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Code No: 07A1EC03
Set No. 1
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.


Code No: 07A1EC03
Set No. 1

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


Code No: 07A1EC03
Set No. 1
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


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]


Code No: 07A1EC03
Set No. 2
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 as
shown 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]


Code No: 07A1EC03
Set No. 2

Figure 3
4. Determine the moment of inertia of the section shown in gure 4 about the cen-
troidal axes. [16]

Figure 4
5. Determine the forces in the truss shown in gure 5. [16]

Figure 5


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 gure 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, = 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]


Code No: 07A1EC03
Set No. 2

Figure 7b
by S = PL3 / 48EI. Where L = 5 M, E = 2 ×105 N/mm2, I = 1.73 × 10-5 m4.

with the beam. [16]


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. 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


Code No: 07A1EC03
Set No. 3

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


Code No: 07A1EC03
Set No. 3

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. Determine
i. 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]


Code No: 07A1EC03
Set No. 4
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]


Code No: 07A1EC03
Set No. 4

Figure 4
5. Determine the forces in the trusses shown in gure 5. [16]

Figure 5
6. (a) De ne Newton’s 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]


Code No: 07A1EC03
Set No. 4

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.

with the beam. [16]

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