Engineering MEchanics Part - B

8/10/2019 Engineering MEchanics Part - B

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1. The magnitude of the resulatant of two concurrent forces including an angle of 90 between them is root of 13 kN. When the included angle between the forces is 60, themagnitude of their resultant is root of 19kN. Find the magnitude of the two forces.

2. The lines of action of three forces are concurrent at the origin O passing through points A,B and C having coordinates A[-1,2,4] and B[3,0,-3] and C[2,-2,4]. Themagnitude of forces are F A =40 N, F b =10N and F C =30N. Find the magnitude anddirection of their resultant.

3. A table 600x600 mm is mounted on 3 legs shown in fig. there are 4 loads acting onthe table. Determine the reaction at the supports.

4. Find the reaction ar the supports A and B for the beam as shown in fig

5. Determine the moment of inertia of the area shown below with respect to centroidalaxes respectively parallel and perpendicular to the side AB

6. Determine the centroid of the plane area shown in fig


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7. Two stopping points of an electric tram car are 450mm apart. The maximum speed ofthe car is 20Km/hr and it covers the distance between the stops in 100 sec. If bothacceleration and retardation are uniform and the later is twice as great as former. Finethe value of each of them and also how for the car runs at maximum speed.

8. A 40 N mass is dragged alon the surface of the table by means of a cord which passesover a frtiction less pulley ar the edge of the table and is attached to a 12N mass. If thecoefficient of friction between 40N mass and the table is 0.15, determine theacceleration of the system and the tension in the cord.

9. Two weights each of 100 N are suspernded from a compound pulley as shown in fig.Find i) angular acceleration of the pulley ii) linear acceleration of the blocks A and Biii) Tension in the string. Take weight of the pulley as 300 N and its radius of gyration0.25m


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10. A force of 300N is required just to move a block up a plane inclined at 20 to the

horizontal, the force being applied parallel to the plane. IF the inclination of the planeis increased to 25, the force required just to move the block up is 340 N, the forceacting parallel to the plane. Determine the weight of the block and the coefficient offriction

L110811. Determine the tension in the cables AB, AC and AD if the crate shown in fig isweighing 9.07kg

12. Determine the reactions at supports A,B,C and D for the beam shown in fig


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13. Determine the resultant of the coplanar non-concurrent force system shown in fig.

calculate its magnitude and direction and locate its position with respect to the sidesAB and AD.

14. Find I xx , Iyy through centroid of the fig with uniform thickness of 3cm throughout

15. Derive an equation for the mass moment of inertia of cone16. A stone is projected with a speed of 30m/s at an angle of elevation of 50. Find its

velocity

i) After two seconds

ii) At the highest point of its path

iii) At a height of 6m

Find also the time interval between the two points at which the stone attains a speed of 23m/s


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17. In the oblique central impact shown in fig, the coefficient of restitution is 0.8. The flat

disks shown , slide on a smooth horizontal surface. Determine the final velocity ofeach disk directly after impact.

18. Determine whether the block shown in fig having a mass of 40kg is in equilibriumand find the magnitude and direction of the friction force. Take s = 0.40 and k =0.30

19. Determine the least value of P required to cause the motion impend the system shownin fig. Assume coefficient of friction on all contact surface as 0.2

C11020. A 30kg block is suspended by two springs having stiffness as shown. Determine the

unstretched length of each spring after the block is removed.


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25. Determine the magnitude and direction of single force P as shown which keeps the

system in equilibrium

26. Determine the moment of inertia of the section shown in the fig XX and YY axes

27. Prove that the mass moment of inertia of a cube of mass m about a centroidal axis parallel to a side is ma 2 /6, where a is the length of the side,

28. Determine the principal moment of inertia of the following section about point A


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29. Two men of mass 60kg and 90kg dive off from the end of a boat of mass 400kg so

that their relative velocity with respect to the boat is 8m/s. If the boat is initially at restdetermine its final velocity for the following conditionsi) If two men dive simultaneouslyii) The 60kg man dives first followed by 90kg maniii) The 90kg man dives first followed by 60kg man

30. Car A is accelerating in the direction of motion at the rate of 1.2m/s 2. Car B isrounding a curve at a constant speed of 54kmph at 150m radius. Determine thevelocity and acceleration that car B appears to have to an observer in the car A hasreaches a speed of 72kmph for the positions represented.

31. A reciprocating engine mechanism is shown in fig. The crank OA is of length 150mmand rotating at 600 rpm. The connecting rod AB is 700mm long. Determinei) Angular velocity of the connecting rodii) Velocity of piston Biii) Velocity of point C on the connecting rod at a distance of 200mm from A when is 45 0


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32. A uniform rod shown in the figure is acted upon by 30 N force which always acts perpendicular to the bar. If the bar has an initial clockwise angular velocity o=10rad/sec when = 0 0, determine the angular velocity at the instant = 90 0

33. In the following figure , the blocks A and B have masses 45 kg and 60kg respectively.The drum has a moment of inertia of 16kgm 2 about its axis of rotation. Radius ofinner pulley is 300mm whereas for outer pulley is 900mm. Determine the distancethrough which the blocks A falls, before it reaches a speed of 2m/s.

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34. Find the magnitude and direction of the force A so that the resultant of the system offorce shown in fig is horizontal and has a magnitude of 14.4kN.

35. Find the magnitude and the points of meeting of the line of action of th resultant withthe side kL for the system of forces shown in fig


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36. A uniform rod of length 2m is supported on a knife edge at its centre. A container is

suspended from the rod at 0.5m from one end and a block of weight 4kN is suspendedat 1.6m from the same end. Find the weight of the container so that the rod remainshorizontal.

37. A beam is loaded as shown in fig. Find the equivalent single force for the system offorces and the equivalent force-couple at P and at S. Use vector approach.

38. A frustum of a solid cone of height 250mm has a base diameter of 300mm and top

diameter of 150mm. It has an axial hole of diameter 60mm. Determine the position ofthe centre of gravity of the solid.39. Find the product of inertia of the section shown in fig. With respect to the x and y

axes. All dimensions are in mm. Also find the principal axes and the principalmoments of inertia of the section.

40. A stone is projected form a point P on a 30 inclive at an angle of 65 with the plane

with velocity of 10m/s. The stone hits the inclined at Q below P. Find the time offlight, difference in height between P and Q and also the range along the incline.


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41. A car P is running towards east at a uniform speed of 40kmph. When the car P justcrosses the intersection shown in fig, another car Q starts from rest in the north 50mfrom the intersectin and travels towards south with a uniform acceleration of 1.5m/s 2 .Find the position, velocity and acceleration of Q relative to P, three seconds after Pcrosses the intersection.

42. A force of 300N is required just to move a block up a plane inclined at 20 to thehorizontal, the force being applied parallel to the plane. IF the inclination of the planeis increased to 25, the force required just to move the block up is 340N, the forceacting parallel to the plane. Determine the weight of the block and the coefficient offriction

43. A small pulley of radius 100mm is connected to the shaft on an electric motor. A belt

connects this pulley with a bigger pulley of radius 300arm. Contact angle between the bigger pulley and the belt is 230. The maximum tension punishable in the belt is2000N. The coefficient of friction s between the belt and both the pulleys is 0.25.Find the torque exerted by the belt on the bigger pulley. Also check that s utilised inthe lax of bigger pulley at the time of slipping in the smaller pulley is less than 0.25

S404344. Calculate the moment of inertia about XX axis. (XX axis is the centroidal axis) for the

plane figure shown in fig. Assume AB as the reference axis to locate XX.


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45. Locate the centroid for the following sections as shown in fig

46. Determine the resultant of the force system acting in plane shown. Locate the distancefrom A where the resultant cuts the x axis.

47. A container weighing 450kN is suspended at P by using two cables PB and PAanchored as shown in fig. A horizontal force F keeps the Q container in the current

position. Find the magnitude of force F and forces in cable PA and PB.


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48. Two identical rollers each of weight 5kN rest in between an inclined wall and a

vertical wall as shown in fig. Determine the reactions at the points of contact P, Q andR. Assume the wall surface to be smooth.

49. A shaft is subjected to forces in x,y and z direction as shown in fig. Replace theseforces by a resultant R at origin O and a couple

50. A rod CD of 8kg length 0.8m is welded to a uniform dics of mass 5kg and radius0.16m. A spring of constant k=100N/mm is attached to a disc as shown in fig. when

the rod CD is horizontal the spring is unstretched. Assembly is released from restfrom the position shown. What is angular velocity of the disc and rod if it has rotatedthrough /2 angle ( use work energy principle)


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51. Two bodies of weights w 1 and w 2 respectively are connected by an inextensible string

passing over a frictionless pulley. The coefficient of friction between w 1 and plane is0.2 what is the velocity of the weights before w 1 reaches the top edge of plane.Calculate the velocity of weights after 2 secs if w 1 = 100N; w 2 = 80N ; = 30

0 refer

fig ( use impulse momentum principle)

52. A pulley assembly shown in fig weighs 50kg with a radius of gyration of 0.5m. The blocks A and B are connected through strings wrapped around the pulleys. Determinethe acceleration of each block and tension in each string.

53. Blocks A and B connected through a cord rest on inclined planes are shown in fig,What is the tension in the cord is the friction at block A reaches the maximum valus?State whelther the system is at rest or motion


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S482154. A spherical ball of weight 500N is suspended vertically by a string 500mm long. Find

the magnitude and direction of the least force that can hold the ball 100mm above the

lowest point. Find also the tension in the string. Ignore the size of the ball.55. Two forces P and Q are acting at the origin. The force P whose magnitude is 70 N isdirected towards (3,-6,2). The force Q is inclined at 45 0, 60 0 and 60 0 respectively to x,Y and Z axes. Determine the magnitude of Q so that the resultant of P and Q will bein XZ plane. Also determine the magnitude and direction cosines of the resultant.

56. A system of three forces 10N , 10N and 5N act at A, B and C respectively in thedirection of AB, BC and CA. If A,B and C form an equilateral triangle, find anequivalent force system consisting of three forces acting at the points A,B and C and

parallel to the opposite sides57. Find the magnitude and nature of forces in each member of he trusses given in fig

58. A ladder 3m long and weighing 200N is resting on the horizontal floor and leaningagainst a verticall wall, making 30 0 with the wall. The friction coefficient at theground and wall contact surfaces are 0.35 and 0.25 respectively. It has to support aweight of 100N at the top. To prevent slipping, a string is tied to the foot of the ladderand attached to the wall in the horizontal position. Determine the minimum tensionrequired in the string for this condition. Find also the minimum angle with the floor atwhich the above ladder with the weight at the top could be placed without slipping inthe absence of the string


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59. In fig calculate so that the motion of lower block can just occur down the plane.The weight A and B are 30 N and 90 N respectively. The coefficient of friction for allcontact surfaces is 1/3.

60. Find the moments of inertia of the section given in the fig about the horizontal andvertical centroidal axes. Also find the polar moment of inertial and minimum raidus ofgyration ( all dimension are in mm)

61. Derive the expression for mass moment of inertia of circular plate about any axis passing through centre and i) lying on the plate ii) perpendicular to plate and hencefine mass moment of inertia of a steel plate of radius 100mm and thickness 1mmabout each of the above axes. Take specific gravity of steel as 7.8.

62. A stone falls past a window 2 m high in 0.5 s. Find the height above the window fromwhere the stone is dropped.

63. A shot is fired with a velocity of 30m/s from a point 15m in front of a vertical wall

6m high. Find the angle of projection with the horizontal to enable the shot to justclear the wall. Explain the double answer.

64. Two identical balls of radius 150mm are moving with velocities of 5m/s and 8m/salong parallel lines 200mm apart. If the coefficient of restitution is 0.6, determine themagnitude and direction of their velocities after they collide.

C12365. Determine the magnitude T of the tension in the supporting cable and the magnitude

of the force on the pin at A for the jib crane shown in fig. The beam AB is standar 0.5

m I beam with a mass of 95 kg per meter of length.


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66. A string ABCD hangs from fixed points A and D carrying a mass of 50kg at B and a

mass of m kg at C. AB is inclined at 60 0 to the horizontal. BC is horizontal and CD isinclined at 45 0 to the horizontal. Determine the tension in AB,BC,CD and the mass m

67. Locate the centroid of the cross section of an angle 150 by 100 by 12mm shown in fig

68. Determine the moment of inertia of the area shown in fig i) about the vertical gravityaxis YY ii) about a horizontal axis a-a 50mm below the base


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69. A body having a mass of 46 kg rests on a horizontal plane shown in fig for which =0.4. a force P acts on the body an angle of 20 0 with the horizontal. Find its magnitudefor impending motion.

70. A flexible cable which supports the 100kg load is passed over a fixed circular drumshown in fig and subjected to a force P to maintain equilibrium. The coefficient ofstatic friction between the cable and the fixed drum is 0.3. i) for = 0, determine themaximum and minimum values which P may have in order not to raise or lower theload ii) For P 500 n, determine the minimum value which the angle may have

before the load begins to slip.

71. Two automobiles A and B traveling in the same direction in adjacent lanes arestopped at a traffic signal. As the signal turns green , automobile A accelerates at aconstant rate of 2m/s 2 . Two seconds later automobile B starts and accelerates at aconstant rate of 3.6 m/s 2 Determine i) when and where B will overtake A ii) Thespeed of each automobile at that time

72. The two blocks shown in fig are originally at rest. Neglecting the masses of the pulleys and the effect of friction in the pulleys and between the blocks and the inclinedeternine i) the acceleration of each block ii) the tension in the cable


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73. A driver of a light truck applies the brakes when travelling 40km/hr , it skids 3m

before stopping. How far will the truck skid if it is travelling 88km/hr when the brakes

are applied?74. Block A has a mass of 3 kg and is sliding on a rough horizontal surface with a

velocity 2m/s when it makes a direct collision with block B which has a mass of 2kgand is originally at rest. If the collision is perfectly elastic, determine the velocity ofeach block just after collision and the distance between the blocks when they stopsliding. The coefficient of kinetic friction between the blocks and the plane is 0.3

1151675. Determine the resultant of the concurrent force system shown in figure

76. Fig shows a 10kg lamp supported by two cables AB and AC find the tension in eachcable

77. Forces 32kN,24kN and 120kN are concurrent at origin and are respectively directedthrough the points whose coordinates are A(2,1,6), B(4,-2,5),C(-3,-2,1) and D(5,1,-2).Determine the magnitude of the resultant and the angles it makes with coordinateaxes.

78. Distinguish between Moment of a force about a point and Moment of a force about an

axis


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79. Find the resultant force and its location of the force system shown in figure. The (x,z)coordinates of the points of application of the forces are given in metres.

80. Two identical rollers, each of weight 500N are supported by an inclined plane makingan angle of 30 0 to the horizontal and vertical wall as shown in the figure. Sketch thefree body diagram of the two rollers. Assuming smooth surfaces, find the reactions atthe support points.

81. Derive the expressions for the location of the centroid of a triangular area shown infigure by direct integration.

82. Locate the centroid of the plane area shown in the figure below

83. An area in the form of L section is shown in figure. Find the moments of inertia I xx ,Iyy , Ixy about its centroidal axes. Also determine the principal moments of inertia.

84. A bullet is fired making an angle 30 0 to the horizontal from a hill which strikes thetarget which is 80 m lower than the horizontal passing through the firing point. Theinitial bullet velocity is 100m/s. find the maximum height above horizontal to whichthe bullet will rise, the velocity of bullet when it strikes the target, and the total timerequired for the bullet when it strikes the target.


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85. Block P of weight 100 N and block Q of weight 50 N are connected by a rope that

passes over a smooth pulley as shown in figure. Find the acceleration of the blocksand the tension in the rope, when the system is released from the rest. Neglect themass of the pulley.

86. A 2000kg automobile is driven down a 5 0 inclined plane at a speed of 100km/h whenthe brakes are applied causing a constant total breaking force (applied by the road onthe tires) of 7kN. Determine the distances travelled by the automobile as it comes to astop)

87. A ladder of weight 1000 N and length 4 m rests as shown in figure, if a 750 N weightis applied at a distance of 3m from the top of ladder, it is at the point of sliding.Determine the coefficient of friction between ladder and the floor.

88. A rope is wrapped three times around a rod as shown in figure. Determine the force Trequired on the free end of the rope, to support a load of W = 20kN. Take =0.30

89. Figure shows a stepped pulley. The smaller radius is 150mm and the bigger radius is200mm. Two loads P and Q are connected by inextensible taut cords. Load P moveswith an initial velocity of 0.2m/s and has a constant acceleration of 0.25m/s 2 bothdownwards. Determine the number of revolutions turned by the pulley in 4 secondsand velocity and the distance travelled by load Q after 4 seconds. Acceleration of

point B located on the rim of the pulley at t=0. Give both magnitude and direction.


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C136990. A spherical ball of weight 500N is suspended vertically by a string 500mm long. Find

the magnitude and direction of the least force that can hold the ball 100mm above thelowest point. Find also the tension in the string. Ignore the size of the ball.

91. A mass AB is supported by a hinge at A(0,0,0) and two guy wires BC and BD. Themast is subjected to a load of 100kN at B(4,3,5). IF the coordinates of C and D are(4,0,5) and (0,3,5) respectively, determine the forces in BA, BC and BD. The load

acts in the negative z direction.92. A system of three forces 10N, 10N and 5N act at A,B and C respectively in the

direction of Ab, BC and CA. IF A,B and C form an equilateral triangle. Find anequivalent force system consisting of three forces acting at the points A,B and C and

parallel to the opposite forces.93. For the system of forces shown in fig a, find P and Q such that the resultant of the

system passes through A and B

94. Find the moments of inertia of the section given in the fig about the horizontal andvertical centroidal axes. Also find the polar moment of inertia and minimum radius ofgyration( all dimensions are in mm).


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95. Derive the expression for mass moment of inertia of a cylinder of massM, length L

and radius R about the centroidal axis perpendicular to the axis and also about theaxis.

96. An effort of 150N is required to just move a body up a rough plane inclined at 12 0 with the horizontal, the force required was 172N. Find the weight of the body and thecoefficient of friction.

97. A weight of 10N resting on a n inclined plane that makes an angle of 30 withhorizontal is connected by a string passing over a frcitonless pulley at the upper endof the plane. On the free end of the string a weight of 20N is connected. If thecoefficient of friction between the plane and 10N weight 0.2, calculate the time taken

by the hanging weight to descend by 1m.98. What is meant by Translation in rigid body motion? Explain its two types.99. A wheel is attached to the shaft of an electric motor of rated speed of 2000rpm. When

the power is switched on the unit attains the rated speed in 10 seconds and when the power is switches off, the unit comes to rest in 100 seconds, assuming uniformlyaccelerated motion determine the number of revolutions the unit turns (1) to attain therated speed (2) to come to rest.

100. A cycle is traveling along a straight road with a velcotiy of 10m/s. Determinethe velocity of point situated at the middle of one of the spokes at angle of 30 0 withhorizontal in the front whell ( with respect to the centre of the wheel ). The radius ofthe cycle wheel is 400mm.

101. Distinguish with sketches between constrained motion of a rigid body with a point and that with a line.

Q2720102. Determine the tension in the cables AB, AC and AD if the crate shown in fig

is weighing 10kg.


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105. The 8m pipe AB shown in fig has a fixed end at A. A steel cable is stretched

from B to a point C on the vertical wall. If the tension in the cable is 1200 N,Determine the moment about A of the forces exerted by the cable at B.

106. Determine the smallest force P required to lift the 15kN load shown in fig. Thecoefficient of static frciton between A and C and between B and D is 0.3 and that

between A and B is 0.4.


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107. Assuming the coefficient of rolling resistance to be 3.0mm, determine the

horizontal force required to move a 2700kg automobile along a horizontal road at aconstant speed. The diameter of each tyre is 1150mm. Neglect all forms of frictionexcept rolling resistance.

108. A wheel 250mm in diameter carries a load of 10kN, If a horizontal force of100 N is necessary to move it over a level surface, determine the coefficient of rollingresistance.

109. For the section shown in fig determine the principal moments of inertia andlocate the principal planes.

110. Find the moments of inertia about the centroidal axes for the section shown infig.


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111. The 50kg block shownin fig rests on a horizontal plane for which thecoefficient of kinetic friction is 0.3. If the block is pulled by a 350N force as showndetermine the velocity of the block after it has moved 65m starting from the rest. Use

principal of work and energy.

112. A stone is thrown vertically upward from the top of a 30 m high building witha velocity of 15m/s. Taking the acceleration of stone as 9.81m/s 2 and taking that asconstant, determine the velocity v and elevation SY of the stone above the ground atany time t, the maximum altitude reached by the stone and the time when the stonestrikes the ground.

ETGE181113. The three concurrent forces in space F1, F2 and F3 acting at A shown in fig an

unknown force F, attached to the system makes the particle A in equilibrium. Find themagnitude and direction of the unknown force F

114. Two cables which have known tensions are attached to the top of the towerAB. A third cable AC is used as a guy wire as shown in figure. Determine the tensionin AC if the resultant of the forces exerted at A by the three cables acts verticallydownward.


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115. Find the resultant of the system shown in fig. Find the point of intersection of

its line of action with AC and CD. The 27nm couple applied at the C is removed andreplaced by a couple of unknown magnitude M. Determine the value of M if theresultant forces is pass through C.

116.

A truss of 8m span is loaded as shown in fig. Find the support reactions

117. Locate the centroid of the area shown below


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118. Find the moment of inertia of an unsymmetrical I section of top flange 60 x 20mm, bottom flange 100 x 20mm and web 20 x 60mm about its centroidal axes

119. The equation of motion of a particle is given acceleration a in terms of time tas below a = 3t 2+2t+4 in which acceleration is in m/s 2 and time t is in seconds. It isobserved that the velocity of the particle is 12m/s after 4 seconds and thedisplacement of the particle is 8m after 4 seconds. Determine the velocity after 8seconds and displacement after 2 seconds

120. The figure shows a body of weight 300N on a smooth horizontal plane isattached by a string to a 30N weight which hangs vertically. Find the acceleration ofthe system and the tension in the string.

121. Find the force P inclined at an angle of 32 0 to the inclined plane making anangle of 25 0 with the horizontal plane to slide a block weighing 125kN. Up theinclined plane and down the inclined plane when =0.5

122. In the engine system shown in figure the crank AB has a constant clockwiseangular velocity of 300rpm. For the crank position indicated find the angular velocityof the connecting rod and velocity of the piston.

V4594123. State and prove Varignons theorem. 124. The resultant of two forces f 1 and F 2 acting at a point is R. If F 2 is doubled R is

also doubled and if the direction of F 2 is changed R is again doubled. Prove thatF1:F2:R= 2: 3: 2

125. Forces 32kN, 24kN, 24kN and 120kN are concurrent at origin and arerespectively directed through the points whose coordinates are A(2,1,6), B(4,-2,-5),C(-3,-2,1) and D(5,1,-2). Determine the resultant.

126. Find the resultant of the force system shown in fig and its position from A. (force in kN and distance in m)


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127. For the force system shown in fig determine the direction and magnitude ofthe resultant from 0

128. Find the reaction at supports for the beam shown in fig.

129. The weight of the plate is 350N and is supported by three wires as shown infig, Determine the tension in the wires

130. Reduce the force system shown in fig into force couple system at 0

131.

Calculate the moment of inertia of the section shown in fig about its centroidalxx and yy axis.

132. State and prove perpendicular axis theorem133. Find the mass moment of inertia of a thin circular disc ( I xx,Iyy,Izz)134. A block of wt 1290N rests on a horizontal surface and supports another block

of weight 570 N on top of it as shown in fig. Find the force P applied to the lower block that will be necessary to cause slipping to impend. Coefficient of friction


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139. A force of magnitude 10kN starts from a point A(2,1,-3) and passes thorugh

the point B (6,3,1). Represent the force in terms of unit vectors i,j,k. Also find thecomponents of the force along the three directions and the angle made by the forcewith these directions.

140. Two cylinders of diameter 50mm and 25mm weighing 150N and 50Nrespectively are placed as shown in fig. Assuming all contact surfaces to be smoothand find the reactions at A, B, C and D.

141. For a hanging weight of 300N at A as shown in fig. find the forces in themembers AB, AC and AD of the wall bracket.

142. For the plane section shown in fig determine the moment of inertia about itshorizontal and vertical centroidal axes.


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143. From first principles derive the expressions for the mass moment of inertia of

a thin circular plate about its polar axis and a sphere.

144.

A body of weight 100 N is placed on a 300

inclined plane. Determine theminimum force to be applied on the block and parallel to the plane to just move the body up the plane and just prevent the body from sliding down the inclined plane.Take the coefficient of friction as 0.2.

145. A body of mass 5kg moving with an unknown speed hits centrally a stationary body B of mass 10kg. The speed of the body B after impact is 8m/s, if the coefficientof restitution is 0.6, find the velocity of A before and after impact. Also find thekinetic energy lost during impact.

146. The end A of the rod AB 1.8m long shown in fig moves with a velocity of6m/s towards left. When =25 0, determine the angular velocity of the rod and the

velocity of the end B.

147. What is the angular acceleration of the pulley shown in fig if its mass momentof inertia is 20kgm 2?


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H252148. Determine the magnitude direction and position of a single force P which

keeps in equilibrium the system of forces acting ath the corners of a rectangular blockas shown in the fig. The position of force P may be stated by reference to axes withorigin O and coinciding with the edges of the block

149. Two smooth circular cylinders each of weight 1000N and radius 15cm areconnected at their centres by a suing AR of length 40cm and rest upon a horizontal

plane. A third cylinder of weight 2000N and of same radius is above the these twocylinders as shown in the fig. Determine the force in the string AR and the pressure

produced on the floor at the points of contact D and E


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150. Determine the moment of inertia of the shaded area shown in the following fig

151. Prove that the mass moment of inertia of a right circular cone of base radiusR, height H and mass M about its axis is 3/10 MR 2.

152. A ladder 5m long and 250N weighs is placed against a vertical wall in a position where its inclination to the vertical is 30 0. A man weighing 800 N climbs theladder. At what position will he induce slipping? The coefficient of friction betweenthe wall and floor with the ladder is 0.2.

153. A leather belt is required to transmit 9kW from a pulley 120cm in diameterrunning at 200rpm. The angle embraced is 165 0 and the coefficient of friction between

the leather belt and pulley is 0.3. The safe working stress for the leather belt is140N/cm 2 thickness of the belt is 10mm and the density of the leather is 1gm/cm 3.Determine the width of the belt taking the centrifugal tension into account.

154. The angle of rotation of a body is given by the equation = 2r 3-5t 2+8t+6. Here is expressed in radians and t in seconds. Determine angular velocity and angular

acceleration when t is 0 and 4 seconds.155. A train of weight 1960 kN starts from rest and attains a speed of 120km/hr in 5

minutes. If the friction resistance of the track is 10N per kN of the trains weight,determine the average pull required. Take gas 9.8m/s 2.

156. Three locations A, B and C at a distance of 100m each are located along a

straight road. A car starting from rest and with uniform acceleration passes thelocation A and takes 10 seconds to reach B and further 8 seconds to reach location C.


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Calculate magnitude of acceleration of car, velocity of car at A, velocity of car at Band distance of location A from the starting point.

157. A body of weight 196.2 N slides up a 30 0 inclined plane under the action of anapplied force 300N acting parallel to the inclined plane. The coefficient of friction is0.2. If the body moves from rest, determine acceleration of the body ,the distancetravelled by the body in 4 seconds, velocity of the body after 4 seconds, kineticenergy of the body after 4 seconds, work done in the body in 4 seconds, momentum ofthe body after 4 seconds and impulse applied in 4 seconds.

158. Two bodies of mass m 1 and m 2 and of initial velocities u 1 and u 2 are having adirect impact. Prove that the loss of kinetic energy due to impact in terms of masses of

two bodies and their velocities before impact is( )

( )[1-e 2].

H313159. The resultant of force system shown in fig is 520N alon the negative direction

of y axis. Determine P and .

160. Three concurrent forces in space F 1, F 2,F3 are acting at A as shown in fig. Anunknown force F attached to the system makes the particle A in equilibrium. Find the

magnitude and direction of the unknown force F .


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161. A system of parallel forces are acting on a rigid bar as shown in fig. reduce thesystem to a single force, a single force and couple at A and a single force and coupleat B.

162. The coordinates of points A and B in meters are A[1,2,3] and B[4,3,2]. Aforce of magnitude 10kN passes through these points and is directed from A towardsB. Find the moment of these force about origin, about c[1,1,1], about x axis and aboutan axis passing through points D[2.5,1.5,4] and E[4,3,5].

163. Find the centroid of the plane area shown in the fig.

164. Find the product of inertia and principal moment of inertia of the sectionshown below.


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165. A ball of mass 0.5kg moving with a velocity of 1m/s impinges on a ball ofmass 1kg, moving with a velocity of 0.75m/s. At the time of impact, the velocities ofthe balls are parallel and inclined at 60 0 to the line joining centres. Determine thevelocities and directions of the balls after impact. Take e = 0.6.

166. Two cars are travelling towards each other on a lane road at 16m/s and 12m/srespectively when 120m apart, both drivers realize to apply brakes. They succeed instopping simultaneously and just short of collision. Assuming constant deceleration ofeach car determine time required for the cars to stop, deceleration of each car anddistance travelled by each car.

167. A ladder 4m long leans against a smooth vertical wall at an angle 60 0 with thehorizontal. The weight of the ladder is 700N. When a person weighing 600 N standson a rung 1.2m from the bottom of the ladder, the ladder is just about to slide.Calculate the coefficient of friction between the ladder and the floor.

168. A 5kg uniform disc is attached upon a couple with constant magnitude of10Nm. Find the work done when the disc has completed 2 revolutions starting fromrest. Find the angular velocity of disc. Take the radius of the disc as 0.4m.

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Engineering MEchanics Part - B