Classical-mechanics Jntu Model com

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Set No. 1Code No: 07A1EC03

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. If

the 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 gure 2 graphically.

[16]

Figure 2

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


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Figure 3a

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

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

Figure 3b

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

through its centroid. [16]

Figure 4


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gure 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

gure 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 in bearings for which

are coe cient of friction is . Through what angle will it rotate after the

driving force is removed? [4+12]

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


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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]


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CLASSICAL MECHANICS






1. Determine and locate the resultant R of the forces and one couple acting on the

beam as shown in gure 1. [16]

Figure 1

2. In a shop-unloading operation, 1000 kg automobile is supported by a cable asshown in gure 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 gure 3. [16]


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Figure 3

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

troidal axes. [16]

Figure 45. Determine the forces in the truss shown in gure 5. [16]

Fi ure 5


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

positions and speeds shown in gure 6. The car A has a constant acceleration of0.8m/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, = 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 ro d as shown in

gure 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]


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Figure 7b


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


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


with the beam. [16]


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CLASSICAL MECHANICS






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 pro jection of F on x-y plane, and

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

Figure 2

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


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Figure 3a

(b) Determine the co ordinates of the centroid of the quadrant PQ of the are of a

circle of raduis r showin gure 3b. [8+8]

Figure 3b



Figure 4

5. Tabulate the member forces for the structure shown in ure 5. 16


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Figure 5

6. (a) The velo city of a particle is V = 0 1 - pt T .

The particle starts from the origin with an initial velocity 0, determine

i. its position and its acceleration at t = 4T,

ii. its average velo city during the interval t = 0 to t = T.

(b) The motion of a rotor is de ned by de relation = 8t3 - 6 (t - 2)2, where

and t are expressed in radians and seconds, respectively. Determinei. When the angular acceleration is zero

ii. The angular co ordinate and angular velocity at that time. [8+8]

7. (a) What is the energy of motion for a rigid body rotating about a xed axis?

(b) A 70kg sprinter starts from rest and accelerate uniformly for 5.8s over a dis-

tance of 34.5m. Neglecting air resistance, determine the average power devel-

oped by the sprinter. [6+10]

8. (a) The amplitude and maximum velocity of a particle is 40 cm and 2m/sec. A

particle moves in SHM. Determine the maximum acceleration of the particle

and the period of its motion.

(b) The particle which moves in SHM has maximum velocity of 100 mm/sec and

maximum acceleration of 2 m / sec2. Determine the amplitude and frequency

of the motion. [8+8]


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CLASSICAL MECHANICS






1. Replace the given system of forces acting on a bo dy as shown in gure 1 by a single

force and couple acting at the point A. [16]

Figure 1

2. Five strings are tied at a point and are pulled in all directions, equally spaced, from

one another. If the magnitude of the pulls on three consecutive strings is 70 N, 40

N and 55 N respectively, nd graphically the magnitude of the pulls on two other

strings, if the system is in equilibrium. [16]

3. Find the centroid of the area shown in gure 3. [16]


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Figure 4

5. Determine the forces in the trusses shown in gure 5. [16]

Figure 5

6. (a) De ne Newtons law of gravitation.

(b) A 2 kg revolves in a horizontal circle as shown in gure 6b at a constant speed

of 1.8 m /s. L = 600 mm determine

i. The angle that the cord forms with the vertical

ii. The tension in the cord. [4+12]


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Figure 6b

7. A solid cylinder of weight W and radius r rolls, down an inclined plane which

makes angle with the horizontal axis. Determine the minimum coe cient of

friction and the acceleration of the mass center for rolling, without slipping. [16]


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


(a) equivalent spring constant of the beam

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


with the beam. [16]

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