I B.Tech Regular Examinations, May/Jun 2008

CLASSICAL MECHANICS

( Common to Mechanical Engineering, Chemical Engineering, Mechatronics,

Production Engineering and Automobile Engineering)

Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks

⋆ ⋆ ⋆ ⋆ ⋆

1. (a) The resultant of the two forces when they act at an angle of 650 is 20 N. Ifthe same forces are acting at right angles their resultant is 16.5 N. Determine

the magnitude of the two forces.

(b) A force of 100N makes angles of 300, 600 and 1000 with x,y, z axes respectively.

Find the components of the force along the x,y and z axes. [8+8]

2. Determine the resultant of the force system as shown in figure 2 graphically.

[16]

Figure 2

3. (a) Find the centroid of the inverted T section shown in Figure 3a.

1 of 4

Code No: 07A1EC03 Set No. 1

Figure 3a

(b) Determine the centre of gravity of the composite body consisting of a cylinder

of radius ‘r’ attached to a hemisphere of raduis ‘r’ as shown in figure 3b.[8+8]

Figure 3b

4. Find the moment of inertia of the plane area shown in figure 4 about X and Y axes

through its centroid. [16]

Figure 4

5. Determine the forces induced in the members of the pin-jointed truss shown in

2 of 4

Code No: 07A1EC03 Set No. 1

figure 5. Show the values on a neat diagram of the truss. Mention clearly the

nature of the forces (tension or compression) in each memeber. [16]

Figure 5

6. Bars AB and BE, each of weight 3.2 kg are welded together and are pin-jointed to

two links AC and BD. The assembly is released from rest in the position shown in

figure 6 and Neglecting the masses of the links determine

(a) the acceleration of the assembly

(b) the forces in the links. [16]

Figure 6

7. (a) What is the advantage of work-energy theorem?

(b) A shaft of radius r rotates with constant angular speed ω in bearings for which

are coefficient of friction is µ. Through what angle φ will it rotate after the

driving force is removed? [4+12]

8. The central deflection of a simply supported beam with a central point load is given

by S = PL3 / 48EI. Where L = 5 M, E = 2 ×105 N/mm2, I = 1.73 × 10−5 m4.

3 of 4

Code No: 07A1EC03 Set No. 1

The beam is of uniform cross section with a static load “P”. Determine

(a) equivalent spring constant of the beam

(b) the frequency of vibration of a 60kg block attached to the centre of the beam.

Neglect the mass of the beam and assume that the load remaining in contact

with the beam. [16]

⋆ ⋆ ⋆ ⋆ ⋆

I B.Tech Regular Examinations, May/Jun 2008

CLASSICAL MECHANICS

( Common to Mechanical Engineering, Chemical Engineering, Mechatronics,

Production Engineering and Automobile Engineering)

Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks

⋆ ⋆ ⋆ ⋆ ⋆

1. Determine and locate the resultant R of the forces and one couple acting on thebeam as shown in figure 1. [16]

Figure 1

2. In a shop-unloading operation, 1000 kg automobile is supported by a cable as

shown in figure 2. A rope is tied to the cable at A and pulled in order to centre the

automobile over its intended position. The angle between the cable AB and the

vertical is 40, while the angle between the rope and the horizontal is 300. What is

the tension in the rope AC? [16]

Figure 2

3. Determine the centroid of the area shown in figure 3. [16]

1 of 4

Code No: 07A1EC03 Set No. 2

Figure 3

4. Determine the moment of inertia of the section shown in figure 4 about the cen-

troidal axes. [16]

Figure 4

5. Determine the forces in the truss shown in figure 5. [16]

Figure 5

2 of 4

Code No: 07A1EC03 Set No. 2

6. Two cars A and B are traveling in adjacent highway lakes and at t = 0 have the

positions and speeds shown in figure 6. The car A has a constant acceleration of

0.8m/sec2 and that B has a constant deceleration of 0.6 m/s2 determine

(a) when and where A will overtake B

(b) the speed of each car at that time. [16]

Figure 6

7. (a) A body of mass 18 kg slides up an incline of 300 under the action of an applied

force 300N along the incline and in the presence of friction, µ = 0.2. If the

body moves from rest determine, after a period of 6 secs;

i. Acceleration of the body

ii. Distance traveled by the body

iii. Kinetic energy of the body

iv. Work done on the body.

(b) A 2kg collar can slide without friction along a horizontal rod as shown in

figure 7b and is released from rest at A. The undeformed lengths of springs

BA & CA are 30cm and 25cm respectively and the constant of each spring is

490KN/m. Determine the velocity of the collar when it has moved 3 cm to

the right. [8+8]

3 of 4

Code No: 07A1EC03 Set No. 2

Figure 7b

8. The central deflection of a simply supported beam with a central point load is given

by S = PL3 / 48EI. Where L = 5 M, E = 2 ×105 N/mm2, I = 1.73 × 10−5 m4.

The beam is of uniform cross section with a static load “P”. Determine

(a) equivalent spring constant of the beam

(b) the frequency of vibration of a 60kg block attached to the centre of the beam.

Neglect the mass of the beam and assume that the load remaining in contact

with the beam. [16]

I B.Tech Regular Examinations, May/Jun 2008

CLASSICAL MECHANICS

( Common to Mechanical Engineering, Chemical Engineering, Mechatronics,

Production Engineering and Automobile Engineering)

Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks

⋆ ⋆ ⋆ ⋆ ⋆

1. Three forces of magnitude 150 N, 300 N and 500 N are acting at the origin O(0,0,0)and are directed from the points A(3,2,4), B(3,-2,-4) and C(-1,-3,-4) respectively to

the origin. Determine the magnitude of the resultant. [16]

2. A force F with a magnitude of 150 N is applied at the origin O of the axes x, y and

z as shown in Figure 2. The line of action of F passes through a point A whose

co-ordinates are 2 m, 4 m and 6 m. Determine

(a) the x, y, and z scalar components of F

(b) the projection of F on x-y plane, and

(c) the projection of F along the line OB. [16]

Figure 2

3. (a) Find the centroid of the area shown in figure 3a

1 of 3

Code No: 07A1EC03 Set No. 3

Figure 3a

(b) Determine the coordinates of the centroid of the quadrant PQ of the are of a

circle of raduis ‘r’ showin figure 3b. [8+8]

Figure 3b

4. Find the moment of inertia of the plane area shown in figure 4 about X and Y axes

through its centroid. [16]

Figure 4

5. Tabulate the member forces for the structure shown in figure 5. [16]

2 of 3

Code No: 07A1EC03 Set No. 3

Figure 5

6. (a) The velocity of a particle is V = ν0 1 − Sin

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