R05010105 A P P L I E D M E C H A N I C S

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Code No: R05010105
Set No. 1
I B.Tech Supplimentary Examinations, Aug/Sep 2008
APPLIED MECHANICS
(Civil Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks

1. Calculate the magnitude of the force supported by the pin at B for the bell crank
loaded and supported as shown in Figure 1. [16]

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Figure 1

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2. (a) Explain the types of friction with examples.
(b) Two equal bodies A and B of weight ‘W’ each are placed on a rough inclined
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plane. The bodies are connected by a light string. If A = 1/2 and B = 1/3,
show that the bodies will be both on the point of motion when the plane is
inclined at tan-1 (5/12). [6+10]
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3. (a) Distinguish between open and crossed belt drives.
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(b) A belt weighing 1000 3 has a maximum permissible stress of 2 5 2
Determine the maximum power that can be transmitted by a belt of 200 ×
12 if the ratio of the tight side to slack side tension is 2. [6+10]
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4. (a) Di erentiate between ‘polar moment of inertia’ and ‘product of inertia’
(b) Find the moment of inertia and radius of gyration about the horizontal cen-
troidal axis. shown in Figure 4b. [6+10]
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Code No: R05010105
Set No. 1

Figure 4b
5. A rectangular parallelopiped has the following dimensions.
Length along x-axis = ‘ ’
Height along y-axis = ‘a’

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Breadth along z-axis = ‘b’
Density of the material is ‘w’
Determine the mass moment of inertia of the parallelopiped about the centroidal
axes.
[16]

6. Cycle is travelling along a straight road with a velocity of 10m/s. Determine the

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velocity of point A on the front wheel as shown in gure6 Radius of cycle wheel =
0.4m and distance of A from C=0.2m. [16]

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Figure 6
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7. (a) A homogeneous sphere of radius of a=100 mm and weight W=100 N can
rotate freely about a diameter. If it starts from rest and gains, with constant
angular acceleration, an angular speed n=180rpm, in 12 revolutions, nd the
acting moment. .
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(b) A block starts from rest from‘A’. If the co e cient of friction between all sur-
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faces of contact is 0.3, nd the distance at which the block stop on the hori-
zontal plane. Assume the magnitude of velocity at the end of slope is same as
that at the beginning of the horizontal plane.
As shown in the Figure7b [8+8]
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Code No: R05010105
Set No. 1

Figure 7b
8. (a) A homogeneous circular disk of radius ‘r’ and weight ‘W’ hangs in a vertical
plane from a pin ‘O’ at its circumference. Find the period for small angles
of swing in the plane of the disk

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(b) A slender wire 0.90 m long is bent in the form of a equilateral triangle and
hangs from a pin at ‘O’ as shown in the gure8b. Determine the period for
small amplitudes of swing in the plane of the gure. [16]

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Figure 8b
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Code No: R05010105
Set No. 2
APPLIED MECHANICS
(Civil Engineering)

1. (a) A Prismatic bar AB of weight ‘W’ is resting against a smo oth vertical wall at
‘A’ and is supported on a small roller at the point ‘D’. If a vertical force F
is applied at the end ‘B’, Find the position of equilibrium as de ned by the
angle ‘ ’.{As shown in the Figure1a}.

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ogFigure 1a
(b) Two rollers of weights P and Q are connected by a exible string DE and rest
on two mutually perpendicular planes AB and BC, as shown in gure 1b. Find
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the tension (‘T’) in the string and the ‘ ’ that it makes with the horizontal
when the system is in equilibrium. The following numerical data are given.
P= 270 N, Q = 450 N, = 300. Assume that the string is inextensible and
passes freely through slots in the smo oth inclined planes AB and BC. [6+10]
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Figure 1b
2. (a) Explain the principles of operation of a screw jack with a neat sketch.
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Code No: R05010105
Set No. 2
(b) Outside diameter of a square threaded spindle of a screw Jack is 40 mm. The
screw pitch is 10 mm. If the coe cient of friction between the screw and the
nut is 0.15, neglecting friction between the nut and collar, determine
i. Force required to be applied at the screw to raise a load of 2000N
ii. The e ciency of screw jack
iii. Force required to be applied at pitch radius to lower the same load of 2000
N and
iv. E ciency while lowering the load
v. What should be the pitch for the maximum e ciency of the screw? and
vi. What should be the value of the maximum e ciency? [6+10]
3. (a) Obtain the conditions for the maximum power transmitted by a belt from one
pulley to another.
(b) A shaft running at 100 r.p.m drives another shaft at 200 r.p.m and transmits

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12 kW. The belt is 100 mm wide and 12 mm thick and = 0.25. The distance
between the shafts is 2.5 meters and the diameter of the smaller pulley is 500
mm.
Calculate the stress in
i. An open belt

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ii. A crossed belt, connecting the two pulleys. [6+10]
4. (a) Di erentiate between centroid and center of gravity.
(b) Determine the product of inertia of shaded area as shown in Figure 4b about
the x-y axis.
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Figure 4b
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5. Derive the expression for the moment of inertia of a cylinder length ‘ ’, radius ‘r’ and
density ‘w’ about longitudinal centroidal axis and about the centroidal transverse
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axis. [16]
6. (a) A train is traveling at a speed of 60 km/hr. It has to slow down due to certain
repair work on the track. Hence, it moves with a constant retardation of 1
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km/hr/second until its speed is reduced to 15 km/hr. It then travels at a
constant speed of for 0.25 km/hr and accelerates at 0.5 km/hr per second
until its speed once more reaches 60 km/hr. Find the delay caused.
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Code No: R05010105
Set No. 2
(b) The motion of a particle in rectilinear motion is de ned by the relation
= 2 3 - 9 2 + 12 - 10 where s is expressed in metres and t in seconds. Find
i. the acceleration of the particle when the velocity is zero
ii. the position and the total distance traveled when the acceleration is zero.
[8+8]

7. (a) A body weighing 20 N is projected up a 200 inclined plane with a velocity of
12 m/s, coe cient of friction is 0.15. Find
i. The maximum distance S, that the body will move up the inclined plane
ii. Velocity of the bo dy when it returns to its original position.
(b) Find the acceleration of the moving loads as shown in gure 7b. Take mass
of P=120 kg and that of Q=80 Kg and co e cient of friction between surfaces
of contact is 0.3. Also nd the tension in the connecting string. [8+8]

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Figure 7b
8. In a mechanism, a cross-head moves in straight guide with simple harmonic motion.
At distances of 125 mm and 200 mm from its mean position, it has velo cities of 6
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m/sec and 3 m/sec respectively. Find the amplitude, maximum velo city and perio d
of vibration. If the cross-head weighs 2N, calculate the maximum force on it in the
direction of motion. [16]
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Code No: R05010105
Set No. 3
APPLIED MECHANICS
(Civil Engineering)

1. (a) A ball of weight ‘W’ rests upon a smo oth horizontal plane and has attached
to its center two strings AB and AC which pass over frictionless pulleys at B
and C and carry loads P and Q, respectively, as shown in Figure1a. If the
string AB is horizontal, nd the angle that the string AC makes with the
horizontal when the ball is in a position of equilibrium. Also nd the pressure
R between the ball and the plane.

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Figure 1a
(b) Determine the forces S1 and S2 induced in the bars AC and BC in Figure1b.

together at C and to the foundation at A and B.
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due to the action of the horizontal applied load at C. The bars are hinged
[8+8]
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Figure 1b
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3. A cross belt drive is to transmit 7.5 KW at 1000 r.p.m of the smaller pulley.
The diameter of the smallest pulley is 250mm and velocity ratio is 2. The centre
distance between the pulley is 1250mm. A at belt of thickness 6 mm and of
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co e cient friction 0.3 is used over the pulleys. Determine the necessary width of
the belt if the maximum allowable stress in the belt is 1 75 2 and density of
the belt is 1000 3.
[16]
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Code No: R05010105
Set No. 3
4. (a) Di erentiate between centroid and center of gravity.
(b) Determine the product of inertia of shaded area as shown in Figure 4b about
the x-y axis. [6+10]

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Figure 4b
5. (a) De ne mass moment of inertia and explain Transfer formula for mass moment
of inertia.
(b) Derive the expression for the moment of inertia of a homogeneous sphere of

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radius ‘r’ and mass density ‘w’ with reference to its diameter. [8+8]

6. A roller of radius 0.1m rides between two horizontal bars moving in opposite direc-
tions as shown in gure6 Assuming no slip at the points of contact A and B, locate
the instantaneous center ‘I’ of the roller. Also locate the instantaneous center when
both the bars are moving in the same directions. og [16]
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Figure 6
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Code No: R05010105
Set No. 3

Figure 7b
8. (a) Explain how a simple pendulum di er from a compound pendulum brie y
with the help of di erential mathematical equations.
(b) Determine the sti ness in N/cm of a vertical spring to which a weight of
50 N is attached and is set vibrating vertically. The weight makes 4 oscillations
per second. [8+8]

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Code No: R05010105
Set No. 4
APPLIED MECHANICS
(Civil Engineering)

1. (a) State and prove Lame’s theorem.
(b) A prismatic bar AB of 7m long is hinged at A and supported at B as shown
in Figure 1b. Neglecting friction, determine the reaction Rb produced at B
owing to the weight of the bar. Q = 4000 N, Take = 250. [6+10]

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Figure 1b

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3. (a) Deduce an expression for centrifugal tension of belt drive.
(b) The maximum allowed tension in a belt is 1500 N. The angle of lap is 1700
and coe cient of friction between the belt and material of the pulley is 0.27.
Neglecting the e ect of centrifugal tension, calculate the net driving tension
and power transmitted if the belt speed is 2 m/s.
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[6+10]

4. (a) Find the centroid of the ‘Z’ section shown in Figure 4a.
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Code No: R05010105
Set No. 4

Figure 4a
(b) Find the moment of inertia about the horizontal centroidal axis.shown in Fig-
ure 4b. [6+10]

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Figure 4b
5. A thin plate of mass ‘m’ is cut in the shape of a parallelogram of thickness ‘t’ as
shown in gure5. Determine the mass moment of inertia of the plate about the
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x-axis. [16]
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Figure 5
6. (a) A baloon is ascending with a velocity of 20 m/s above a lake. A stone is
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dropped to fall from the balloon and the sound of the splash is heard 6 seconds
later. Find the height of the balloon when the stone was dropped. Velocity of
sound is 340 m/s.
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Code No: R05010105
Set No. 4
(b) The acceleration of a particle in rectilinear motion is de ned by the relation
= 25 - 4 2 where ‘a’ is expressed in 2 and ‘s’ is position coordinate
in metres. The particle starts with no initial velocity at the position s = 0.
Determine
i. the velo city when s = 3metres
ii. the position where the velocity is again zero
iii. the position where the velocity is maximum. [8+8]


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Figure 7b
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8. A centrifugal pump rotating at 400 rpm is driven by an elastic motor at 1200
rpm through a single stage reduction gearing. The moment of inertia of the pump
impeller at the motor are 1500 kg.m2 and 450 kg.m2 respectively. The lengths of
the pump shaft and the motor shaft are 500 and 200 mm, and their diameters are
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100 and 50 mm respectively. Neglecting the inertia of the gears, nd the frequency
of torsional oscillations of the system. G = 85 GN/m2.
[16]
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R05010105 A P P L I E D M E C H A N I C S

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