Engineering manuval.pdf

CMR INSTITUTE OF TECHNOLOGY
UGC AUTONOMOUS
Approved by AICTE, Permanently Affiliated to JNTUH, Accredited by NBA &
Accredited by NAAC with ‘A’ Grade.
Kandlakoya (V), Medchal Dist – 501 401
www.cmritonline.ac.in
DEPARTMENT OF MECHANICAL ENGINEERING
CERTIFICATE
ACADEMIC YEAR: 2018-19
This is to certify that the bonafide record work done by
Mr. / Ms. ________________________________________________________________
bearing H.T. No. ______________________ of I-B.Tech.-II-Semester in the
Engineering Mechanics Laboratory is satisfactorily completed.
Faculty In-charge Course Coordinator

I-B.Tech.-II-Semester (ME) Engineering Mechanics Lab
CMR Institute of Technology Page i
ENGINEERING MECHANICS LAB
I -B.Tech.-II-Sem L T P C
Subject Code: ESC-108 0 0 3 1.5
Course Objectives:
1. To make students understand force system and the resultant of force system
2. To make students experimentally calculate the reactions at the support of a given
beam
3. To make students understand the principle of moment using a bell crank lever
4. To make students understand the concept of friction between two surfaces
5. To make students understand the concept of moment of inertia of a flywheel
6. To understand the concept of mechanical advantage and velocity ratio
Course outcomes:
After completion of the course the student will be able to:
1. Determine the resultant of a given force system
2. Calculate the reactions at the support of a given beam
3. Apply the principle of moment to calculate unknown forces
4. Determine the frictional force between two surfaces
5. Determine moment of inertia for given flywheel
6. Determine the mechanical advantage and velocity ratio for simple machines
.
List of Experiments: (Perform any 10 Experiments)
1. To verify Polygon Law of Forces using Universal Force Table
2. To verify the Principle of Moments using Bell Crank Lever
3. To verify the Force in the Members of a Jib Crane
4. To verify the Law Of Moments by Rotating Disc Apparatus
5. To determine the Moment of Inertia of a Fly Wheel
6. To determine the Mechanical Advantage, Velocity Ratio and Efficiency of Square Threads
Screw Jack
7. Determination of coefficient of friction by the Inclined Plane Apparatus
8. To verify the Polygon Law Of Forces using Gravesand Apparatus
9. To verify the principle of forces in beam of Parallel Forces Apparatus
10. To determine the Mechanical Advantage, Velocity Ratio and Efficiency of Worm and Worm
Wheel
11. To study the performance of Differential Axle and Wheel and find its velocity Ratio and Law
of Machine
12. To determine the Radius of Gyration and Mass Moment of Inertia of the given specimen
using Compound Pendulum

CMR Institute of Technology Page ii
CMR INSTITUTE OF TECHNOLOGY
VISION: To create world class technocrats for societal needs.
MISSION: Impart global quality technical education for a better future by providing
appropriate learning environment through continuous improvement and customization.
QUALITY POLICY: Strive for global excellence in academics & research to the
satisfaction of students and stakeholders.
Department of Mechanical Engineering (ME)
Vision: To be a centre of excellence committed to provide quality education and research
for nurturing technically competent and socially responsible mechanical engineering
professionals
Mission
• Provide fundamentals and state of art technical knowledge in frontier areas of
Mechanical Engineering.
• Emphasize on collaborative research and consultancy by initiating MOUs with
industries and R&D organizations.
• Enrich self learning, professional ethics, entrepreneurship and leadership through
effective interaction with stakeholders to handle real world challenges.
I. PROGRAMME EDUCATIONAL OBJECTIVES (PEO’s)
1. Core capabilities / competence: Enrich fundamental knowledge in mathematical,
scientific and engineering concepts with core competency in diversified fields to analyze
and solve the mechanical engineering problems. [PO’s: 1,2,3,4,5,6,7,8,9,10,11,12 ] &
[PSO’s: 1, 2, 3]
2. Career advancement: Inculcate design & analysis skills on par with technological
changes in core and allied domains for pursuit of higher education & research, careers
and entrepreneurship. [ PO’s: 1,2,3,4,5,6,7,8,9,10,11,12] & [PSO’s: 1, 2, 3]
3. Life-long Learning: Infuse life-long learning, ethical and professional implications /
responsibilities along with ability to communicate effectively to adapt to innovation and
change with a sense of social and environmental concern. [PO’s: 1,2,3,6,7,8,9,10,11,12]
& [PSO’s: 2,3]
II. PROGRAMME OUTCOMES (PO’s)
1. Engineering knowledge: Apply the knowledge of mathematics, science, engineering
fundamentals, and an engineering specialization to the solution of complex engineering
problems. [PEO’s: 1, 2, 3] &[PSO’s: 1, 2, 3]
2. Problem analysis: Identify, formulate, review research literature, and analyze complex
engineering problems reaching substantiated conclusions using first principles of
mathematics, natural sciences, and engineering sciences. [PEO’s: 1,2,3] &[PSO’s:
1,2,3]

CMR Institute of Technology Page iii
3. Design/development of solutions: Design solutions for complex engineering problems
and design system components or processes that meet the specified needs with
appropriate consideration for the public health and safety, and the cultural, societal, and
environmental considerations. [PEO’s:1,2,3] &[PSO’s: 1, 2, 3]
4. Conduct investigations of complex problems: Use research-based knowledge and
research methods including design of experiments, analysis and interpretation of data,
and synthesis of the information to provide valid conclusions. [PEO’s: 1, 2] & [PSO’s:
1, 2, 3]
5. Modern tool usage: Create, select, and apply appropriate techniques, resources, and
modern engineering and IT tools including prediction and modeling to complex
engineering activities with an understanding of the limitations. [PEO’s:1,2] &[PSO’s:
1,2,3]
6. The engineer and society: Apply reasoning informed by the contextual knowledge to
assess societal, health, safety, legal and cultural issues and the consequent
responsibilities relevant to the professional engineering practice. [PEO’s: 1, 2, 3]
&[PSO’s: 3]
7. Environment and sustainability: Understand the impact of the professional engineering
solutions in societal and environmental contexts, and demonstrate the knowledge of, and
need for sustainable development. [PEO’s: 1, 2, 3] &[PSO’s: 1, 3]
8. Ethics: Apply ethical principles and commit to professional ethics and responsibilities
and norms of the engineering practice. [PEO’s: 1, 2, 3] &[PSO’s: 3]
9. Individual and team work: Function effectively as an individual, and as a member or
leader in diverse teams, and in multidisciplinary settings. [PEO’s: 1, 2, 3] &[PSO’s: 1,
2, 3]
10. Communication: Communicate effectively on complex engineering activities with the
engineering community and with society at large, such as, being able to comprehend and
write effective reports and design documentation, make effective presentations, and give
and receive clear instructions. [PEO’s: 1, 2, 3] &[PSO’s: 1, 2, 3]
11. Project management and finance: Demonstrate knowledge and understanding of the
engineering and management principles and apply these to one’s own work, as a
member and leader in a team, to manage projects and in multidisciplinary environments.
[PEO’s: 1, 2, 3] &[PSO’s: 1, 2, 3]
12. Life-long learning: Recognize the need for, and have the preparation and ability to
engage in independent and life-long learning in the broadest context of technological
change. [PEO’s:1,2,3]&[PSO’s: 1, 2, 3]
III. PROGRAMME SPECIFIC OUTCOMES (PSO’s)
1. Apply fundamentals of mathematics, basic sciences and engineering by using state of art
technologies to solve the problems related to thermal and production fields [PO’s:
1,2,3,4,5,7,9,10,11,12 ] & [PEO’s: 1,2,3]
2. Implement profound knowledge of engineering to model, design, analyze the mechanical
components & systems using design tools such as CATIA, ProE, ANSYS, ABAQUS,
for future research and career advancement. [PO’s: 1,2,3,4,5,9,10,11,12] & [PEO’s:
1,2,3]
3. Ensure employability and career development skills through Industry oriented mini & major
projects, internship, industry visits, seminars and workshops. [PO’s: 6,7,8,9,10,11,12]
&[PEO’s: 1,2,3]

CMR Institute of Technology Page iv
IV. COURSE OBJECTIVES
Course
Objectives
Course Objective Statements
Objective - 1 To make students understand force system and the resultant of force
system.
Objective - 2 To make students experimentally calculate the reactions at the support
of a given beam
Objective - 3 To make students understand the principle of moment using a bell
crank lever
Objective - 4 To make students understand the concept of friction between two
surfaces
Objective - 5 To make students understand the concept of moment of inertia of a
flywheel
Objective –6 To understand the concept of mechanical advantage and velocity ratio
V. COURSE OUTCOMES
After completion of the course the student will be able to
Course
Outcome
Course Outcome Statements
CO – 1 Determine the resultant of a given force system
CO – 2 Calculate the reactions at the support of a given beam
CO – 3 Apply the principle of moment to calculate unknown forces
CO – 4 Determine the frictional force between two surfaces
CO – 5 Determine moment of inertia for given flywheel
CO- 6 Determine the mechanical advantage and velocity ratio for simple
machines
VI. COURSE MAPPING WITH PEO’S, PO’S, PSO’S
(No correlation: 0; Low: 1; Medium: 2; High: 3)
Cour
se
Title
PEO1
PEO2
PEO3
PO1
PO2
PO3
PO4
PO5
PO6
PO7
PO8
PO9
PO10
PO11
PO12
PSO1
PSO2
PSO3
EM
Lab
3 0 1 3 3 2 2 0 1 0 0 2 2 0 1 3 2 1

CMR Institute of Technology Page v
VII. MAPPING OF COURSE OUTCOMES WITH PEO’S, PO’S, PSO’S
(No correlation: 0; Low: 1; Medium: 2; High: 3)
Course
Outco
mes
PEO1
PEO2
PEO3
PO1
PO2
PO3
PO4
PO5
PO6
PO7
PO8
PO9
PO10
PO11
PO12
PSO1
PSO2
PSO3
CO - 1 3 0 1 3 3 2 2 0 1 0 0 2 2 0 1 3 2 1
CO – 2 3 0 1 3 3 2 2 0 1 0 0 2 2 0 1 3 2 1
CO – 3 3 0 1 3 3 2 2 0 1 0 0 2 2 0 1 3 2 1
CO – 4 3 0 1 3 3 2 2 0 1 0 0 2 2 0 1 3 2 1
CO – 5 3 0 1 3 3 2 2 0 1 0 0 2 2 0 1 3 2 1
CO-6 3 0 1 3 3 2 2 0 1 0 0 2 2 0 1 3 2 1

CMR Institute of Technology Page vi
INDEX
ENGINEERING MECHANICS LAB
S.
No.
Name of the Experiment Page
Date of
Experiment
Date of
Submission
Faculty
Sign
1 UNIVERSAL FORCE TABLE
2 BELL CRANK LEVER
APPARATUS
3 JIB CRANE APPARATUS
4 LAW OF MOMENTS
APPARATUS
5 MOMENT OF INERTIA OF
FLY WHEEL
6 SCREW JACK APPARATUS
7 COMBINED INCLINED
PLANE AND FRICTION
SLIDE APPARATUS
8 POLYGON LAW OF FORCE
APPARATUS
9 PARALLEL LAW OF FORCE
APPARATUS
10 WORM AND WORM WHEEL
APPARATUS
11 DIFFERENCIAL AXEL AND
WHEEL
12 COMPOUND PENDULUM

CMR Institute of Technology Page 1
Experiment – 1
UNIVERSAL FORCE TABLE
AIM:-
To verify polygon law of forces using Universal Force Table.
APPARATUS:-
Universal force table apparatus complete with freely moving and adjustable guide pulleys
(fig-1), a ring with five strings, weight hangers, weight etc.
COMPONENTS:-
1. Rope pulley
2. Slotted weight
3. Rope
4. central ring
THEORY:-
Polygon law of forces state that if a number of coplanar forces acting on a particle are
represented in magnitude and direction by the sides of a polygon taken in order, then their
resultant is represented in magnitude and direction by the closing side of the polygon taken in
order.
PROCEDURE:-
1. Clamp the pulleys to the graduated disc of the force table and make it horizontal by
adjusting the screws at its base.

2. Tie each end of five strings to the circumference of a small ring and place it round the pin
.Attach the other end of the strings to weight hangers, hanging over the pulley.
3. Put small weights on the weight hangers in such a manner that the ring is placed
symmetrically round the axis and it does not touch the axle of the apparatus or the plane
surface of the graduated scale.
4. Note the position of any one string on the disc and then find the angles between the
strings as θ1, θ2 ,θ3,θ4 and θ5
5. Note down the magnitudes of weights W1, W2, W3, W4 and W5 acting on the string.
6. Draw the space diagram of the forces F1= W1, F2= W2, F3= W3, F4= W4 and F5= W5 as
shown in fig.2(a).
7. Draw the vector diagram abcde as shown in fig.2(b).If the last force F5 represented by the
side ea falls short or is greater than the side which would complete the polygon ,then
measure the side which would complete the polygon and find the percentage error
between the force F5 and the force required to complete the polygon.
8. Measure the angle a’
ab i.e. α which would be equal to θ5.If they are different, then find
the percentage error between these angles taking any of them to be true angle.
9. Repeat the experiment with different set of weights.
PRECAUTIONS:-
1. The graduated disc should be made horizontal by adjusting the screws at its base. This
can be checked with the help of a sprit level.
2. The ring should not touch the pin or the disc.

3. The pulleys should be frictionless i.e well lubricated.
4. The positions of the strings should be carefully noted only after the system has come to
test completely.
RESULT:-

QUESTIONS:-
1. What is parallelogram law of forces?
2. What is triangular law of forces?
3. What is polygon law of forces?
.
4. What is force system?
5. What is coplanar concurrent force system?

Experiment – 2
BELL CRANK LEVER APPARATUS
AIM:-
To verify the principle of moments using bell crank lever.
APPARATUS REQUIRED: - Bell Crank Lever apparatus, slotted weight, spirit meter, spring
balance, meter scale and pointer
Fig. 2.1 Bell Crank Lever Apparatus
THEORY:-
The bell crank lever is an apparatus used to verify the law of moments. The bell crank is used to
convert the direction of reciprocating movement. A bell crank is a type of crank that changes
motion around a 90 degree angle. The name comes from its first use, changing the vertical pull
on a rope to a horizontal pull on the striker of a bell, used for calling servants in upper class
British households. The fixed point of the lever about which it moves is known as the fulcrum.
The bell crank consists of an "L" shaped crank pivoted where the two arms of the L meet.
Moving rods (or ropes) are attached to the ends of the L arms. When one is pulled, the L rotates
around the pivot point, pulling on the other arm.
Changing the length of the arms changes the mechanical advantage of the system. Many
applications do not change the direction of motion, but instead to amplify a force "in line", which
a bell cranks, can do in a limited space. There is a tradeoff between range of motion, linearity of
motion, and size. The greater the angle traversed by the crank, the more non-linear the motion
becomes (the more the motion ratio changes).
According to law of moments “the moment of a force about an axis is equal to the sum of
moment of its component about the same axis.”

F
x
r
M 
=

PROCEDURE:-
1. Make the longer arm of the lever horizontal by adjusting with wing nut provided at the
end of spring balance longer screw, by using a spirit meter when there is no load on
longer arm.
2. Adjust the initial spring balance reading as zero.
3. Hang a small weight (W) on the hook fixed in the lever. This will make the longer arm
move down ward and the spring balance will show some reading on balance
4. Note the final spring balance reading.
5. Change the position of load and repeat the steps B to D for different loads and calculate
the moments.
6. Take at least six readings
ANALYTICAL CALCULATION
Fig 2.1Free body diagram
Free body diagram of the bell crank lever shown in fig 2.1 here
W=Force applied on lever
D= Varing distance on lever
S’=Theoretical Spring Force
S=Experimental Spring Force
d=Fixed distance, measure from the fulcrum of equipment
As the system is in equilibrium
0
0 =
M
W*D-S’*d=0

OBSERVATIONS:-
PRECAUTIONS:-
1. There should be minimal disturbance as long as the pointer is concerned.
2. Only one person must take all the readings, because eye –judgment for matching the
pointer with the mark on the lever will vary from individual to individual.
3. Weights should not touch the table.
4. Add weights in the hanger gently.
5. The pointer should exactly coincide with the mark on the bell crank lever.
6. The optimum starching of spring should be kept in mind.
7. The apparatus should be kept on smooth and leveled surface.
8. Proper lubrication of the joints of two arms of the lever should be done so as to reduce
frictional force.
9. Zero .error of the spring should be properly noted.
RESULT:-

QUESTIONS:-
1. Define moment of a force?
2. What is couple?
3. What is crank shaft?
.
4. What is the purpose of shaft?
5. What is lever?

Experiment – 3
JIB CRANE APPRATUS
AIM:-
To verify the force in the members of a jib crane.
APPARATUS:-
Jib crane apparatus weights, metre rod etc.
THEORY:-
The experiment is based upon “the triangle law of forces”. Triangle law of forces states that
If two coplanar concurrent forces acting upon a body can be represented in magnitude and
direction by two sides of a triangle taken in order , then their resultant is represented in
magnitude and direction by the third side of the triangle taken in opposite order.
PROCEDURE:-
1. Note down the initial reading of spring balance in the tie and the compression balance in
the jib.
2. Attach a known weight W hook to the hanging chain.
3. Note down the final readings on the balances of tie and jib separately.
4. Subtract the initial readings from the final readings. The difference between the two
readings of the tension spring balance will give the observed value of the force in the tie
and that of the compression spring, the observed value of the force in the jib.
5. Measure the lengths of vertical post, tie rod and jib.
6. From the measurements of length (taken to a suitable scale) draw the space diagram as
shown in Fig.4(a).Name the members by Bow’s notation.

7. For the three forces T,C and W acting at point C, draw vector diagram on some suitable
scale as shown in fig.4(b).Then vector pr and qr represent forces in the tie(tension) and
jib (compression) respectively.
8. In triangle ABC, measure the angles α, β, and  .Using sine formula, calculate the values
of C and T.


 Sin
T
Sin
C
Sin
W
=
=
9. Calculate the percentage error in the observed and calculated values of forces in the jib
and tie rod.
OBSERVATIONS:-

1. Zero error (Initial reading) in the tension spring balance =……
2. Zero error (Initial reading) in the compression spring balance =…..
3. Length of tie =…..
4. Length of the jib =…..
5. Height of post =….
PRECAUTIONS:-
1. The weights should be suspended gently without any jerk.
2. The jib and tie spring balances must be properly oiled for free moment.
3. The initial and final readings of the tie balance and composition balance should be taken
carefully.
4. Measure the length accurately.
RESULT:-

QUESTIONS:-
1. What is lami’s theorem?
2. What is triangular law of force?
3. Define tension?
.
4. Define compression?
5. Define coplanar force sytem?

Experiment – 4
LAW OF MOMENT APPARATUS
AIM: -
To verify the law of moment by rotating disc apparatus.
THEORY & FORMULA USED:-
The law of moment’s states that if a number of coplanar forces acting on a rigid body
keep it in equilibrium then the algebric sum of their moments about any point in their plan is
zero.
PROCEDURE:-
1. Put weights in the two pans A and B. such that w1 is the weights in the pan A plus
weight of the pan & W2
weight in the pan B plus weight of pan B. Note down W1
.
2. Rotating disc should be placed at a Centre point note the thread are showed at zero on
the scale.
3. Now (W1 x X1)
will be equal to (W2
x X2
) that is both the clockwise and anticlockwise
and anticlockwise moments will be equal.
4. Take different sets of reading and find out the value of both the moments.
5. If both the moment are not equal then find out the percentage error between the clockwise
moment and the anti-clockwise moment.

OBSERVATIONS:-
W1 = weight in the pan A
W2 = weight in the pan B
X1 = distance from the Centre point of the apparatus to the end of thread shadow show in the
mirror scale of which pan A
X2
= distance from the Centre point of the apparatus to the end of thread shadow show in the
mirror scale of which pan B
S. Weight of pan + Weight of pan + X1
X2
Percentage
No. Weight in pan (W1) Weight in pan (W2) (c.m.)
(c.m.)
Error
1.
2.
3.
PRECAUTIONS:-
1) Weights should be placed in the pans A and B gently.
2) Take in to the account the weights of the pan.
3) Lubricate the apparatus.
4) Distance should be noted down careful
RESULT:-

QUESTIONS:-
1. What is rigid body?
2. What is resistance body?
3. Define principle of moment?
.
4. What is weight?
5. What is principle of transmissibility of force?

Experiment – 5
MOMENT OF INERTIA OF FLYWHEEL
AIM: -
To find the moment of Inertia of a Fl y Wheel.
APPARATUS USED:-
1. Fly Wheel
2. Meter Scale
3. Weight
DESCRIPTION OF APPARATUS:-
A flywheel is a large heavy wheel, through the center of which passes a long
cylindrical axle. The center of gravity lies on its axis of rotation so that when it is mounted
over ball bearing, it comes to rest any desired position.
To increase the moment of inertia, it is usually made thick at the rim.
To count the number of revolution made by the wheel, a lime is marked on the circumference.
A string is wound on the axle, attached to the peg carries a mass M.

THEORY:-
When a weight is suspended to the free end of a cotton string which is wrapped round tin:
shaft and the other end of which is tied to the shaft and it is allowed to fall to touch the ground
then P.E. energy possessed by the falling weight has partly been used to give motion to the fly
wheel and partly used in overcoming frictional resistance present in the bearings.
1. Initial Potential Energy (P.E.) =Wxh when h is the height of the weight from
the level ground.
2. Initial Kinetic energy (K.E.) = 0. Final P.E = 0.
3. Final 2
2
2
2
. w
g
I
v
g
W
E
K +
= ,where ½ (W/g) v2
is the K. E of the falling wt.
And ½ I (w2
/g) is the K. E. of the fly wheel and shaft combined and w is the
final angular velocity of the wheel or of the shaft.
4. Work done due to frictional resistance = F x h where F is the force of friction
acting tangentially to the shaft.
From law of conservation of Energy we can write
2
2
2
2
2
2
)
(
2
)
(
2
2
2
w
Wv
h
W
gh
Iw
Wv
xh
F
W
g
Fxh
w
g
I
v
g
W
WXh
−
−
+
=
−
+
+
=
But v (final velocity) is given by the formula (u+v)/2 = h/2 where t is the time taken for the
weight to fall a distance h so that h/t is the average velocity.
PROCEDURE:-
1. Attach a mass M (about 500 grams) to one need of the thin thread and loop is made at the
other end which is fastened at the peg.
2. The thread is wrapped evenly round the axle of wheel.
3. Allow the mass to descend slowly & count the number revolution N1 during descent.

4. .When the thread has unwound itself & detached from the axle after N1 turns, start the
stop watch. Count the number revolution before the flywheel comes to rest & stop the
stop watch. Thus N2 are known.
5. With the help of Vernier caliper, measure the diameter at several point. Thus find R.
6. Repeat the experiment with three different masses.
7. Calculate the value of I using the given formula.
MATHEMATICAL CALCULATIONS:-
Moment about axis OX,
Consider an elementary ring of radius ‘x’ and thickness dx
Moment of inertia of this elementary ring about axis OX
2
2
dmx
=
dx
x
xdxx
3
2
2
2



=
=
Integrating the above equation we get moment of inertia about OX axis
4
2
mr
IOX =
By symmetry
4
2
mr
IOY = and
2
2
mr
IOZ =

OBSERVATIONS:-
S.No Total load
applied M kg
No of
revolutions
of Flywheel
before the
mass
reattached
N1
No of
revolutions of
Flywheel to
come to rest
after mass
deatached
N2
Mean
N2
Time of N2
revolution
T seconds
Mean T
sec
PRECAUTIONS:-
1. Note the time accurately to the fraction of a second
2. Note the value of F when the motion just begins and the fly wheel does not move
with any acceleration
3. Oil the bearings to reduce friction
4. Overlapping of the string should be avoided.
5. Note the time thrice for the same weight (W)
RESULT:-

QUESTIONS:-
1. What is area moment of inertia?
2. What is mass moment of inertia?
3. What is radius of gyration?
4. What is the unit of MI?
5. What is the purpose of flywheel?

Experiment – 6
SCREW JACK APPARATUS
AIM:-
To determine the mechanical advantage, velocity ratio and efficiency of a square
threads screw jack.
THING REQUIRED:-
1. Screw jack apparatus
2. Weights
3. String
4. Meter rod
5. Out side calliper
6. Pan.
THEORY:-
Screw jack is used to raise heavy loads .The apparatus works on the simple principle of
screw and nut .The axial distance between the corresponding points on two consecutive
threads is known as pitch .Let this pitch be p and d , the diameter of the flanged table on
which the load W is to be applied and lifted .Let the table turn through one revolution
Distance through which load rises in one revolution = p
Effort moved in one revolution =πd
Weight on the table =W kg
Total effort in two pans including weights of the pans=P kg
The Mechanical Advantage (M.A)=W/P
Efficiency  =(M.A/V.R)x100, V.R =Velocity Ratio

PROCEDURE:-
1. Measure the circumference of the flanged table with an inextensible thread and
meter rod and calculate the flanged table diameter. Alternatively, measure the
diameter of the flanged table with the help of vernier calipers.
2. Wrap the string round the circumference of the flanged table and pass it over one
pulley .Similarly wrap another string over the circumference of the flanged table
and take it over the second pulley. The free ends of the both the strings are tied to
two pans in which the weights are to be placed.
3. Measure the pitch of the thread with the help of vernier calipers.
4. Place the load W on the flanged table and put some weights in the pans so that the
load W is just lifted. The effort P is equal to sum of weights placed in the both the
pans.
5. Increase the load and find the corresponding efforts applied for the consecutive
readings .Take at least five readings.
6. Calculate the M.A. , VR., and percentage of efficiency  each case.
OBSERVATION TABLE:-
S.No Load on table
Kg
Effort P=P1+P2
Kg M.A=W/P  =(M.A/V.R)x100
PRECAUTIONS:-
1. Use the the pulleys to find the value of effort P to avoid the side thrust.
2. The load and effort should be moved slowly.
3. Add weights in the pan gently.
4. Lubricate the screw to decrease friction.
5. The string should not overlap.
6. There should be no knot in the string.
RESULT:

QUESTIONS:
1. What is pitch?
2. How you measure the pitch
3. Explain machine is self locking?
4. On which principle screw jack works?
5. What is the nature of the graph of actual effort vs Load?
6. What is the nature of the graph of efficiency vs Load?

Experiment – 7
COMBINED INCLINE PLANE AND FRICTION SLIDE
APPARATUS
AIM:-
Determination of Coefficient of friction by the inclined plane apparatus.
DESCRIPTION:-
When a body slides upon another body, the property by virtue of which the motion of one
relative to the other is related is called friction. The frictional force is directly proportional to the
normal reaction. Suppose a body of weight is to be lifted by inclined plane & this requires effort
when this load just move upward a frictional force acts downward which oppose its motion.

APPARATUS:-
1. Inclined Plane
2. 4 sliding boxes with different surfaces
3. String
4. Pan
5. Thread
THEORY:-
When a body slides upon another body, the property by virtue of which the motion of one relative to
the other is related is called friction. The frictional force is directly proportional to the normal reaction
‘N’.
N
F
N
F
N
F
=
=



Suppose a body of weight W is to be lifted by inclined plane & this requires effort P. when this load
just move upward a frictional force F acts downward which oppose its motion.
Component of load W parallel to the plane =
Component of load W perpendicular to the plane =
Considering equilibrium parallel to the plane
P = F + W sin
F = P – W sin ……(i)
Considering equilibrium perpendicular to the plane
N= W cos ……….(ii)
From (i) & (ii)
Co – efficient of friction,



cos
W
WSin
P
N
F −
=
=

PROCEDURE:-
1. Take the inclined plane apparatus & keep it first horizontal and put the slider on it.
2. Increase the inclination of inclined board gradually till the slider just begins to slide
downwards on it.
3. Note the angle in this position. This is called angle of repose.
4. Place the slider on the plane with the desired angle α.
5. Tie the slider to the pan with the help of thread passing over the pulley.
6. Put the weight in the pan till the slider just start moving. Note down the weight.
7. Measure the angle of inclination from the scale provided & finds the value of μ.
8. Calculate M.A., V.R., efficiency.
OBSERVATIONS:-
S.No Total weight of the slider
W
Weight of pan plus
weights in the pan
P



cos
W
WSin
P −
=

PRECAUTIONS:-
1. The plane should be clean & smooth.
2. The guide pulley should move freely. It should be lubricated to make it frictionless.
3. Weight should be added gently in pan.
4. The slider should just begin to move slowly, it should not move abruptly.
5. The direction of thread should be parallel to the inclined plane.
RESULT:-

QUESTIONS:
1. What is friction?
2. What are the different types of friction?
3. What is dynamic friction?
4. What is angle of friction?
5. What is angle of repose?

Experiment – 8
POLYGON LAW OF FORCE APPARATUS
AIM:-
To verify the polygon law of forces
APPARATUS:-
1. Gravesand apparatus
2. Paper Sheet
3. Weight box
4. Thread
5. Drawing pins
6. Pans
7. Set square
8. Pencil
.

THEORY:-
“Polygon law of apparatus” states that if a number of forces acting on a particle are
represented in magnitude & direction by sides of a polygon taken in same order, then their
resultant is represented in magnitude and direction by the closing side of the polygon taken in the
opposite direction.
PROCEDURE:-
Set the board in a vertical plane & fix the paper sheet with drawing pins
1. Pass a thread over two pulleys
2. Take a second thread & tie the middle of this thread to the middle of first thread
3. Pass the ends of second thread over the other set of two pulleys
4. Take a third thread & tie its one end to the point of first two threads
5. Attach pans to the free ends of the threads
6. Place the weights in the pans in such a manner that the knot comes approximately in
the Centre of the paper.
7. Mark the line of forces & write down the magnitude of forces
8. Remove the paper from the board & produce the line to meet at Centre point O
9. Select a suitable scale & draw the vector diagram by moving in one direction. draw a b
parallel to A B & cut it equal to force P; draw b c parallel to B C & cut it equal to Q;
draw c d parallel to C D & cut it equal to force R; draw d e parallel to D E & cut it equal
to force S. vector a e will be the resultant force T1 taken in the opposite direction &
should be equal to force T which proves the law of polygon forces. If area is not equal
to T then percentage error is found as follows.

PRECAUTIONS:-
1. Pans/weights should not touch the board
2. There should be only one central knot on the thread which should be small
3. While calculating the total force in each case the weight of the pan should be added to the
weights put into the pan.
4. Make sure that all pans are at rest when the lines of actions of forces are marked
5. All the pulleys should free from friction.
RESULT:-

QUESTIONS:
1. What is polygon law of force?
2. What is force?
3. What are characteristics of force ?
4. What is resultant?
5. Write the SI unit of force?

Experiment – 9
PARALLEL FORCES APPARATUS
AIM:-
To verify the principle of forces in beam of Parallel Forces Apparatus with the help of
beam supported at its ends.
THINGS REQUIRED:-
Parallel Forces Apparatus 10 Kg tubular Type, Conical Weights, and Aluminum hangers
for hanging weights.
APPARATUS:-
The apparatus comprising of two tubular weight gauges of 10 kg, one straight wooden
beams of 1m, a wooden platform for the support of the dial gauges, three weight hangers for
hanging the weights on the wooden beams, three weights weighing 2kg aggregate. The beam is
provided with angular slots on them in order to place the hanger in it, the distance between each
groove is 5cms. The weight of each hanger will be neglected.
The whole apparatus is well designed & painted.
THEORY:-
If systems of coplanar forces acting on a rigid body keep it in equilibrium then the algebraic sum
of their moments about any point in their plane is zero. Normally a beam is analyzed to obtain
the maximum stress and this is compared to the material strength to determine the design safety
margin. It is also normally required to calculate the deflection on the beam under the maximum
expected load. The determination of the maximum stress results from producing the shear and
bending moment diagrams.

The sign convention used for shear force diagrams and bending moments is only
important in that it should be used
consistently throughout a project. The sign
convention used on this page is as below.
NOMENCLATURE:-
e = strain
σ = stress (N/m2)
E = Young's Modulus = σ /e (N/m2)
y = distance of surface from neutral surface (m).
R = Radius of neutral axis (m).
I = Moment of Inertia (m4 - more normally cm4)
Z = section modulus = I/ymax(m3 - more normally cm3)
M = Moment (Nm)
w = Distributed load on beam (kg/m) or (N/m as force units)
W = total load on beam (kg ) or (N as force units)
F= Concentrated force on beam (N)
S= Shear Force on Section (N)
L = length of beam (m)
x = distance along beam (m)

PROCEDURE:-
1. First of all arrange the apparatus by placing the beams on the given tubular gauges as
shown in the figure. Note the zero error in the compression balances. When the beams
are supported at it ends.
2. Suspend three different weights from the sliding hook against any division marked
on the beam.
3. Note the reaction on the beam given by the readings of compression balances and
takes into account the zero error from each reading.
4. Find the sum of clockwise moment about the mid points of the beam and find also the
sum of anti-clockwise moment about its each reading.
5. Find the % age error between clockwise and anti-clockwise moment.
6. Suspend three or four weights at different graduated division of the beam and find
%age error between clockwise and anti –clockwise moments as before.
CALCULATIONS:-
Taking Moment About A,
RB Χ L – W1L1 – W2L2 = 0
RB = W1L1 + W2L2
L
But RA + RB = W1 + W2
RA = (W1 + W2) - RB

Take in this manner about seven readings.
PRECAUTIONS:-
1. Zero error of the compression balances must be taken in to account,
2. Weights should not be put on the beam with a jerk.
3. Slightly press h beam in to remove any frictional resistance at the supports before
taking readings.
RESULT:-

QUESTIONS:
1. What is parallel force system?
2. What is beam?
3. What are the different types of loads?
4. What are the different types of beams?
5. What is point and udl load?

Experiment – 10
WORM AND WORM WHEEL APPARATUS
AIM: - To determine the mechanical advantage, velocity ratio and efficiency of a worm and
worm wheel.
APPARATUS REQUIRED:-
1. Worm and worm wheel apparatus
2. Conical weight
THEORY:-
As the pulley moves through N revolutions, n teeth of the wheel pass completely through the
worm .If there are N teeth in pulley of the worm to rotate completely the worm moves
through n revolution the load is raised up by the a distance equal to the length of the
circumference of the pulley of the worm wheel.
V.R = (N x Circumference of pulley of worm)/Circumference pulley of worm wheel
PRECEDURE:-
1. Wrap the sting round the pulley of the worm the free end of which is to be tied to the
effort.
2. Wrap another string to carry the load of the pulley the worm wheel in such a manner
that as the effort is applied is lifted up.
3. Suspend a small weight W through the free string, which should just move the load
upward.
4. Note W and P, so that mechanical advantage is given by W/P.
5. Increase the load gradually and increase effort correspondingly and take in this way
about seven readings.
6. Measure the circumference of the pulley of the worm and also that of the worm
wheel.
7. The percentage efficiency is given by = ( W*100)/PV
OBSERVATIONS:-
Circumference of the pulley of the worm = 2ΠR1=--------------------
Circumference of the pulley of the worm wheel =2ΠR2=----------------------
Number of teeth in the worm wheel is N =
V.R = (N x 2ΠR1)/ 2ΠR2
Mechanical Advantage = W/P=---------------------
Efficiency =( W*100)/PV
RESULT:-

QUESTIONS:
1. What is velocity ratio?
2. What is mechanical advantage
3. What are the advantages of gears?
4. What are the different types of gears?
5. What is the purpose of worm and worm gear?

Experiment – 11
DIFFERENCIAL AXEL AND WHEEL
AIM: - To study the performance of differential axle and wheel and find its velocity ratio,
efficiency and law of machine etc
Apparatus: Differential axle and wheel consisting of effort wheel, larger axle, smaller axle,
thread, pan, weights
THEORY:-
i. Parts of machine: Differential axle and wheel consisting of effort wheel, larger axle and
smaller axle.
ii. Working of machine: The load axle is made up of two parts to the same shaft which is
mounted on the shaft ball bearing in order to reduce the frictional resistance. The effort string
is wound around the axle to which the effort pan is attached.
VELOCITY RATIO: In one revolution of effort wheel, displacement of effort wheel is Sp =
πD1
Distance travelled by load = (πd1-πd2)/2
Sw = (πd1-πd2)/2
Therefore V.R. = Sp / Sw = (πD1) / ((πd1-πd2)/2)
= 2 πD1 / (πd1-πd2)
PROCEDURE:-
i. Check that string is wound properly on wheel A, B, and C.
ii. Different loads are applied and corresponding efforts are recorded.
iii. To keep friction constant readings are taken at particular point.
iv. From above observation V.R., M.A., and efficiency of machine are calculated.
OBSERVATIONS:-
1. Circumference of Effort wheel: πD1
2. Circumference of bigger axle: πd1
3. Circumference of smaller axle: πd2
4. Distance travelled by effort: Sp = πD1
5. Distance travelled by load: Sw= (πd1-πd2)/2
6. Velocity Ratio = Sp/Sw = (πD1) / ((πd1-πd2)/2) = 2 πD1 / (πd1-πd2)

OBSERVATION TABLE:-
S.NO
Load (W)
Newton
Effort
(Pa)
Newton
M.A. =
W/Pa
η%=
M.A./V.R.
* 100
Pi =
W/V.R.
Pf = Pa-
Pi
1
2
3
4
5
RESULT: -
i. V.R. of machine =
ii. Efficiency of machine =
iii. Percentage of efficiency of machine =
iv. Law of machine is given as P = mW+C
CONCLUSION: -
i. As the efficiency is greater than 50%, machine is reversible.
ii. Velocity ratio remains constant.
iii. Effort of machine increases with load.
iv. Graph of effort against load is a straight line represents linear motion.

QUESTIONS:-
1. What are different parts of machine?
2. Why velocity ratio remains constant?
3. Machine is reversible / irreversible?
4. How you calculate M.A.?
5. What is the nature of the graph of Ideal effort vs Load?

Experiment – 12
COMPOUND PENDULUM
AIM:- To determine the radius of gyration and mass moment of inertia of the given
rectangular rod experimentally.
APPARATUS REQUIRED:-
1. Vertical frame,
2. Rectangular rod,
3. Stop watch
4. Steel rule etc
THEORY:-
In this experiment we shall see how the period of oscillation of a compound, or physical,
pendulum depends on the distance between the point of suspension and the center of
mass. The compound pendulum you will use in this experiment is a one metre long bar of
steel which may be supported at different points along its length, as shown in Fig. 1.

I-B.Tech.-I-Semester (CE) Engineering Mechanics Lab
CMR Institute of Technology
PROCEDURE:-
1. Suspend the pendulum in the first hole by choosing the length 5 cm on the
length slider.
2. Click on the lower end of the pendulum, drag it to one side through a small
angle and release it. The pendulum will begin to oscillate from side to side.
3. Repeat the process by suspending the pendulum from the remaining holes by
choosing the corresponding lengths on the length slider.
4. Draw a graph by plotting distance d along the X-axis and time period T along
the Y-axis. (A spreadsheet like Excel can be very helpful here.)
5. Calculate the average value of l/T2
for the various choices of T, and then
calculate g as in step 2 above.
6. Determine kG and IG as outlined in steps 3 and 4 above.
7. Repeat the experiment in different gravitational environments by selecting an
environment from the drop-down environment menu. If the pendulum has
been oscillating, press the Stop button to activate the environment menu.
FORMULAE USED:-
1. Time period T= t/N sec
T = 2π√((K2
+ l 2
)/gl))
2. Experimental time period
Where K= experimental radius of gyration
l= distance from point of suspension to centre of gravity of rod
L= total length of the rod
Kt = L/√12 =0.2866L
3. Theoretical radius of gyration,
4. Natural frequency fn = 1/T (Hz) and Moment of inertia Im = mk2
kg-m2
Tabularform :
Sl. Distance
Time for 5 Time Natural
Experimental radius of
oscillations period T frequency
No. L1 (m)
t (sec) (sec) fn (Hz)
gyration (Kexp)
RESULT: -

I-B.Tech.-I-Semester (CE) Engineering Mechanics Lab
CMR Institute of Technology
QUESTIONS:
1. What is radius of gyration?
2. Define time period.
3. What natural frquency?
4. What is mass moment of inertia?
5. What is polar moment of inertia?

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