coefficient of friction for allcontacting surfaces be 0.25, find the minimum force P required to drive thewedge. Assume the reaction of the surface y-y as zero.{As shown in the Figure4}

3. A cross belt drive is to transmit 7.5 KW at 1000 r.p.m of the smaller pulley. Thediameter of the smallest pulley is 250mm and velocity ratio is 2. The centre distance

between the pulley is 1250mm. A flat belt of thickness 6mm and of coefficientfriction 0.3 is used over the pulleys. Determine the necessary width of the belt ifthe maximum allowable stress in the belt is 1.75N/mm2 and density of the belt is1000Kg/m3

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Figure 2:

Figure 3:

Figure 4:

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4. (a) Explain the transfer formula for product of inertia

(b) Find the moment of inertia about shaded are parallel to x axis.{As shown in the Figure5}

Figure 5:

5. Determine the mass moment of Inertia of the cast iron flywheel as shown in(figure6). (cross section) with respect to the axis of rotation. The flywheel hassix elliptical spokes 30 40 mm in cross section. Cost iron weighs 7200 kg/m3.

Figure 6:

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 thetwo 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?

7. If Wa:Wb:Wc is in the ratio of 3:2:1 , find the accelerations of the blocks A, B, andC. Assume that the pulleys are weightless.{As shown in the Figure7}

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Figure 7:

8. Determine the frequency of torsional vibrations of the disc shown in (figure8) below,if both the ends of the shaft are fixed and diameter of the shaft is 40mm. The dischas a mass of 600Kg, and a radius of gyration of 0.4m.Taking modulus of rigidityfor the shaft material as 85GN/m2.l1=1m, and l2= 0.8m.

Figure 8:

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1. (a) State and prove lamis theorem of 7m long.

(b) A prismatic bar AB is hinged at A and supported at B as shown in Figure1.Neglecting friction, determine the reaction Rb produced at B owing to theweight Q of the bar.

Figure 1:

2. (a) A solid right circular cone of attitude h= 305 mm and reduces of base r =75 mm has its center of gravity C on its geometric axis at the distance h

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above the base. This cone rests on an inclined plane AB, which makes anangle of 300 with the horizontal and for which the coefficient of friction is = 0.5. A horizontal force P is applied to the Vertex O of the cone of thefigure2 as shown. Find the maximum and minimum values of P consistentwith equilibrium of the cone. If the weight W = 405 N.

Figure 2:

(b) What must be the angle between the plane faces of a steel wedge used forsplitting logs if there is to be no danger of the wedge slipping out after eachblow of the sledge?

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3. (a) Derive an expression for ratio of tensions of a belt in standard form

(b) The centre of two pulleys of diameter 120mm and 420mm are 300mm apart.They are connected by an open belt. If the coefficient of friction for the largerpulley be 0.28, what would be its value for the smaller pulleys simultaneously?

4. (a) From the first principles determine product of inertia for right angle triangleof base b and altitude h.

(b) State and prove transfer formula for product of inertia.

5. (a) Define mass moment of inertia and explain Transfer formula for mass momentsof inertia

(b) Derive the expression for the moment of inertia of a homogeneous sphere of

radius r and mass density w with reference to its diameter.

6. (a) A small grinding wheel is attached to the shaft of an electric motor which hasa rated speed of 3000r.p.m . When the power is turned on, the unit reachesits rated speed in 5secs and when the power is turned off, the unit comes torest in 60secs. Assuming the acceleration to be uniform, find the number ofrevolutions that the motor executes

i. in reaching its rated speed and

ii. to come to rest.

(b) A cord is wrapped around a wheel which is initially at rest as shown in (figure3)

force is applied to the cord and is gives an acceleration a=6t m/s2where t isin seconds. Determine

i. The angular velocities of the wheel

ii. The angular position of radial line OP as a function of time.

Figure 3:

7. (a) A homogeneous solid cylinder of weight 100 N whose axis is horizontal rotates

about 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 thediameter of cylinder as 100cm.

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(b) A block of mass 5Kg resting on a 300 inclined plane is released. The block aftertravelling 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 the Figure4}

Figure 4:

8. A vertical U-tube manometer contains a liquid of mass density as shown in the(figure5). A sudden increase of pressure on one column forces the level of the liquiddown, When the pressure is released, the liquid column start vibrating. Neglectingthe frictional damping, determine the period of vibration. Comment if the periodis affected by changing the liquid, diameter of the tube or length l of the liquidcolumn.

Figure 5:

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r050210804 Engineering Mechanics

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