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Course Objectives:
I.
Students should develop the ability to work comfortably with basic engineering mechanics
concepts required for analyzing static structures.
II.
Identify an appropriate structural system to studying a given problem and isolate it from its
environment, model the problem using good free-body diagrams and accurate equilibrium
equations.
III.
Identify and model various types of loading and support conditions that act on structural
systems, apply pertinent mathematical, physical and engineering mechanical principles to the
system to solve and analyze the problem.
IV.
Understand the meaning of centre of gravity (mass)/centroid and moment of Inertia using
integration methods and method of moments.
V.
To solve the problem of equilibrium by using the principle of work and energy, impulse
momentum and vibrations for preparing the students for higher level courses such as
,Mechanics of Solids, Mechanics of Fluids, Mechanical Design and Structural Analysis etc...
UNIT-I
Short Answer Type
S.
No.
JN
Question
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
State and explain newtons law of gravitation
Explain the terms - concurrent and non concurrent force system :
planar and non planar system of forces
Define the term resultant and equilibrant
Define the term moment of a force
Explain the procedure to find the resultant of several forces acting at
a point
What is a couple? State its characteristics
Explain the terms 1)unit vector 2) position vector
Explain dot product of vectors
Explain the characteristics of the cross products
Define the moment of a force about a point write an expression in
Blooms
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the vector form
11.
Define parallelogram law of forces and give mathematical formulae
12.
Explain in brief free body diagrams.
13.
State triangle law and explain Lami’s theorem.
14.
Define the law of polygon of forces.
15.
Define moment of a couple. Give at least five examples where effect
of couple is realized.
16.
Define equilibrium of a body and give conditions of equilibrium
when subjected to forces.
17.
Two coplanar forces act towards a point with an angle of 45 0
between them. If their resultant is 100kN and one of the forces is
20kN calculate the other force.
18.
Two forces act at an angle of 1200. The bigger forces is 60N and the
resultant is perpendicular to the smaller one. Find the smaller force.
19.
Two equal forces 10N each act at right angles to each other. Find
the magnitude and direction of the resultant if that produces the
same effect as the two forces.
20.
A Single force of 10 N is resolved into two concurrent forces of 6 N
each. Find the angle between them.
Essay Questions
1.
a)
Define Lami’s theorem
b)
A machine weighing 5KN is supported by two chains attached
to some points on the machine. One chain goes to hook in the
ceiling and has an inclination of 45 degrees with horizontal.
The other chain goes to eye bolt in the wall and is inclined at
30 degrees to the horizontal. Find tensions induced in the
chains
2.
a)
Derive an equation for resultant using parallelogram law of
forces
b)
Find the magnitude of the two forces such that if they act at
right angles their resultant is sq. root 10N. But if they act at 60
degrees their resultant is sq. root 13N
3.
a)
Explain the different types supports and support reactions
b)
A beam AB is supported and loaded as shown in fig.1. Find
the reactions at the supports.
4.
a)
b)
State and explain the theorem of Varignon
Two spheres, of each of weight 1000 N and radius of 25 cm
rest in horizontal channel of width 90 cm as shown in fig 1.
Find the reactions on the points of contact A, B and D
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a)
b)
Write the equations of equilibrium when the body is in space
A ball of weight Q = 12 N rests in a right - angled trough, as
shown in fig 1. Determine the forces exerted on the sides
ofthe trough at D (RD) and E (RE) if all surfaces are
perfectly smooth.
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6.
a)
State and explain the laws of forces:
(i).Law of parallelogram of forces (ii). Law of triangle
of forces, (iii) Law of polygon of forces
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A rigid bar is subjected to a system of parallel forces as shown
in Fig 1. Reduce this system to (i) a single force, (ii) a
single force-moment system at A and
(iii) a single force-moment system at B.
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5.
7.
a)
b)
Draw different types of supports and corresponding reactions
A system of connected flexible cables as shown in figure
issupporting two vertical forces 240 N and 300 N at points B
and D. Determine the forces in various segments of the cable.
Evaluation
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8.
a)
b)
9.
a)
Explain the classification of different system of forces
Determine the magnitude and the direction of the resultant of
two forces 7 N and 8 N acting at a point with an included
angle of 60o with between them. The force of 7 N being
horizontal
Define free body diagram, Transmissibility of a force and
resultant of a force
Two forces are applied to an eye bolt fastened to a beam.
Determine the magnitude and direction of their resultant using
(a) the parallelogram law, (b) the triangle rule.
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a)
Two identical rollers, each of weight 100 N, are supported by
an inclined plane and a vertical wall as shown in figure
below. Assuming smooth surfaces, find the reactions
induced at the points of support A, B and C.
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10.
b)
Determine the magnitude and direction of the resultant force Evaluation
as shown in fig
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b)
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13
a)
b)
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14
Write the Equilibrium equations for concurrent force system
in space
A force 100 N is directed from A (2, 0, 4) to B (3, 3, 5). What
is the moment of force about the origin?
A horizontal line ABCD measuring 9m is acted upon by
forces of magnitude 400,600,400 and 200N at points A, B, C
and D respectively with downward direction. These points are
so located that AB=BC=CD=3m. The line of action of the
forces and inclined at 900, 600, 450 and 300 respectively with
AB. Make calculations for the magnitude, position and
direction of the resultant.
Derive an equation for resultant using parallelogram law of
forces.
Two equal forces act on a particle such that the square of their
resultant is equal is equal to the three times of their product.
Find the angle between the forces.
The resultant of two forces acting at a point is 65kN. It is
observed that one force is double than the other and if the
direction of one of them is reversed the resultant becomes 45
kN. Find the magnitudes of forces and the angle between
them.
Find the magnitude of two forces such that if they act at right
15
angle, their resultant is
is
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10 , but they act at 60 their resultant
13
A particle is acted upon by forces equal to P, 2P, 3 3P and
4P. The angle between the first and second, the second and
third and fourth are 600, 900 and 1500 respectively. Find the
magnitude and direction of the resultant force.
The five forces 20N, 30N, 40N, 50N and 60N are acting at
one of the angular points of a regular hexagon, towards the
other five angular points taken in order. Find the direction and
magnitude of the resultant force.
The following forces act at a point
a. 30kN inclined at 350 towards North to East.
b. 22kN towards North
c. 30kN inclined at 300 towards North to West
d. 35kN inclined at 250 towards South to West.
Find the magnitude and direction of the resultant force.
Three forces acting at a point have a resultant of 100N
towards north-east. One of the forces is of 50 N towards the
east. The next force act towards 300 north of west and has a
magnitude of 40N. Determine third force in magnitude and
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direction.
Explain different conditions of equilibrium.
A lamp weighign 5 N is suspended from the ceiling by means
of a wire. It is pulled to one side by a horizontal cord, until the
wire makes an angle of 600 with the ceiling. Find the tension
in the wire and cord.
UNIT-II
Short Answer Type
20
a)
b)
Question
Explain the types of friction with examples?
Define the following i) Friction ii) Angle of friction
iii)
Limiting friction
3.
Define the following
(i)Angle of Repose (ii)Coefficient of frictions
4.
Differentiate between static and dynamic friction?
5.
State laws of solid friction
6.
Distinguish between quarter turn and compound belt drive
7.
What is meant by cross belt drive? Explain
8.
Define coefficient of friction and limiting friction
9.
Distinguish between initial tension and centrifugal tension
10.
Write down the conditions for transmission of maximum power.
11.
Define friction and how can we appreciate the use of friction in
practice?
12.
What are the effects of friction?
13.
State the laws of solid friction.
14.
Define coefficient of friction and angle of friction. How these are
related to each other?
15.
What do you understand by the limiting friction? And define angle
of repose.
16.
Derive the least inclined force required to drag body resting on a
horizontal plane in terms of weight of the dody, angle of the
inclined force and angle of friction.
17.
What is the principle of a screw jack?
18.
Derive an expression for the effort required to move a body up an
inclined plane when the effort is parallel to the plane.
19.
Draw a neat sketch of a screw jack and mark salient parts on it.
20.
Derive the expression for efficiency of screw jack.
Essay Questions
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2.
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b)
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Blooms Taxonomy
Level
Program
Outcomes
Obtain an equation for the length of the belt in an open belt
Analysis
drive
A ladder 6m long and with 300N weight is resting against a
Knowledge
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wall at an angle of 60 to the ground. A man weighing 750N
climbs the ladder. At what position along the ladder from
bottom does he induce slipping? The coefficient of friction for
both wall and the ground with ladder is 0.2.
Derive a relation for the efficiency of a screw jack, taking
Analysis
friction into account
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a)
b)
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a)
b)
5.
a)
b)
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b)
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3.
An open belt running over two pulleys 1200 mm and 500 mm
diameters connects two parallel shafts 4000 mm a part. The
maximum tension in the belt is 1830 N. Coefficient of
friction between the belt and the pulley is 0.3.The driven
pulley of 1200 mm diameter runs at 200 rpm. Determine :
a) Power transmitted
b) torque on each of two shafts
Derive an expression for length of crossed belt drive
A ladder 5m long weighing 200N leans against a smooth
vertical wall at an angle of 600 with horizontal. A man
weighing 700N stands at mid-height of ladder when it is about
to slip. Calculate the coefficient of friction between the ladder
and ground
Draw a neat sketch of simple screw jack and derive an
expression for minimum effort required to raise a load
Find the effort required at the end of the lever 300mm long of
a screw jack, the mean diameter of the screw is 26mm, load
acting is 10KN, helical angle is 150, and coefficient of friction
between screw and nut is 0.22.
What is angle of repose? Prove that angle of repose is equal to
the angle of friction.
A shaft running at 100 rpm drives another shaft at 200 rpm
and transmits 12kW. The belt is 100 mm wide and 12mm
thick and coefficient of friction is 0.25. the distance between
the shaft is 2.5 m and the diameter of smaller pulley is 500
mm.
Calculate the stress in (i) an open belt and (ii) crossed belt,
connecting two pulleys
Explain the difference between coefficient of friction and
angle of friction.
A body weighing 50N is just pulled upon inclined plane of 300
by a force of 40N applied at 300 above the plane. Find the
coefficient of friction.
What is a wedge? Explain how wedge is used to raise the
heavy load.
A block over lying a 100 wedge on a horizontal floor and
leaning against a vertical wall and weighing 1500N is to be
raised by applying horizontal force to the wedge. Assume the
coefficient of friction between all the surfaces in contact to be
0.3. Determine the minimum horizontal force to be applied to
raise the block.
Derive an expression for the velocity ratio of a belt drive
considering the thickness of the belt.
A leather belt is required to transmit 9KW from a pulley
1200mm in diameter running at 200rpm. The angle embraced
is 1650 and coefficient of friction between leather belt and
pulley is 0.3. If the safe working stress for the leather belt is
1.4N/mm2, the mass of the leather is 100Kg/m3 and the
thickness of the belt is 10mm, determine the width of the belt
taking the centrifugal tension in to the account.
Derive an expression for the ratio of tensions for a flat belt
passing over a pulley when it is just on the point of slipping.
An open belt drive connects two pulleys 100mm and 500mm
diameter on parallel shafts 4m apart. The maximum tension in
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a)
the belt is 1830N. The coefficient of friction is 0.3. The driven
pulley of 1200mm diameter runs at 200rpm. Calculate (a)
power transmitted (b) torque on each of two shafts.
Draw a neat sketch of differential screw jack and explain its
working.
The following are the specifications for a differential screw
jack:
i)
Pitch of the smaller screw is 5mm
ii)
Pitch of the larger screw is 10mm
iii)
Lever arm length from center of screw is 500mm
The screw jack raises a load of 15KN with an effort of 185N.
Determine the efficiency of the differential screw jack at this
load.
A weight 500N just starts moving down a rough inclined
plane support by a force of 200N acting parallel to the plane
and it is at the point of moving up the plane when pulled by a
force of 300N parallel to the plane. Find the inclination of the
plane and the coefficient of friction between the inclined plane
and the weight.
A cord connects two bodies A and B of weights 450 N and
900N. The two bodies are laced on an inclined plane and cord
is parallel to inclined plane. The coefficient of friction for
body –A is 0.16 and that for B is 0.42. Determine the
inclination of the plane to the horizontal and tension in the
cord when motion is about to take place down the plane.
A belt is running over a pulley of diameter 800mm at 140
rpm. The angle of contact is 1650 and coefficient of friction
between the belt and pulley is 0.25. if the maximum
permissible tension in the belt is 2.5 kN. Find the power
transmitted by the belt.
The initial tension in an open flat belt is 2000 N. The angle of
contact of smaller pulley is 1350 and μ is 0.25. The smaller
pulleys diameter is 36cm and rotates at 300 rpm. Find the
power transmitted by the belt.
A flat belt transmits 15000 W from a shaft running at 300 rpm
to another parallel shaft running at the same rpm. The
maximum permissible tension in the belt is 3kN. Find the
radius of the pulley consider μ=0.25
Two pulleys, one having diameter 450 mm and other having
diameter 200 mm are mounted on parallel shaft and are 2000
mm apart. For open-belt arrangement, find power transmitted
if larger pulley rotates at 250 rpm and μ=0.3 and maximum
tension in the belt is 1.5kN.
A belt of density 1.5 gm/cm3 has a maximum permissible
stress of 300 N/cm2. Determine the maximum power that can
be transmitted by a belt of 15 cm x 1.5 cm if the ratio of the
tension is 2.5.
For an open-belt drive transmitting 4kW, the distance between
the centre of pulley ‘A’ and the centre of pulley ‘B’ is 100cm.
diameters of pulleys A and B are 30cm and 20cm respectively.
The coefficient of friction between belt and pulley is 0.2. The
pulley A is rotating at 200rpm. If the permissible tensile force
per cm width of belt is 180N, determine the width of the belt
necessary.
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A leather belt of 1cm thick and 12.5cm width drives a pulley
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of 120cm diameter at 180rpm. The angle of lap is 1900. The
density of belt material is 1.15gm/cm3. If the stress in the belt
is limited to 200N/cm2, determine (a) power transmitted
neglecting centrifugal tension and (b) considering centrifugal
tension. Take =0.3.
20
What maximum power is transmitted if the cross section of Analysis
the belt is 10cm2 and maximum stress is limited to
2400N/cm2. Density of the belt material =5 cm3. The ratio of
effective tension=2.
UNIT-III
Short Answer Type
Blooms
S.No.
Question
Taxonomy
Level
1.
Define and Explain centre of gravity and Distinguish between centre
Knowledge
of gravity and centroid
2.
Derive an expression for the centre of gravity of a plane area using
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method of moments.
3.
Describe the various methods of finding the centre of gravity of a
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body
4.
What do you understand by axes of reference? Explain
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Prove that the first moment of area wrt the centroidal axis is zero
5.
Explain the difference between the centre of gravity and centre of
Comprehension
mass.
6.
Explain the difference between the centre of gravity and centre of
Comprehension
mass.
7.
How would you find out the centre of gravity of a section, with a cut
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out hole?
8.
State and prove first theorem of Pappus.
Evaluation
9.
State and prove second theorem of Pappus.
Evaluation
10.
Where does the centre of gravity of the following section lies
(i).Semi circle, (ii).Trapezium, (iii).Hemisphere, (iv).Right circular
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solid cone
11.
Define C.G and moment of inertia.
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12.
Illustrate the centre of gravity of hemisphere.
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13.
Define
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Radius of gyration and
b.
Perpendicular axis theorem.
14.
Write the moment of inertias of the following plane figures.
a.
Hollow rectangle
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b.
Semi-circle and
c.
Quadrant
15.
Derive an equation for M. I of a rectangular section of height ‘h’ and
Comprehension
width ‘b’ about its centroidal axis.
16.
Define radius of gyration and express it mathematically.
Comprehension
17.
State parallel axis theorem with a line diagram.
Knowledge
18.
Find the C.G of a channel section 100 mm x 50 mm x 15mm.
Evaluation
19.
What is the built-up section?
Evaluation
20.
Give the expression for finding centroid.
Knowledge
Essay Questions
S.
Question
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a)
b)
a)
Evaluation
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1. Find the moment of inertia of the shaded area shown in
fig. about its centroidal axis parallel to X-axis.
Find the centre of gravity of the “T “lamina as shown in figure.
All dimensions are in mm
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3.
Find the centroid of a semi circular lamina of radius R from its
base
Locate the centroid of shaded area obtained by removing a
semicircle of diameter ‘a’ from a quadrant of a circle of radius
‘a’ as shown in figure.
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b)
Determine the coordinates of centroid of the shaded area as Evaluation
shown in figure, if the area removed is semicircular. All
dimensions are in mm
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b)
Find the centroid of the plane lamina shown in _gure
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Find the centroid of the shaded plane area shown in figure.
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Uniform lamina shown in fig consists of rectangle, a semi circle
and a triangle. Find the centre of gravity.
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a)Find the centroid of the plane lamina shown in _Figure
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5.
a)
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6.
a)
State and prove parallel axis theorem of area moment of inertia.
b)
Find the moment of inertia for the shaded area parallel to x –
axis. As shown in the Figure
Evaluation
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a)
b)
State and prove perpendicular axis theorem.
Find the moment of inertia of the area in the given figure about
the axis ‘AB’
Evaluation
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Determine the moment of Inertia of a triangle with respect to its
centroidal x axis parallel to the base.
Find the moment of the inertia of the section shown in the
figure 5 about horizontal and vertical centroidal axes. All
dimension in cm R = 8.
Evaluation
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a)
Find the moment of inertia about the horizontal centroidal axis
of shaded portion for the Figure
b)
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Determine the moment of inertia of the inverted T-section Evaluation
shown in figure about an axis passing through the centroid of
the section and perpendicular to the stem
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11.
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Derive an expression for the moment of inertia of a circular ring
of uniform cross section of radius ‘R’ about its diametrical axis
Derive an expression for the moment of inertia of a circular
plate of radius ‘R’ and thickness ‘t’ about its centroidal axis
Determine the moment of inertia of a solid sphere of radius ‘R’
about its diametrical axis.
Find the Mass moment of inertia of a rectangular plate of size a
x b and thickness‘t’ about its centroidal axis.
Find the Mass moment of inertia of a solid cone of height “ H “
and base radius R about 1) axis of rotation 2) an axis through
the vertex mormal to the axis of rotation.
Derive an expression for centroid of triangular area.
Derive an expression for centroid of sector of a circle.
Determine the Centroid of the parabolic spandrel as shown in
figure.
12.
14.
15.
W
16.
17.
18.
State and prove Pappus-Guldinus First theorem
State and prove Pappus-Guldinus Second theorem
20.
Give the expressions for centroid and moment of inertia of any
five basic geometrical shapes with figures and details.
UNIT – IV
Short Answer Type
Knowledge
a,e,l,k
Evaluation
a,e,l,k
Knowledge
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Knowledge
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Knowledge
Analysis
a,e,l,k
a,e,l,k
Comprehension
a,e,l,k
Knowledge
Knowledge
a,e,l,k
a,e,l,k
Evaluation
a,e,l,k
Blooms
Taxonomy
Level
Program
Outcomes
Define the terms velocity and acceleration
Knowledge
a,e,l,k
Define angular displacement angular velocity angular acceleration
Knowledge
a,e,l,k
A stone is thrown vertically upwards and returns in 5sec.How high
does it go
A body falling freely under the action of gravity passes two points
9m apart vertically 0.2sec.from what height above the higher point
did it start to fall?
Knowledge
a,e,l,k
Knowledge
a,e,l,k
JN
S
.
N
o
.
1
.
2
.
3
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4
.
a)
b)
TU
19.
a,e,l,k
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13.
Knowledge
Question
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a,e,l,k
Comprehension
a,e,l,k
Knowledge
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Evaluation
a,e,l,k
Knowledge
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Evaluation
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Knowledge
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Knowledge
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Knowledge
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Knowledge
a,e,l,k
A ball is thrown vertically upwards with a velocity of 40m/sec.
Find the position after 5 seconds.
Comprehension
a,e,l,k
A shot is fired horizontally from a gun at a height of 9m from the
ground. Find the initial velocity of shot, if it strikes the ground at a
horizontal distance of 1000m.
Explain projectile & trajectory and give examples.
Comprehension
a,e,l,k
Knowledge
a,e,l,k
The horizontal range of projectile is 4 3 time its maximum height.
Find the angle of projection.
Evaluation
a,e,l,k
Prove that the equation of the path of projectile is a parabola.
Knowledge
a,e,l,k
Evaluation
a,e,l,k
Explain law of conservation energy.
Explain D’Alembert’s principle.
A force of 10 N acts on a body continuously for 10 seconds and
causes it to describe 10m in that line. Find the mass.
(Use s  ut 
1 2
gt and F=ma, where u=0)
2
TU
Derive the equation for distance travelled in nth term.
JN
1
4
.
1
5
.
1
6
.
1
7
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1
8
.
1
9
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2
0
.
Comprehension
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ld
8
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9
.
1
0
.
1
1
.
1
2
.
1
3
.
Explain the term recoil of gun. How will you find the velocity of
the bullet?
Explain types of motion and distinguish between uniform motion
and accelerated motion
A car weighing 18kn rounds a curve of 60mts radius banked at an
angle of 300.find the frictional force acting on the tires when the is
travelling at 96.54kmph.the coefficient of friction between tires and
road is 0.6.
Derive a relation for the distance travelled by a body in the nth
second.
Define the terms i) velocity of projection ii) angle of projection iii)
time of flight iv) range of a projectile
Obtain an equation for the trajectory of a projectile and show that it
is a parabola.
W
5
.
6
.
7
.
JNTU World
Show that horizontal range of projectile in
u 2 sin 2
g
(Where, u=initial velocity of projection)
Essay Questions
S.
Question
Blooms
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Program
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N
o.
1.
3.
4.
W
5.
TU
6.
a)
JN
7.
The motion of a particle in rectilinear motion is defined by the
relation
where s is in meters and t
in seconds. Find (a) Acceleration of particle when the velocity
is zero (b) the position and the total distance travelled when
acceleration is zero.
An auto is accelerated from rest to a speed of 100kmph and
then immediately decelerated to a stop. If the total elapsed
time is 20sec, determine the distance covered. The acceleration
and deceleration are both constant but not necessarily of the
same magnitude
A train travelling 96kmph has to slow down an amount of
work being done on the line. Instead of continuing a constant
speed it, therefore moves with a constant retardation of
1.6kmph/s until the speed is reduced of 24kmph. It is then
travels at a constant speed for 400m and then accelerates at
0.8kmph/s until its speed is once more 90kmph. Find the delay
period
The distance covered by a freely falling body in the last one
second of its motion and that covered in the last but one
second are in the ratio 5:4. Calculate the height from which the
body was dropped and the velocity with which it strikes the
ground
A stone is thrown vertically upwards with a velocity of
19.6m/s from the top of a tower 24.5m height. Calculate the a)
time required for the stone to reach the ground. b) velocity of
the stone in its downward travel at the point in the same level
as the point of projection. c) The maximum height to which the
stone will rise in its flight
An aircraft is moving at a speed of 150kmph at an altitude of
750m towards a target on the ground, release a bomb which
hits the target. Estimate the horizontal distance of the aircraft
from the target when it releases the bomb. Calculate also the
direction and velocity with which the bomb hits the ground
Two bodies of weight 20N and 10N are connected to ends of a
light in extensible spring passing over a smooth pulley. The
weight of 20N is placed on a horizontal surface while the
weight of 10N is hanging free in air. The horizontal surface is
a rough one, having coefficient of friction between the weight
20N and the plane surface equal to 0.3. Determine a) the
acceleration of the system b) The tension in the string
Explain the terms momentum of a body and angular
momentum of a body.
Two bodies of weights 40N and 25N are connected to the two
ends of a light in extensible spring passing over a smooth
pulley. The weight of 40N is placed on a rough horizontal
surface while the weight of 25N is hanging free in air. The
angle of plane is 150. Determine a) the acceleration of the
system b) The tension (µ=0.2) in the string. C) The distance
moved by the weight 25N in 3 seconds starting from rest
State D’Alemberts Principle. Explain it for a rigid body in
plane motion giving equations.
Explain the laws of motion for a body in rotational motion
b)
8.
a)
b)
9.
Taxonomy
Level
Outcomes
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Evaluation
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or
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2.
JNTU World
a)
Knowledge
a,b,d,e,j,k,l
Analysis
a,b,d,e,j,k,l
Analysis
a,b,d,e,j,k,l
Analysis
a,b,d,e,j,k,l
Evaluation
a,b,d,e,j,k,l
Comprehension
a,b,d,e,j,k,l
Evaluation
a,b,d,e,j,k,l
Comprehension
a,b,d,e,j,k,l
Comprehension
a,b,d,e,j,k,l
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1
2
1
3
1
4
JN
1
5
W
1
1
TU
1
0.
A wheel rotating about a fixed axis at 20rpm is uniformly
accelerated for 70seconds, during which time it makes 50
revolutions. Find the a) angular velocity at the end of this
interval and b) the time required for the speed to reach 100
revolutions per minute
A stone is dropped into a well while splash is heard after 4.5
seconds. Another stone is dropped with an initial velocity, v
and the splash is heard after 4 seconds. If the velocity of the
sound is 336m/s, determine the initial velocity of second stone
A particle starts moving along a straight line with initial
velocity of 25m/s, from O under a uniform acceleration of 2.5m/s2. Determine.
i. Velocity, displacement and the distance travelled at t=5
sec.
ii. How long the particle moves in the same direction? What
are its velocity, displacement and distance covered then?
iii. The instantaneous velocity, displacement and the distance
covered at t=15 sec,
iv. The time required to come back to O, velocity
displacement and distance covered then and
v. Instantaneous velocity, displacement and distance covered
at t=25 sec.
Two stations P and Q are 5.2km apart. An automobile starts
from rest from the station P and accelerates uniformly to attain
a speed of 48 kmph in 30 seconds. This speed is maintained
until the brakes are applied. The automobile comes to rest at
the station Q with a uniform retardation of one metre per
second. Determine the total time required to cover the distance
between these two stations.
A motorist is travelling at 90 kmph, when he observes a traffic
light 250m ahead of him turns red. The traffic light is timed to
stay red for 12 sec. If the motorist wishes to pass the light
without stopping, just as it turns green. Determine
(i) The required uniform deceleration of motor and
(ii) The speed of the motor as it passes the traffic light.
Determine the time required for a car to travel 1km along a
road if the car starts from rest, reaches a maximum speed at
some intermediate point, and then stops at the end of the road.
The car can accelerate or decelerate at 1.5m/s2.
The velocity of particle moving in a straight line is given by
the expression
v=t3-t2-2t+2
The particle is found to be at a distance 4m from station A
after 2 seconds. Determine :
i. Acceleration and displacement after 4 seconds and
ii. Maximum / Minimum acceleration
A ball is thrown from horizontal level, such that it clears a wall
6m high, situated at a horizontal distance of 35m. If the angle
of projection is 600 with respect to the horizontal, what should
be the minimum velocity of projection?
A ball is thrown from top of building with speed 12m/s at
angle of depression 300 with horizontal, strikes the ground 11.3
m horizontally from foot of the building. Determine height of
building.
1
6
1
7
Knowledge
a,b,d,e,j,k,l
Evaluation
a,b,d,e,j,k,l
or
ld
b)
JNTU World
Knowledge
a,e,l,k
Analysis
a,e,l,k
Comprehension
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Knowledge
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Knowledge
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Evaluation
a,e,l,k
Knowledge
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1
8
1
9
a)
2
0
An aeroplane is flying in horizontal direction with a velocity of
540 km/hr and at a height of 2200 m. When it is vertically
above the point A on the ground, a body is dropped from it.
The body strikes the ground at point B. calculate the distance
AB (ignore air resistance). Also find velocity at B and time
taken to reach B.
A body is projected at an angle such that its horizontal range is
3 times the maximum height. Find the angle of projection.
A projectile is aimed at a target on the horizontal plane and
falls 12 m short when the angle of projection is 150, while it
overshoots by 24m when the angle is 450. Find the, angle of
projection to hit the target.
A particle projected from a point A, with the angle of
projection equal to 15 0 falls short of a mark B on the horizontal
plane through A by 22.5 and when the angle of projection is
450 if falls beyond B by same distance. Show that for the
particle to fall exactly at B, the angle of projection must be
Evaluation
a,e,l,k
Knowledge
a,e,l,k
Analysis
a,e,l,k
or
ld
b)
JNTU World
Knowledge
a,e,l,k
1 1  3 
sin   , the velocity of projection being the same in all
2
4
JN
TU
W
the three cases. Also determine the velocity of projection.
UNIT-V
Short Answer Type
S.
N
Question
o.
1. Define the following terms:
(i)
Work
(ii)
Energy
(iii)
Impulse and momentum
2. What are the units of work done? What is the relation between
work done and power?
3. Explain the principle of conservation of energy.
4. State law of conservation of momentum.
5. Explain work-energy method and its applications
6. Explain the terms simple harmonic motion, amplitude, frequency,
oscillation and period of simple harmonic motion.
7. What are the important types of free vibrations? What type of
stresses is produced in case of free vibrations of different types?
8. What are the different methods of finding the natural frequency of
free longitudinal vibrations? Explain in detail any two methods.
9. Define and explain the term torsional vibrations.
1 Find the expression for natural frequency of free torsional
0. vibrations when (i) the effect of inertia of the shaft is not
considered (ii) the effect of inertia of the shaft is considered.
1 Express the equations for the frictional losses interms of load and
1. effort.
1 Define:
2.
i.
Machine
ii.
Effort
iii.
MA
iv.
VR
Blooms
Taxonomy
Level
Knowledge
Program
Outcomes
a,e,l,k
Knowledge
a,e,l,k
Comprehension
Comprehension
Comprehension
Comprehension
d,j
a,e,l,k
a,e,l,k
a,e,l,k
Knowledge
a,e,l,k
Knowledge
a,e,l,k
Knowledge
Knowledge
a,e,l,k
a,e,l,k
Knowledge
a,e,l,k
Knowledge
a,e,l,k
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v.
Efficiency
vi.
Ideal machine
How levers are classified? Explain them in brief with sketches and
give one example for each.
Explain with the aid of sketch how the speed reduction is achieved
using worm and worm wheel.
Derive an expression for VR in worm & worm wheel.
Comprehension
d,j
Comprehension
a,e,l,k
Comprehension
a,e,l,k
Comprehension
a,e,l,k
Knowledge
a,e,l,k
Obtain the expression for the VR in a simple screw jack used to lift
loads.
Given an expression for velocity ratio of rack and pinion.
Knowledge
a,e,l,k
Knowledge
a,e,l,k
In a simple lifting machine an effort of 400 N lifted a load of 10kN.
What is mechanical advantage? If the machine has an efficiency of
60% what is the VR?
Essay Type Questions
S
.
N
Question
o
.
1 a Derive work energy equation for translation.
. )
b The bullet weighing 0.3 N and moving at 660m/s penetrates the
) 45 N body emerges with a velocity of 180m/s as shown. How
far and How long the body moves? Take coefficient of friction
as 0.4
Knowledge
a,e,l,k
Blooms Taxonomy
Level
Program
Outcomes
Analysis
a,e,l,k
Knowledge
a,e,l,k
Analysis
a,e,l,k
Evaluation
a,e,l,k
Evaluation
a,e,l,k
Knowledge
a,e,l,k
1
4.
1
5.
1
6.
1
7.
1
8.
Explain the principles of screw jack.
TU
W
1
9.
2
0.
What are the applications of screw jack?
or
ld
1
3.
JNTU World
Derive an expression for kinetic energy of a body rotating about
a fixed axis
A bullet of mass 25gms moving horizontal with a velocity of
600m/s strikes a wooden block of mass 5Kg resting on a rough
horizontal surface. The bullet after striking the block remains
buried in the block and both travels a distance of 90cms before
coming to rest. Determine: (a) average resistance between the
block and horizontal surface (b) coefficient of friction between
block and horizontal surface.
Prove that the work done by body is equal to change in its
kinetic energy
A hammer of mass 1500Kg drops from a height of 60cms on a
pile of mass 750Kg. find (i) the common velocity after impact
assuming plastic impact (ii) average resistance of the ground the
JN
2 a
. )
b
)
3 a
. )
b
)
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6 a
. )
Explain mathematically the effect of variations in g
(acceleration due to gravity) on the oscillations of a simple
pendulum
A flywheel 50KN and having radius of gyration 1m lost its
speed from 400rpm to 280rpm in 2 minutes. Calculate (i) torque
acting on it (ii) change in Kinetic Energy (iii) change in angular
momentum.
Derive the work energy equation for translation.
TU
b
)
A block of mass 5Kgs resting on a 300 inclined plane is
released. The block after travelling a distance of 0.5m along the
inclined plane hits a spring of stiffness 15N/cm. Find the
maximum compression of the spring. Assume coefficient of
friction between the block and inclined plane is 0.2.
What is a simple pendulum? Derive an equation for the time
period
Two blocks A and B are connected with the inextensible string
as shown in figure. The system is released from rest. Determine
the velocity of block A after it has moved 1.5m. Assume the
coefficient of friction between block A and the plane is 0.25,
masses of A and B are 200Kgs and 300Kgs respectively.
7 a
. )
b
)
b
)
9 a
. )
b
)
a,e,l,k
Knowledge
a,e,l,k
Knowledge
a,e,l,k
Evaluation
a,e,l,k
Comprehension
a,e,l,k
Analysis
a,e,l,k
Knowledge
a,e,l,k
Knowledge
a,e,l,k
Knowledge
a,e,l,k
Evaluation
a,e,l,k
Knowledge
a,e,l,k
Evaluation
a,e,l,k
3
A man wishes to move a wooden box of 1m to a distance of 5m
with least amount of work. If the block weighs 1KN and
coefficient of friction is 0.3, find whether he should tip it of
slide it?
How a Torsional pendulum differs from simple pendulum?
Derive an expression for the time period of a Torsional
pendulum.
Determine the magnitude and the direction of the resultant of
two forces 7 N and 8 N acting at a point with an included angle
of 60o with between them. The force of 7 N being horizontal
Define the term coefficient of restitution. State the principle of
conservation of linear momentum of a particle.
Determine the velocity of block B shown in figure after 5s
staring from rest.
JN
8 a
. )
Knowledge
or
ld
5 a
. )
b
)
pile comes to rest after penetrating 5cms in to the ground.
Define the law of conservation of momentum and prove it
W
4 a
. )
b
)
JNTU World
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1
3
1
4
JN
1
5
Find the length of a seconds pendulum assuming the value of g
as 9.81m/s2.
A man wishes to move wooden box of 1 metre cube to a
distance of 5m with the least amount of work. If the block
weighs 1 kN and the coefficient of friction is 0.3, find whether
he should tip it or slide it.
A mass of 20kg is projected up an inclined of 26 0 with velocity
of 4m/s. If μ=0.2
i. Find maximum distance that the package will move along
the plane and
ii. What will be the velocity of the package when it comes
back to initial position?
A body weighing 300 N is pushed up a 300 plane by a 400 N
force acting parallel to the plane. If the initial velocity of the
body is 1.5 m/sec and coefficient of kinetic friction is μ=0.2,
what velocity will the body have after moving 6m?
Find the power of a locomotive, drawing a train whose weight
including that of engine is 420 kN up an incline 1 in 120 at a
steady speed of 56kmph, the frictional resistance being 5N/kN.
While the train is ascending the incline, the steam is shut off.
Find how far it will move before coming to rest, assuming that
the resistance to motion remains the same.
Two particles of masses 10kg and 20kg are moving along a
straight line towards each other at velocities of 4m/s and 1m/s
respectively. Determine the velocities of the particles
immediately after their collision. Also find the loss of kinetic
energy.
A block weighing 2500N rests on a level horizontal plane for
which coefficient of friction is 0.20. This block is pulled by a
force of 1000N acting at an angle of 30 0 to the horizontal. Find
the velocity of the block after it moves 30m starting from rest. If
the force of 1000 N is then removed, how much further will it
move? Use work energy method.
A wagon weighing 500 kN starts from rest, runs 30 metre down
one per cent grade and strikes the bumper post. If the rolling
resistance of the track is 5 N/kN, find the velocity of the wagon
when it strikes the post.
If the bumper spring which compresses 1 mm for every 15kN
determine by how much this spring will be compressed.
TU
1
2
Define the following (i) Kinetic Energy (ii) Potential Energy.
W
1 a
0 )
.
b
)
1
1
1
6
1
7
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a,e,l,k
Knowledge
a,e,l,k
Analysis
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Comprehension
a,e,l,k
Knowledge
a,e,l,k
Knowledge
a,e,l,k
Evaluation
a,e,l,k
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a,e,l,k
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JN
2
0
Evaluation
W
1
9
A 10,000 kN train is accelerated at a constant rate up a 2%
grade. The track resistance is constant at 9N/kN. The velocity
increases from 9m/sec to 18m/sec in a distance of 600 metres.
Determine the maximum power developed by the locomotive.
Find the power required to pull a train up an incline of 1 in 200
at a speed of 36 kmph, if the weight of the train is 3000 kN and
the track resistance is 5 N/kN. Also determine the maximum
speed with which the train moves up on incline of 1 in 100 with
the same power.
A mine cage weights 12kN and can carry a maximum load of
20kN. The average frictional resistance of the side guides is
500N. What constant cable tension is required to give a loaded
cage an upward velocity of 3m/sec from rest in a distance of
3m?
TU
1
8
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