ii b. tech i semester, supplementary examinations, may ... · code no: r21031 r10 set - 1 ii b....

Code No: R21031 R10 SET - 1

II B. Tech I Semester, Supplementary Examinations, May – 2013 ENGINEERING MECHANICS (Com to ME, AE, AME, MM) Time: 3 hours Max. Marks: 75

Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~~ 1. a) Determine the tension in the cables AB and AC necessary to support the 50 kg cylinder

shown in Fig. 1. B y

8 m 700 N F

4 m

2 m 600 N

A x

800

z

Fig. 2

b) Determine the magnitude and direction of force F shown in Fig. 2 so that the particle A is

in equilibrium. 2. a) The link shown in Fig. 3 is pin jointed at A and rests against a smooth support at B.

Compute the horizontal and vertical components of the reaction at A.

B 0.9 m

30o A 100 N-m

1.2 m 0.6 m

Fig. 3 50 N

b) A uniform concrete slab is supported horizontally by means of three parallel cables as shown in Fig. 4. Determine the tension in each cable.

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Code No: R21031 R10 SET - 1 3. a) Locate the centroid for the rod bent in to the shape of a parabolic arc as shown in Fig. 5.

y 1 m

1 m

x O Fig. 5

b) Locate the center of mass of the composite assembly shown in Fig. 6. The conical frustum has a density of 1000 kg/m3 and hemisphere has a density of 3000 kg/m3. There is a 25 mm radius cylindrical hole in the center.

4. a) Derive the transfer formula for product of inertia.

b) Determine the moment of inertia of the shaded area shown in Fig. 7 about the x-axis.

500 N

C

B

4m

A D 800 N

3 m 3 m

Fig. 8 5. a) What are the assumptions made in the analysis of trusses?

b) Determine the force in each member of the truss shown in Fig. 8.

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Code No: R21031 R10 SET - 1 6. a) Packages, each having a mass of 3 kg, are delivered from a conveyor to a smooth circular

ramp with a velocity of 1.5 m/s as shown in Fig. 9. If the effective radius of the ramp is 0.6 m, determine the angle at which each package begins to leave the surface.

V= 1.5 m/s

r θ

Fig. 9

b) A man weighs 800 N and jumps onto a boat, which is originally at rest. If he has a horizontal component of velocity of 1.2 m/s just before he enters the boat, determine the weight of the boat if it has a velocity of 0.6 m/s once the man enters it.

7. a) A roller moves within two conveyor belts, of which top belt moves with at the speed of 10

m/s and bottom one moves at 8 m/s. Determine the linear and angular velocity of the roller if the diameter of the roller is 60 cm. Fig. 10.

A C

ω

300 300

D

Fig. 10 B Fig. 11

b) The beam BD shown in Fig. 11 is supported by two rods having negligible mass. Determine the force created in each rod at the instant when θ=30o and ω= 5 rad/s. The lengths AB=CD=0.6 m and BD=1 m and center of gravity of the beam is at its mid length.

8. a) State the laws of coulomb friction.

b) Define (i) angle of static friction (ii) angle of kinetic friction (iii) cone of friction c) Determine the smallest force P required to move the block B if (i) block A is restrained by

the cable CD as shown in Fig. 12 (ii) cable CD is removed. Take coefficients of static and kinetic friction, respectively, as 0.3 and 0.25 at all surfaces of contact.

P

C D 150 kg

A

225 kg

B

Fig. 12

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II B. Tech I Sem ester, Supplementary Examinations, May – 2013 ENGINEERING MECHANICS (Com to ME, AE, AME, MM) Time: 3 hours Max. Marks: 75

Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~~ 1. a) Determine the tension in the cables AB and AC necessary to support the 60 kg cylinder

shown in Fig. 1. y F=-20 i - 100 j + 60 k

B

600 mm

x

A 300 mm

z 800 mm

Fig. 2 b) Determine the moment of the force F shown in Fig. 2 about the axis AB.

2. If the cable CED shown in Fig. 3 can sustain a maximum tension of 60 0 N before it fails,

determine the greatest vertical force that can be applied to the boom. Also determine the reactions at the ball and soc ket joint A.

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Code No: R21031 R10 SET - 2 3. a) Locate the centroid for the shaded area shown in Fig. 5.

b) Determine the location x of the centroid of the solid made from a hemissphere, cylinder and cone as shown in Fig. 6.

4. a) Determine the product of inertia of the triangular area with respect to the x-y axes (Fig.7).

G r

R

. O

Fig. 8

b) If the plate shown in Fig. 8 has a density of 8000 kg/m3 and a thickness of 12 mm, determine the mass mom ent of inertia about an axis directed perpendic ular to its plane and passing through point O. Take r = 120 mm and R=240 mm.

5. a) State and explain the neceessary conditions for determinacy of trusses.

b) Using the method of section, determine the forces induced in the members MD, DJ and DE of the K-truss shown in F ig. 9. C D E

B F

M 5 m N

A 2.5 m

G

5 m L 5 m K 5 m J5 m I5 m H 5 m

90 kN 90 kN 90 kN 90 kN 90 kN

Fig. 9

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Code No: R21031 R10 SET - 2 6. a) A ball B of mass 12 Kg is attached to the end of a rod whose mass is negligible. If the rod is

subjected to a torque of T= 3t2 + 5t + 2, where t is in seconds, determine the speed of the ball when t= 2 sec. The ball has a speed of 2 m/s when t=0. The length of the rod is 1.5 m. Fig. 10.

M 1 m

90o

1.5 m

B

V

2 m

Fig. 10 Fig. 11

b) A block of weight 60 N is released from rest at A and slides down the smooth circular

surface AB. it then continues to slide along the horizontal rough surface until it strikes the spring. Determine how far it compresses the spring before stopping. The stiffness of the spring is 100 N/m. Fig. 11.

7. a) The disc B shown in Fig. 12 moves along the radial slot with a constant velocity of 3 m/s

measured relative to the slot in the disc. The disc has a constant angular velocity of 4 rad/s. Determine the absolute velocity and acceleration of B at the instant shown in the Figure.

O. G

50 N

150 mm 30o

Fig. 12

Fig. 13

b) A solid circular cylinder of mass 20Kg shown in Fig. 13 is subjected to a force of 60 N as

shown. Determine the acceleration of the mass cylinder and the corresponding angular acceleration. The static and kinetic coefficients of friction between the cylinder and the horizontal surface are 0.25 and 0.2 respectively.

8. a) A screw jack has a pitch of 12 mm with a mean diameter of thread equal to 45 mm. A lever

of 700 mm long is used to raise a load of 1800 Kg. If the coefficient of friction is 0.1, what force is necessary when applied normal to the lever at its free end?

b) Two blocks A and B, each having a mass of 6 Kg are connected by the linkage as shown in Fig. 13. If the coefficient of static friction at the contact surfaces is 0.5, determine the largest vertical force P that may be applied to pin C of the linkage without causing the blocks to move. Neglect the weight of the links.

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Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~~ 1. a) Replace the forces shown in Fig. 1 by a force-couple system at O.

b) A pipe AB of length 8 m has one end fixed at A as shown in Fig. 2. A steel cable is stretched from B to a point C on the vertical wall. If the tension in the cable is 1000 N, determine the moment about A of the force exerted by the cable at B.

2. If the rod shown in Fig. 3 is subjected to the 400 N force, determine the reactions at the ball

and socket joint A and the tension in the cables BD and BE.

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Code No: R21031 R10 SET - 3 3. a) Locate the centroid of the area between the cubic curve and the x-axis shown in Fig. 5.

b) Determine the volume of the circular seal ring generated by revolving the shaded area (Fig. 6) about the y-axis through an angle of 360 degrees.

4. a) Determine the product of inertia of the triangle shown in Fig. 7 with respect to the x-y axes.

b) Determine the moment of inertia of the homogeneous pyramid of mass m with respect to the z-axis that is passing through the centroid of its base and its apex. The density of the material is ρ. Fig. 8.

5. a) Define

i) Determinate truss ii) Stable truss b) Using the method of sections, determine the axial forces in the members CK, DE and IJ of

the truss shown in Fig. 9. D E

C

B 7.5 m

F

5 m

A G

5 m L 5 m K 5 m J5 m

I5 m

H 5 m

120 kN120 kN 120 kN 120 kN 120 kN

Fig. 9

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Code No: R21031 R10 SET - 3 6. a) A barge B weighs 180 kN and supports an automobile of weight 15 kN. If the barge is not

tied to the pier and the automobile is driven one end to the other side of the barge for unloading, determine how far the barge moves away from the pier. Neglect the resistance of the water.

b) A ball of mass 420 grams is sliding down a horizontal smooth cylinder of radius 12 cm, from top point P. determine the reaction exerted by the cylinder on the ball at the angular position θ=25o as shown in Fig. 10.

P θ

Fig. 10 7. a) State the principle of work and energy for a rigid body.

b) State the principle of angular impulse and momentum for a particle. c) A uniform slender bar of mass 60 Kg and length 1.8 m moves with its ends in contact with

smooth surfaces as shown in Fig. 12. Determine the angular acceleration and the normal reactions at A and B at the instant shown. The rod is initially at rest.

B

30o

30o A

Fig. 12 8. a) What is meant by limiting friction? When do you say screw is self locking?

b) The concrete pipe at A rests on top of B and C. If the coefficient of static friction between the pipes is µs and at the ground is µsg, determine their smallest values so that the pipes will not slip. Each pipe has a radius r and weight W and the angle between the centers as indicated in Fig. 13 is θ.

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Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~~ 1. a) A beam AB is subjected to the system of forces shown in Fig. 1. If the equivalent force-

couple system at A is a force of 12 kN acting vertically downwards and a clockwise couple moment of 50 kN-m, determine the value of F, angle θ and the point of application of the force F from A.

b) Determine the magnitude of the moments of the force F =20 i - 40 j + 30 k about the base line AC of the tripod shown in Fig. 2.

2. a) The lever ABC is pin jointed at A and connected to a short link BD as shown in Fig. 3. If

the weight of the members is negligible, determine the force of the pin on the lever at A.

b) Determine the tension in the cables BD and CD as shown in Fig. 4 and the components of the reaction at the ball and socket joint at A.

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Code No: R21031 R10 SET - 4 3. a) Locate the centroid z of the volume segment shown in Fig. 5.

b) State and prove the theorems of pappus. 4. a) Define

i) Product of inertia ii) Mass moment of inertia iii) Radius of gyration b) Determine the moment of inertia of the ellipsoid with respect to the x-axis and express the result in terms of

the mass m of the ellipsoid. Take density of the material as ρ. (Fig. 7) y

b x

Fig. 7 a

5. a) Explain the method of joints for the analysis of trusses. b) Using the method of section, determine the forces in the members CF and DF of the roof

truss shown in Fig. 9. 1 kN

C 1 kN

3 kN

1 kN

B D

A E

2 m

F

2 m 2 m 2 m

Fig. 9

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Code No: R21031 R10 SET - 4 6. a) Two equal-length springs having a stiffness of KA= 350 N/m and KB=250 N/m are nested

together to form a shock absorber. If a 3 Kg block is dropped form an at-rest position 0.8 m above the top of the springs, determine their deformation when the block momentarily stops. (Refer Fig. 10)

0.8 0.6 m V=2 m/s

A

B

Fig. 10 Fig. 11

b) A disc of 2 Kg rests on smooth horizontal surface and is attached to an elastic cord that has a stiffness of 30 kN/m and is initially unstretched. If the disc is given a velocity of 2 m/s perpendicular to the cord, determine the rate at which the cord is being stretched and the speed of the disc at the instant the chord is stretched 0.15 m. The length of the chord is 0.6 m. (Fig. 11)

7. A rod of mass 40 Kg is pin jointed at A and C as shown in Fig. 12. Its angular velocity at the instant shown

in the Fig. 12 is ω1. The spring constant is 800 N/m and the spring has an undeformed length of 0.6 m. Determine the rod’s angular velocity at the instant when the angle made by the rod with the vertical is 90o. The length of the rod AB is 1.2 m.

B 25o

C

15 kN B D

15o

P A

30o

C

A Fig. 13

Fig. 12

8. a) A ladder of length 9 m and weighing 17 N is placed against a smooth vertical wall with its

lower end 3 m from the wall. The coefficient of friction between the ladder and floor is 0.28. Examine whether the ladder will remain in equilibrium or not.

b) Determine the force P needed to lift the load of 15 kN as shown in Fig. 13. The coefficient of static friction between A and C and B and D is 0.3 and that between A and B is 0.4.

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ii b. tech i semester, supplementary examinations, may ... · code no: r21031 r10 set - 1 ii b....

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