07 A1 Ec03 Classical Mechanics

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Code No: 07A1EC03
Set No. 1
I B.Tech Supplimentary Examinations, Aug/Sep 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 homogeneous semi circuilar plate of weight ‘W’ and radius ‘a’ is supported by
three vertical strings so that the plate is horizantal as shown in gure 2. Determine

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the tensions in the three strings. [16]

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Figure 2
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3. (a) Find the centroid of the area shown in gure 3a
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Figure 3a
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Code No: 07A1EC03
Set No. 1
(b) Determine the co ordinates of the centroid of the quadrant PQ of the arc of a
circle if raduis ‘r’ show 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

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through its centroid. [16]

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Figure 4
5. Calculate the forces included in the members of the pin-jointed truss shown in
gure 5. Show the values on a neat diagram of the truss. [16]
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Code No: 07A1EC03
Set No. 1

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Figure 5

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6. (a) The motion of the particle is de ned by the relation x = 6t4 + 8t3 - 14t2-
10t + 16, where x and t are expressed in meters and records, respectively.

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Determine the position, the velocity, and the acceleration as the particle when
t = 3s.
(b) A car is tested for acceleration and braking. In the street - start acceleration

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test, the elapsed time is 8 seconds for a velo city increase from 8 km/h to 80 km
/h. In the braking test, the distance traveled is 40m during braking to a stop
from 80 km / hr. Assuming constant values of acceleration and deceleration,
determine
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i. the acceleration during the street - start test
ii. the deceleration during the braking test. [8+8]

7. (a) A 500kg communications satellite is in a circular geosynchronous orbit and
complete one revolution about the earth in 23 hrs and 58min at an attitude of
35800 km above the surface of the earth. The radius of the earth is 6510km.
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Determine the Kinetic energy of the satellite.
(b) Express the acceleration of gravity ‘g’ at an altitude ‘h’ above the surface of
the earth in terms of the acceleration of gravity go. at the surface the earth,
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the altitude h, and the radius R of the earth. [8+8]

8. A homogeneous wire is bent to form closed semi-circular shape of radius 320 mm.
Pinned at A and point B is pushed down 30 mm and released, determine the
magnitude of the acceleration of B, 10 secs later. As shown in gure 8. [16]
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Code No: 07A1EC03
Set No. 1

Figure 8

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Code No: 07A1EC03
Set No. 2
CLASSICAL MECHANICS

1. Determine the magnitude and direction of a single force which keeps the system in
equilibrium. The system of forces acting is shown in Figure 1. [16]

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Figure 1
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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]
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3. (a) Find the centroid of the plane area shown in gure 3a.
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Code No: 07A1EC03
Set No. 2

Figure 3a
(b) Determine the centre of gravity of a homogeneous hemisphare of radius ‘a’
[8+8]

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Figure 4
5. Calculate the forces induced in the member of a pin-jointed truss shown in gure
5. [16]
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Code No: 07A1EC03
Set No. 2

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Figure 5
6. (a) De ne curvilinear linear motion of a particle.

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(b) Show that the system of the e ective forces for a rigid slab in plane motion
reduces to a single vector, and express the distance from the mass center G

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of the slab to the line of action of this vector in terms of the centroidal radius
of gyration of the slab, the magnitude of the acceleration of G, and the
angular acceleration . [4+12]

7. (a) State the Principle of conservation of momentum og
(b) A golfer hits a 46gm ball with an initial velocity of 48 m/s at angle of 240 with
the horizontal. Determine
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i. the initial KE of the ball
ii. the KE of the ball when it reaches its maximum height. [4+12]

8. The block vibrates in SHM with a period of 5s when the two springs of constants
K1 & K2 are connected in series and 2s when they are in parallel. Determine the
ratio K1 / K2 at the two spring constants. [16]
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Code No: 07A1EC03
Set No. 3
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. Determine the resultant of the force system shown in gure 2 graphically.
[16]

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Figure 2
3. Find the centroid of the area shown gure 3. [16]
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Code No: 07A1EC03
Set No. 3

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Figure 3

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Figure 4
5. A pin jointed frame is supported at A and B and loaded as shown in gure 5. Find
the forces in all the members of the frame and state in each case, whether the force
is tensile or compressive. [16]
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Code No: 07A1EC03
Set No. 3

Figure 5
6. Bars AB and BE, each of weight 3.2 kg are welded together and are pin-jointed to

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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

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(a) the acceleration of the assembly
(b) the forces in the links.
[16]

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Figure 6
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]
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8. Derive an equation of motion for free vibration of mass m shown in gure 8 and
determine the natural frequency. [16]
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Code No: 07A1EC03
Set No. 3

Figure 8

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Code No: 07A1EC03
Set No. 4
CLASSICAL MECHANICS

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]

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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

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

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

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Figure 3
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Code No: 07A1EC03
Set No. 4

Figure 4
5. Tabulate the member forces for the structure shown in gure 5. [16]

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Figure 5

6. (a) De ne curvilinear linear motion of a particle.
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(b) Show that the system of the e ective forces for a rigid slab in plane motion
reduces to a single vector, and express the distance from the mass center G
of the slab to the line of action of this vector in terms of the centroidal radius
of gyration of the slab, the magnitude of the acceleration of G, and the
angular acceleration .
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[4+12]

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;
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Code No: 07A1EC03
Set No. 4
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
8. Derive an expression for the equation of motion of a simple pendulum employing
the principle of conservation of energy. Also nd the frequency and time period.
[16]
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07 A1 Ec03 Classical Mechanics

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