Applied mechanics lab manual

1APPLIED MECHANICS
GOVT. POLYTECHNIC,
KANGRA
APPLIED MECHANICS
LABORATORY
LAB MANUAL

2APPLIED MECHANICS
LIST OF PRACTICALS
1. Verification of the following laws:
a) Parallelogram law of forces.
b) Triangle law of forces.
c) Polygon law of forces.
2. To verify the forces in different members of jib crane.
3. To verify the reaction at the supports of a simply supported beam.
4. To find the mechanical advantage, velocity ratio and efficiency in
case of inclined plane.
5. To find the mechanical advantage (M.A), velocity ratio (V.R) and
efficiency (η) of a screw jack.
6. To find the mechanical advantage, velocity ratio and efficiency of
worm and worm wheel.
7. To find mechanical advantage, velocity ratio and efficiency of single
purchase winch crab.
8. To find M.A, V.R, and cof :
a) First system of pulleys
b) Second system of pulleys.
9. To find out center of gravity of:
a) Regular lamina
b) Irregular lamina.
10. To determine coefficient of friction between three pairs of given
surface.

3APPLIED MECHANICS
EXPERIMENT NO. 1 (A)
AIM: VERIFICATION OF PARALLELOGRAM LAW OF FORCES
APPRATUS:- Gravesand‟s apparatus complete with two freely moving guide
pulleys, weights, thread, a small central ring, white paper sheet, three scale
pans, tape, a mirror strip, set squares and pencil.
THEORY: The „Parallelogram Law of forces‟ states that if a particle is acted
upon by two forces represented in magnitude and direction by the two sides
of a parallelogram drawn from a point, then the resultant is completely
represented by the diagonal passing through the same point.
PROCEDURE:
I) Take any point O on the plane of paper and draw a line OA Parallel
to forces Z. Similarly draw a line OB parallel to force X.
II) Complete the parallelogram OAC‟B as shown in fig. 2
III) Join O to C‟ which is the diagonal of the parallelogram OC‟ to the
given scale gives the resultant of forces X and Z.

4APPLIED MECHANICS
IV) Draw a line OC equal and opposite to OC‟ which should be equal
to the third force Y.
OBSERVATIONS:
Sr. No. Total
weight PQ
(X)
Total
weight QR
(Y)
Total
Weight RP
(Z)
Resultant
R‟
% age
error
Mean Value…………………………….
PRECAUTIONS:
I) The board should be perfectly vertical.
II) The pulleys should be moving freely and if not moving freely,
lubricate them.
III) The weights should not touch the board.
IV) The weights of the pans should be added to the weight in the pan
to find the total force in each string.
V) The directions of forces should be marked only after the system has
come to complete rest.
VI) The direction of forces should be marked with the mirror strip by
keeping the eye, string and its image in the same line.
•••••••••

5APPLIED MECHANICS
EXPERIMENT NO. 1 (B)
AIM: VERIFICATION OF TRIANGLE LAW OF FORCES
THEORY: The triangle law of forces states that if two forces acting on a
particle can be represented in magnitude and direction by the two side of a
triangle taken in order then their resultant will be given by the third side of the
triangle taken in the opposite direction.
PROCEDURE:
I) Fix the paper sheet centrally on the board.
II) Take suitable length of thread and pass it over two pulleys, the ends
of thread are to be attached to pans which are to carry weights.
III) Take another piece of thread and tie to the middle of first thread
which is to carry another weight.
IV) Place the weights in the pans in such a way that the knot-comes
nearly in the middle of the paper.
V) For ensuring free movement of pulleys, displace the pans from their
original positions.
VI) Mark the directions of the strings on the paper sheet with the help of
a strip of mirror which is put under the string length – wise one by
one to get points for the purpose.
VII) Note the magnitude of forces and mark the lines of forces.
VIII) Remove the paper from the apparatus and produce the forces line
to meet at point O.
IX) Name the forces, X, Y, Z, according the Bow‟s Notation as PQ, QR,
and RS.
X) Choose a suitable scale and draw the line Pq parallel to force X
and cut it equal to the magnitude of X according to the scale
chosen. Now from point q draw the line qr parallel to force Y
according to the same scale. Find the magnitude of rp i.e. R which

6APPLIED MECHANICS
should be equal to the third force Z which proves the triangle law of
forces.
XI) If the magnitude of r p varies from that of the forces QR, then
percentage error =
XII) Repeat the above procedure at least two times more by varying
the loads and tabulate the results.
OBSERVATIONS:
Sr. No. Total
weight PQ
(X)
Total
weight QR
(Y)
Total
Weight RP
(Z)
Resultant
R‟
% age
error
PRECAUTIONS:
lubricate them.
•••••••••

7APPLIED MECHANICS
EXPERIMENT NO. 1 (C)
AIM: VERIFICATION OF POLYGON LAW OF FORCES
THEORY: Polygon law of forces states that if a number of forces acting on a
particle are represented in magnitude and direction by the sides of a
polygon taken in the same order then their resultant is represented in
magnitude and direction by the closing side of the polygon taken in the
opposite direction.
PROCEDURE:
I) Fix the paper sheet centrally on a board with the help of cello tape.
II) Tie five segments of thread to form a knot and pass four of them
over the guide pulleys as shown figure LW-4.
III) Put four weights one each into the pans of the strings passing over
the pulleys.
IV) Attach a pan to the free end of the middle string and put weight
into it.
V) Adjust the weights in the pans in such a way that the knot comes in
the center of paper and allows the system to come in the rest
position.
VI) Put the mirror under the threads turn by turn and mark the points by
keeping the eye, the thread and its image in the same line without
disturbing the system.
VII) Write down the magnitude of forces in each string which will be the
same as the corresponding weights.

8APPLIED MECHANICS
VIII) Draw the vector diagram with suitable scale by drawing vectors ab,
bc, cd, de representing magnitude and directions of corresponding
forces AB, BC, CD, DE as show in fig. LW- 5(a)
IX) Join e to a and measure vector ea with the chosen scale. It should
have the same magnitude and direction as that of the forces EA.
X) The magnitude of ea is different from that of force EA, then
percentage of error =
XI) Repeat the above procedure at least two times more by varying
loads and tabulate the results.
OBSERVATIONS:
Sr.
No.
Suspended Weights of Forces Force ea as
determined
graphically
% age error =
Q=W1 R=W2 S=W3 T=W4 P=W5
PRECAUTIONS:
lubricate them.

9APPLIED MECHANICS
•••••••••

10APPLIED MECHANICS
EXPERIMENT NO. 2
AIM: TO VERIFY THE FORCES IN THE DIFFERENT MEMBERS OF A JIB CRANE.
APPARATUS: Jib Crane apparatus, weights, meter rod, set squares, paper
sheet cello tape etc.
THEORY: This experiment is based on the triangle law of forces. According to
this law if two forces acting on a body can be represented in magnitude and
direction by the two side of a triangle taken in order, then their resultant can
be given by the third side of the triangle, taken in the opposite direction.
Thus with the help of Jib Crane‟s apparatus the three forces i.e. known
load, forces in the tie and that in the Jib are also calculated and the same
are compared with the readings observed from the spring balances, there in.
PROCEDURE:
I) Note the zero error in the compression spring balance and the
tension spring balance separately.
II) Attach a known weight W with the hook of the hanging chain.
III) Note the final reading of the spring balances separately.

11APPLIED MECHANICS
IV) Subtract the initial reading from the final readings. The difference
between the two readings of the spring balances will give the
observed value of the forces in the tie and that of the compression
spring.
V) Measure the height of vertical post from the junction of jib to the
junction of tie and the length of jib and length of tie.
VI) From these measurements, to a suitable scale, draw the space
diagram as shown in this fig LW-7(a) and name the members by
Bow‟s Notation.
VII) Draw ab parallel and equal to W to some convenient scale to draw
vector diagram direction.
VIII) Draw ca parallel to P and bc parallel to Q meeting at c moving in
anticlockwise respectively.
IX) Compare the calculated values of the forces to that of the
observed values and determine the percentage error if any.
X) Repeat the experiment twice by changing the load.
OBSERVATIONS:
Height of Post =
Length of tie =
Length of Jib =
Scale ……………
PRECAUTIONS:
I) The weight should be hung to the hook gently. The initial readings of
balances should be taken into account.
II) The Jib and the tie spring balances must be properly oiled for free
movement.
III) The measurement of length should be done accurately.
IV) The space and force diagram should be carefully and accurately.

12APPLIED MECHANICS
%errorCalculated
forceinkg
TiePJibQ
Observedforce
fromspring
balancesinkg
Tie=P1Jib=Q1
Final
reading
on
balance
inkg
TieJib
Initial
spring
Reading
inKg
TieJib
Lengthof
members
RPQRPQ
Weight W kg
Sr. No.

13APPLIED MECHANICS
EXPERIMENT NO. 3
AIM: To verify the reactions at the supports of a simply supported beam.
APPARATUS: A parallel forces apparatus consisting of a wooden beam, two
compression balances, weights, threads, hooks etc.
THEORY: The experiment is based upon the fundamental principle of
equilibrium which states that if a stationary body, subjected to coplanar
forces, is in equilibrium, the algebraic sum of all the forces and their moments
about any point lying in their plane, is zero.
1) The algebraic sum of vertical forces i.e. ∑F = 0
2) The algebraic sum of moments about a point must be zero i.e. ∑M = 0
PROCEDURE:
I) Place the graduated beam on the compression spring balances.
II) Either adjust the spring balances to zero reading with the help of
adjusting screw or note the initial reading zero reading.
III) Place sliding hooks at different point on the beam and suspend
different weights.
IV) Note down the final readings on the spring balance S1 and S2. These
are called observed readings.
V) Note down the distance of each weight from any one support say
from left.
VI) Take the moments about eh support to calculate the reaction. The
second reaction may be found by subtraction first reaction from
total vertical load. If there is difference in the observed and the
calculated reactions and then calculate the percentage error.
VII) Repeat the experiment by taking different load at different places.

14APPLIED MECHANICS
OBSERVATIONS AND CALCULATIONS:%Errorinreactionsatthe
support
B=A=
Calculated
reactions
RBRA
Distanceof
loadfrom
supportA
X3X2X1
Weight
Suspended
W
3
W2W1
Observe
d
Reaction
at
RBRA
Final
Readingof
Balanceat
BA
Initial
Readingsof
Balanceat
BA
Sr.No.
1
2
3

15APPLIED MECHANICS
By taking moments about A
( )
% age error in the reaction at support A = ………..
% age error in the reaction at support B = ………..
PRECAUTIONS:
1. The apparatus should be placed perfectly horizontal.
2. The balances should be adjusted to zero after placing the beam on
the compression spring balance.
3. The hooks should be place in the groves of the beam.
4. The weights are hung to the hooks gently.
5. The measurement of distances of weights should be done from one
end.
•••••••••

16APPLIED MECHANICS
EXPERIMENT NO. 4
AIM: TO FIND OUT MECHANICAL ADVANTAGE, VELOCITY RATIO AND
EFFICIENCY IN CASE OF AN INCLINED PLANE.
APPARATUS: Inclined plane apparatus, slider Block, Weight box, pan, thread,
meter rod, paper sheet, set squares etc.
THEORY: When a body moves or tends to move over another body its motion
is opposed by a resistance along the surfaces in contact of the two bodies.
The resistance so caused is called force of friction of friction.
Consider a body move up the inclined pane when a force P is applied.
Resolving W into two components.
Mechanical advantage (M.A) =
Velocity ratio (V.R) =
Suppose an effort P moved down through one centimeter, moving the load
along the plane = 1 cm.
Therefore, Vertical up
V.R =

17APPLIED MECHANICS
% efficiency = M.A/V.R x100 = …….
PROCEDURE:
1. Take the suitable inclined plane apparatus and set the plane at a
suitable angle.
2. Place the slider block on the inclined plane and pass the thread over
the frictionless pulley. Let the pan hangs vertically downwards.
3. Note the weights of block and pan. Put some weights in the slider block
and add extra weights in the pan gradually till the slider just tends to
slide over the inclined plane in the upward direction.
4. Note the extra weights placed on the pan, add to it the weight of the
pan, find out the total weight which will be effort P applied to move
the slider block up the inclined plane.
5. Calculate mechanical advantage, velocity ratio and efficiency as
explained and tabulate.
6. Repeat the experiment twice more by varying the load in the slider
block.
OBSERVATIONS:
Nature of surface…………..
Sr.
No.
Weight
of slider
block W.
kg
Weight
of pan
+ wts.
In pan
= P kg
Inclination
of Plane
% age
efficiency
=
M.A. =
W/P
V.R =
cosec
%
efficiency
=
M.A/V.R
x100
1
2
3
PRECAUTIONS:
1. The inclined plane should be smooth and clean.
2. There should be no friction in the pulley. Proper lubrication should be
done to make it frictionless.
3. The weights should be placed gently on the pan.
4. The thread used should be free from knots.
5. The weights should be increased gradually to such a limit that the slider
block just begins to move slowly and not abruptly.
•••••••••

18APPLIED MECHANICS
EXPERIMENT NO. 5
AIM: TO FIND THE MECHANICAL ADVANTAGE, VELOCITY RATIO AND
EFFICIENCY OF SIMPLE SCREW JACK.
APPARATUS: Screw jack apparatus, pans, weights, string, vernier calipers,
meter rod etc.
Theory: The screw jack is a simple machine by means of which heavy loads
can be raised with the application of small effort. It works on the principle of
screw and nut. The screw is rotated with the help of a tommy bar at the end
of which an effort is applied. By doing so, the screw passing through the nut is
raised and so is the load placed on its head.
The screw jack show in Figure is only experimental. It consist of a square
threaded screw which is provide with double flanged circular table at its top
to carry load to be lifted. The heavy body is providing with the two pulleys to
hang the loads which act as an effort.
Let the pitch of the screw be p and D the diameter of the flanged
table on which the load W is to be placed and lifted.
Let the table turns through one revolution.
Then, the distance through which load rises in one revolution = p
Effort moved in one revolution = πD
Weight on the table = W kg

19APPLIED MECHANICS
P = Total effort in the two pans including the weights of pans.
PROCEDURE:
I. Measure the circumference of the flanged table with the help of an
inextensible thread or measure the diameter of table with an
outside calipers.
II. Measure the pitch of thread with the help of vernier calipers.
III. Wrap the string round the circumference of the flanged table and
pass it over one pulley. Similarly warp another string over the
circumference of flanged table and pass it over the second pulley.
The free ends of both the strings be tied to two pans in which the
weights are to be placed.
IV. Note down the weight of each pan.
V. Place the load W on the top of the table and start adding weight in
to the pans so that the load W is just lifted, the effort P is equal to the
sum of weights placed on both the pans.
VI. Calculate the M.A., V.R. and & in each case.
VII. Repeat the experiment twice more by varying the load on the top
of the table and in the pans.
OBSERVATIONS:
Sr.
No.
Circumference
of the Table =
Pitch
of
Screw
P cm
Velocity
Ratio =
Weight
on
Table =
W N
Total
Effort P
= P1 +
P2 + wt.
of pans
M.A
= W/
P
1
2
3
PRECAUTIONS:
1. The circumference of the disc and the pitch of the screw should be
measure precisely.
2. Use both the pulleys to find the total thrust.
3. Lubricate the screw adequately to decrease friction.
4. Make use of both the pulley to find the total effort applied.
5. Put the weights in the pans gently.
6. The string should not overlap on the disc.

20APPLIED MECHANICS
EXPERIMENT NO. 6
AIM: TO FIND THE MECHANICAL ADVANTAGE, VELOCITY RATIO, AND
EFFICIENCY OF A WORM AND WORM WHEEL.
APPARATUS: Worm and worm wheel apparatus, weights string, meter rod,
outside calipers, pan etc.
THEORY: The apparatus consist of a horizontal spindle having worm provided
on it. It is supported between two bearings. On the overhanging portion of
the spindle a pulley is provided to which is attached a string, carrying pan to
its free end where effort is applied. The worm is engaged to the teeth of the
worm wheel which has a projecting drum. Another string is provided on be
drum to which weight to be hanged is hooked. Let,
D= diameter of pulley attached to worm
D = diameter of drum fixed on the wheel
T = number of teeth on worm wheel.
Assuming the worm thread having single start, when one revolution is given to
the pulley only one thread of the worm wheel moves.
Displacement of effort P =
Displacement of load W =
Velocity Ratio V.R =

21APPLIED MECHANICS
Mechanical Advantage =
% age x 100
PROCEDURE:
1. Measure the circumference of both the pulleys and the drum with the
help of a string and meter rod.
2. Wrap the string round the pulley of the worm for effort and also wrap
another string round the drum to carry the load.
3. Suspend a known weight W with the string from the drum and add
weights in the pan, till the load just starts moving upwards.
4. Note down the weight in the effort pan.
5. Calculate the M.A., V.R. and %
6. Repeat the experiment at least twice more by varying the load.
OBSERVATIONS:
Wt. of scale pan =
Diameter of pulley =
Diameter of load drum =
Number of teeth on the worn wheel =
Sr.
NO.
Load W in
kg
Total effort, P
in kg = wt. of
pan + Wt. in
pan
M.A = W/P V.R =
1.
2.
3.
Mean Value…………………………………..
PRECAUTIONS:
i) The bearings of the worm, spindle and teeth of worm-wheel should
be well lubricated to decrease friction.
ii) Weights on the effort pan should be put gently.
iii) The string should not overlap on the pulley or on the drum.
iv) The load and effort should not touch the walls.
v) The load and effort should move slowly.

22APPLIED MECHANICS
EXPERIMENT NO. 7
AIM: TO FIND THE MECHANICAL ADVANTAGE, VELOCITY RATIO AND
EFFICIENCY OF A SINGLE PURCHASE WINCH CRAB.
APPARATUS: Single purchase winch crab apparatus, pan, weights, meter rod,
outside caliper, string etc.
THEORY: It is used to carry the load. It consists of two axles‟ viz. effort axle and
load axle. Both of these are mounted on a rigid frame which is fixed frame
which is fixed on to a wall. The effort axle carries a pinion and a load axle has
drum and a spur wheel which meshes with the pinion. Separate strings are
wound on the drum and their free ends are attached to effort pan and load
respectively.
To find V.R., M.A., and efficiency of a single purchase winch crab, we
may proceed as follows:
Let load lifted = W
Effort applied = P
No. of teeth on the Pinion (A) = T1
No. of teeth on the Gear (B) = T2
Diameter of pulley = D
Diameter of load drum = D
Let the pulley revolves through one revolution.
Distance moved by effort P =
Number of revolutions of spur gear or the load drum =
Distance moved by load =
M.A. = W/P

23APPLIED MECHANICS
%age efficiency =
PROCEDURE:
I) Count the number of teeth of the pinion and spur gear.
II) With the help of string and meter rod measure circumference of the
pulley and the drum.
III) Wrap the string round the effort pulley and attach a scale pan to its
free end.
IV) Wrap the other string round the load drum in such a manner that as
the effort is applied, the load is lifted up.
V) Now suspend a load W with the free end of the string wound on the
drum and add weights in the effort pan so that load starts moving
up gradually.
VI) Note down the values of W and P.
VII) Calculate the V.R., M.A. and efficiency.
VIII) Increase the load W and again find the value of P.
IX) Repeat the experiment at least four times more. To represent
graphically the load versus effort and load versus efficiency curves
proceed as follows.
The load lifted W is taken along the horizontal axis or X – Axis and the effort
is taken along the vertical axis of Y – axis.

24APPLIED MECHANICS
From the tabulated reading marks the points and join them to get a
smooth curve.
It is seen that even at zero value of load, some effort is required to
overcome the friction of the machine.
When the load is increase the effort required to life up the load also
increases.
To represent graphically load versus efficiency, process as given below:
The load is taken along X – axis and the efficiency the Y – axis.
By Marking load and efficiency point corresponding to the load
considered a smooth curve as shown in the fig is completed.
Observations:
Number of teeth of pinion T1 =
Number of teeth of spur gear T2 =
Diameter of pulley D =
Diameter of load drum, d =
Sr. No. Load in W
in Kg
Effort, P in
kg
M.A = W/P V.R =
1.
2.
3.
4.
5.
Mean Value…………………………………

25APPLIED MECHANICS
PRECAUTIONS:
1. Lubricate the pinion and the spur wheel adequately to decrease
friction.
2. The strings on the pulley and drum should not overlap.
3. The weights should be gently put in the scale pan.
4. Add the weight of pan in the total effort.
5. Number of teeth on the pinion and the gear should be carefully
counted.

26APPLIED MECHANICS
AIM: TO DETERMINE THE MECHANICAL ADVANTAGE, VELOCITY RATIO AND
EFFICIENCY OF THE FIRST SYSTEM OF PULLEYS.
APPARATUS: Set of pulleys, scale pan, weights, strings, hooks, meter road, etc.
THEORY: in the first system of pulley numbers of fixed strings are equal to the
number of movable pulleys.
In the figure, pulley number 4 is fixed whereas the others are movable. The
pulleys are assumed to be frictionless and the strings passing over other
different pulleys are as shown in figure. Let W be the weight to be lifted and it
is hanged at the lowest pulley.
When the effort P is applied at the free end of the string, it is moved
downward by distance y.
Therefore,
Distance moved by pulley 3 =
Distance move by pulley 2 =
Distance moved by pulley 1 =

27APPLIED MECHANICS
Therefore, distance moved by load (W) attached to pulley 1 =
If there are „n‟ number of movable pulleys, the distance moved by the load =
Therefore, V.R =
Hence % efficiency =
PROCEDURE:
1. Fix one end of the string passing round each pulley to the hook and the
second end to the block of next pulley.
2. From the lowest pulley, suspend weight W (load).
3. Keep on adding weight in the effort pan till the load just starts moving
up.
4. Note down the value of effort P and the weight W.
5. Note down the distance covered by P and W separately in a fixed
time.
6. Calculate M.A., V.R., and hence the percentage efficiency.
7. Repeat the experiment for different loads.
Sr. No. Load
W
Effort, P
=
Weight
of pan
+
weights
in pan
M.A. =
W/P
Distance
moved
by the
effort (y)
Distance
moved
by the
load (x)
V.R =
y/x
1.
2.
3.
4.
Mean value………………….
PRECAUTIONS:
1. The string should be inextensible and light in weight.
2. The pulleys must be parallel to each other.
3. The pulleys must be well lubricated and free to move.
4. The weights should be placed gently in the pan.
5. The load and effort pan should not touch any object.

28APPLIED MECHANICS
AIM: TO DETERMINE THE MECHANICAL ADVANTAGE, VELOCITY RATIO AND
EFFICIENCY OF SECOND SYSTEM OF PULLEYS.
APPARATUS: Two blocks of pulley each contain two or three pulleys, weights,
pan, meter rod etc.
THEORY: It consists of two blocks of pulleys. The upper block is fixed to a
support whereas the lower block is movable. Either the pulleys in the two
blocks are equal or at least one pulley in the upper block is more that the
lower block. The string is continuously passed over the pulley in the order as
shown in figure.
Let weight attached to the lower block is W.
Let the weights is to be raised by a distance x. The each string of the two
blocks will moved by distance x.
The total distance through which the effort will have to move =
Where n is the number of pulleys.
Therefore, V.R =
To obtain higher value of V.R., number of pulleys can be increased.

29APPLIED MECHANICS
M.A. = W/P
Therefore, percentage efficiency =
PROCEDURE:
I) Take one end of the string and pass it over all the pulleys as shown.
II) From the lower block of pulleys, suspend weight W (load).
III) Attach an effort pan to the free end of the string and place weight
in it. The value of weight should be such that the load W just starts
moving up.
IV) Note down the value of effort P and the weight W.
V) Note down the distance covered by P and W separately in a fixed
time.
VI) Calculate M.A.., V.R., and hence the percentage efficiency.
VII) Repeat the experiment for different loads.
Sr. No. Load
W
Effort, P
=
Weight
of pan
+
weights
in pan
M.A. =
W/P
Distance
moved
by the
effort (y)
Distance
moved
by the
load (x)
V.R =
y/x
1
2
3
Mean value………………………..
PRECAUTIONS:
1. The string should be inextensible and light in weight.
2. The pulleys must be parallel to each other.
3. The pulleys must be well lubricated and free to move.
4. The weight should be placed gently in the pan.
5. The load and effort pan should not touch any object.

30APPLIED MECHANICS
AIM: TO FIND OUT CENTER OF GRAVITY OF REGULAR LAMINA.
APPARATUS: Regular lamina, A stand, Inextensible string, meter rod, pencil etc.
THEORY: The center of gravity of a body is that point at which the whole
weight of the body may be assumed to be acting.
When the body is considered to be composed of infinite number of small
weights each of which is acting vertically downward, then the point where
the resultant of all of these small weights acts, gives the position of the center
of gravity of the body.
The center of gravity of a plane figure or lamina referred to as the
centroid or center of area. A very thin sheet of any cross section is known as
lamina.
The center of gravity of irregular bodies is determined by the principle
of free suspension of bodies, which is as stated below:
If a body is suspended vertically with the help of a string, the forces which
come into play are:-
I) The weight of the body acting vertically downward through its C.G.
II) The tension in the string.

31APPLIED MECHANICS
PROCEDURE:
I) Take a lamina of any regular shape of some suitable material.
II) Tie the string at point A as shown in figure.
III) Suspend the lamina vertically by fixing the other end of the string to
the stand and drawing line along the plumb line.
IV) Now suspend the lamina at some other suitable point so that the
lamina is suspended vertically and again draws the line along the
plumb line.
V) The center of gravity of the lamina will be the point where these two
plumb lines intersect.
VI) Suspended the lamina at another point C and draw the plumb line,
which should pass through the C.G center of gravity already
located.
PRECAUTIONS:
I) The lamina should be of perfectly uniform mass.
II) The point of suspension should be quite small.
III) Draw the plumb line when lamina and string come to rest.
IV) The thickness of the lamina should be uniform.

32APPLIED MECHANICS
AIM: TO FIND OUT THE CENTER OF GRAVITY OF IRREGULAR LAMINA.
APPARATUS:
i) Irregular Lamina
ii) Stand
iii) Inextensible string
iv) Meter rod and pencil.
PROCEDURE:
I) Take the lamina of irregular shape of some suitable material.
II) Tie the string at point A as shown in figure.
III) Suspend the lamina vertically by fixing other end of the string to the
stand and drawing line along the plumb line
IV) Now suspend the lamina vertically at some other suitable point B
and again draw the line along the plumb line.
V) The center of gravity of the lamina will be the point where these two
plumb line intersect.
VI) Suspend the lamina at another point C and draw the plumb line,
which should pass through the center of gravity already located.
PRECAUTIONS:
I) The lamina should be of perfectly uniform mass.
II) The point of suspension should be quite small.
III) Draw the plumb line when lamina and string come to rest.
IV) The thickness of the lamina should be uniform.

33APPLIED MECHANICS
EXPERIMENT NO. 10
AIM: TO DETERMINE COEFFICIENT OF FRICTION BETWEEN 3 PAIRS OF RUBBER
SURFACES. (WOOD GLASS, RUBBER, LEATHER AND GLASS).
APPARATUS: Horizontal plane apparatus, weight box, pan, thread, wooden
block, glass plate rubber piece and leather piece etc.
Theory: The coefficient of friction is the ratio of limiting force of friction to the
normal reaction.
Let a wooden block of weight W be placed on the rough horizontal plane
and this block is just allowed to move by applying a pull „P‟ as show in Fig.
If “F” be the limiting friction and “R” be the normal reaction.
The weights of the block W acts vertically downwards.
The normal reaction R acting vertically upward and when the block is
in equilibrium given as ; R = W.
If a force „P‟ is applied in a direction parallel to the surface by putting weights
in the pan. A force of Friction „F‟ tends to oppose the motion in a direction
opposite to „P‟. IN equilibrium state;
R = W and
F= P
PROCEDURE: (WOOD AND GLASS)
I) Note down the weight of the block and the pan.
II) Place the glass plate on the horizontal plane.
III) Mark a particular region on the horizontal plane.
IV) Place the wooden block in this region. Tie the thread to the hook of
the block and pass over a smooth pulley fixed on the edge of the
apparatus and tie the pan to the free end of the thread.
V) Add some weights on the block as well as into the pan.
VI) Go on increasing the weights into0 the pan till the block just beings
to move.
VII) Note down the weights of the block as well as the pan.
VIII) Repeat the practical by putting different weights to the block and
final out the difference values of weight in the pan.

34APPLIED MECHANICS
IX) Calculate the coefficient of friction „ ‟ between wood and glass.
X) Similarly take out other pairs of surface .i.e., rubber and glass and
leather and glass one by one and repeat the above procedure
systematically covering all the steps and calculate the value of
coefficient of friction.
OBSERVATIONS:
S.No. Weight of block +
weight added in the
block „W‟ in kg
Weight of pan +
weight added in
the pan “P” in kg
1.
2.
3.
RESULT:
I) Coefficient of friction between wood and glass………….
II) Coefficient of friction between rubber and glass…………….
III) Coefficient of friction between leather and glass………………….
PRECAUTIONS:
1. Lubricate the pulley to minimize friction.
2. The thread should be knot free.
3. The plane should be kept perfectly horizontal.
4. The weights in the pan should be added gently.

Applied mechanics lab manual

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