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DELHI COLLEGE OF ENGINEERI NG(Govt. of NCT of Delhi) Main Bawana Road, Delhi-42

Mechanical Engineering Department

Applied Mechanics Laboratory Instruction Sheet -3

Aim: To measure the energy of a rotating fly wheel and determine the momentof Inertia of the flywheel.

Apparatus: Fly wheel mounted on a wall, stop watch, Vernier calliper, thread

and weights (1/2kgf., 1kgf, 100gmf, 50gmf, 20gmf, 10gmf ), etc.

Theory: The principal of conservation of energy is made use of in determining

the M.I. of the fly wheel.

It states that the energy can neither be created nor destroyed though it

can be transferred from one form into any forms in which the energyexist.

As the fly wheel revolves due to a falling weight attached to the axis. Thepotential energy of the falling weight is equal to the K.E. of the falling

body when it drops off plus the energy stored in the fly wheel at that

instant plus the energy lost in the friction in bearings while the body isdescending. Even the energy stored in the fly wheel is lost in over coming

friction in bearing(after the weight has dropped off) bringing the wheel

to a stand still.

From law of conservation of energy:

Formulae:22 I

2

1v

g

W

2

1HW w+=´ (for negligible bearing

friction)

Where atuv += and aH2uv 22 += ,r

v=w

W= weight falling in N

H = height from which the weight fall in meterv= Linear velocity in m/s at the end of fall of H

I = Moment of Inertia of fly wheel in kgxm2

w =Angular velocity of shaft in radian/sec.

r= Radius of shaft in m

Note : Assume, there is negligible bearing friction.

http://www.pdfcomplete.com/cms/hppl/tabid/108/Default.aspx?r=q8b3uige22







2

2 )vg

W

2

1(HW2

Iw

úû

ùêë

é-´´

=\

Fig: Fly-Wheel Apparatus

Procedure:

1. Measure the diameter of the shaft with the help of vernier

calliper and find the mean radius of the shaft(r).2. Wrap the cotton string round the shaft and suspend weight (W)

so that fly can rotate easily.

3. Now marked the height (H) for weight W from centre of mass of Weight W to the earth and keep it same for different value of W

in each observation.

4. Place a weight (W) hold the Pan in which this weight is placed.

Release weight (W) and start the stop watch simultaneously. Stop

the watch as soon as the falling weight has touched the level

ground. This gives the time (t).

5. Repeat the experiment for different values of ‘W’. Repeat the

experiment ten times.

Observations:

1. Diameter of shaft = m

2. Radius of shaft (r) = m

3. Height of fall of weight W marked (H) = m

Weights

Diameter (2r)

Bearing

D

String

ShaftBearing

Fly-Wheel












S.

No.

Falling Weight

(W) in N

Time of fall of

weight (t) insec.

2

2 )2

1(2

w

úû

ùêë

é-´´

=\

v g

W H W

I

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Calculations:

Result:

Precautions:

1. Note the time accurately to the fraction of a second.

2. Friction in the bearings should be minimum possible.

3. Overlapping of the string should be avoided.

4. Mark the height carefully from the centre of mass of weights to

the ground.

Sources of Error:1. There may be positive or negative error in vernier calliper.

2. There may be error in recording time intervals ( in fraction of

seconds).

3. There may be little friction in bearings.

Discussion:

Note: 1. Draw the diagram for Experimental-Setup.

2. Draw the curve between Weight (W) at X-axis and rotational

kinetic energy of flywheel ( 2

2

1w I ) at Y-axis.

3. The standard value of Moment of Inertia for fly wheel is 0.5068

kgxm2














Applied Mechanics Laboratory Instruction Sheet-7

Aim: To verify the law of polygon of forces (concurrent, co-planer which are inequilibrium) with the help of Universal Force Table apparatus.

Apparatus: Force table with adjusting screws, Spirit level, pulleys, Brass ring,

Strings, Hangers, weights(50gmf-40Nos, 10gmf-4Nos),etc.

Theory: The experiment is for co-planer, concurrent forces (acting at a point).

Therefore a polygon can be drawn.

Law of Polygon of forces: If there are n number of co-planer concurrent

forces which are in equilibrium. A polygon can be drawn. Each side of polygon represents the magnitude of forces and there will be vectoraddition of each force. It conclude that the last side of polygon represents

the resultant of (n-1) forces.

The above experiment is for four co-planer concurrent forces which areshown in

fig..

Force polygon

The experimental error can be calculated as given below:

100

F

FFError%

4

44 ´¢

-¢= ®

®®

F1

F 2

F3

F 4

F ` 4

2q

3q 4q ¢

4

q







procedure:

1. First of all adjust universal force table horizontally by usingadjusting screws and spirit level.

2. Take a brass circular ring and 4 threads tied with this ring and

adjust threads on pulleys and ring on nail.3. Now fix one pulley on 0degree mark of table and other three

pulleys at desired angles.

4. Suspend weights at each thread such that each thread shouldpass over the pulley and Brass ring should be concentric with nail.

5. Note down the weights F1, F2, F3 and F4 and angles 1q , 2q , 3q and

4q . Draw the force polygon on graph paper.

6. Repeat the experiment five times by changing angles of pulleys

and weights.

Observations:

Force in (gmf) Angles in degrees % ErrorS.

No. F1 F2 F3 F4 1q

2q

3

q 4

q

(F`4-

F4)x100/ F`4 (

4

q ¢ -

4q )x100/

4q ¢

1.

2.

3.

4.

5.

Calculations:

Result:

Precautions:

1. First of all Universal force table should be made horizontal

with the help of spirit level and levelling screw.

2. Centre of Brass ring should coincide with the centre of nail

on the table.

3. Direction of threads should be radial on the table andvertically downward after passing the pulley. The threadsshould be weightless and inextensible.

4. The weights should not oscillate while taking readings.

5. Friction in pulleys should be minimum and pulleys shouldbe free to move.












Sources of Error:

1. Error in measurement of angles of threads.2. The threads may not be perfect weightless and

inextensible.

3. There may be friction in pulleys and not free to moveproperly.

4. Error to note coincide the centre of Brass ring and nail

of the table.Discussion:

1. Give the significance of the experiment.

2. Give Lami’s theorem and Baryganon theorem of

forces.

Note: 1. Draw the diagram for the experimental set-up.

3. Use graph paper to draw polygons.















Aim: To determine and verify the law of moments of forces for a simplysupported beam carrying transversal loads.

Apparatus: An uniform wooden beam of rectangular cross-section, Spring

balance (2 Nos), Scale, weights (1/2 kgf, 1kgf, 2kgf)

Theory:

The law of moments of forces states that the algebric sum of all

moments acting on a body which is in equilibrium is zero. i.e. the sum of

anticlockwise moments of forces is equal to the sum of clockwisemoments of forces.Now, Take moment about A

g B B xW xW xW xW l R +++=´ 332211

Therefore,l

xW xW xW xW R

g B

B

+++= 332211

Similary B B A RW W W W R -+++= 321

Where B A B R RW += (without using weights)

Formula for % Error is given by

100Pr

% ´-

=l Theoretica

actical l Theoretica Error

Beam carrying loads A R

B R

1

W 2

W 3W

A B BW

Gx1

x2 xg

x3







Procedure:

1. First of all find the weight of beam without using weights.2. Measure the length of beam and length between two supports.

3. Now put three hangers(100gmf each) one by one and add weights

to the hangers.4. Now measure the distance of each weights form end A.

5. Take the readings of Reactions A R and B R .

6. Repeat the experiment ten times.Observations:

Weight of Beam B A B R RW += (without using weights) = kgf

Length of Beam = cms

Distance between two supports of beam = cms

Weights appliedin kgf

Distance formA in cms

Reaction

A R in Kgf Reaction

B R in Kgf %Error

%Error

S.No.

W1 W2 W3 x1 x2 x3 The. Pra. The. Pra. A R B R

Calculations:

Result:

Precautions:

1. Place the beam gradually on the supports.2. check the zero error of the spring balances.

3. Include the weight of hangers while taking readings for the

weight applied.

4. Locate the centre of gravity of beam

5. Include the weight of beam while taking moment.














Sources of Error:

1. Wooden beam may not be uniform.2. Locate the C.G. of beam carefully.

3. parallax should be removed while taking readings of

distances.

Discussion:

Note: 1. Draw shear force and Bending moment diagrams.

2. Draw diagram for experimental-setup.

















Aim: To find out co-efficient of limiting friction between two surfaces usinginclined plane apparatus.

Apparatus: Wooden inclined plane having arrangement to read angle of

inclination, Boxes of different material (i.e. Wood, Glass, Aluminium,

Brass, etc.), weights (100gmf, 50gmf, 20gmf, 10gmf, etc.).

Theory:

Inclined plane

Under downward impending motion of the body (i.e. equilibrium under

downward movement or the body just tend to start downward), The equation

of equilibrium are

am SinW RW 21 =+

aam SinW CosW W 221 =+

aam

CosW

W SinW

2

12 -=

Therefore µ can be calculated for the downward impending motion of

body from the above formula.

MOTION

µR

W1

W2

R

W2 Sin

W2 Cosα







Inclined plane

Under upward impending motion of the body (i.e. equilibrium under

upward movement or the body just tend to start upward), The equation of

equilibrium are

am SinW RW 21 +=

aam SinW CosW W 221 +=

aa

mCosW

SinW W

2

21 -=

Angle of Repose(Ø) : The minimum angle of inclination at which body just

start to slide due to its own weight is called angle of Repose. It is equal to

the angle of friction.

fm Tan=\

% Error may be calculated as (ideal value of µ is calculated from angle of

repose and practical value is calculated from equation of motion either inupward or in downward direction).


100Pr

% ´-

= Idealvalue

ueacticalval Idealvalue Error

Procedure:

1. First of find the value of angle of repose(Ø) for different materials

(like wood, glass, aluminium, brass) by using inclined plane and

box at which the box just start to move downward due to its own

weight and calculate µ. It is supposed to be ideal value of µ. Youmay tap gradually the plane to see the motion of box.

MOTION

µR

W1

W2

R

W2 Sin

W2 Cosα






2. Now for each box find the value of µ by applying weights into

string attached with box and tap the plane gradually until the box just start to move either in downward or upward direction. You

may also put some weights in box to see the downward motion of

box. The value of µ is supposed to be practical value.3. Now repeat the experiment for each box to find the µ for

different materials.

4. % Error can be calculated as the formula given above.

Observations:

Material: Wood vs Wood

Angle of Repose =

Ideal value of µ =

S.

No.

Weight W1

Gmf

Weight W2

gmf

Angleα in degrees

Co-efficient of friction

µ

1. 300

2. 450

Material: Wood vs Glass

Angle of Repose =

Ideal value of µ =

S.

No.

Weight W1

Gmf

Weight W2

gmf

Angleα in degrees


µ

1. 300

2. 45

0

Material: Wood vs Aluminium

Angle of Repose =

Ideal value of µ =

S.

No.

Weight W1

Gmf

Weight W2

gmf

Angleα in degrees


µ

1. 300

2. 450

Material: Wood vs Brass

Angle of Repose =

Ideal value of µ =

S.

No.

Weight W1

Gmf

Weight W2

gmf

Angleα in degrees


µ

1. 300

2. 450










S.

No.

Material % Error

1. Wood vs Wood

2. Wood vs Glass

3. Wood vs Aluminium

4. Wood vs Brass

Calculations:

Result:

Precautions:

1. Clean the surfaces of inclined plane and box while takingreadings.

2. Tapping should be done gradually to see the motion of box.

3. It is conventional that the level of the weighs and boxshould be same.

4. The motion of the box should be such that it just tend tostart (impending motion) while taking readings.

5. The pulley should be frictionless.

Sources of Error:

1. There may be slight friction in pulley.2. There may be improper tapping.

3. Threads may not be inextensible.

Discussion:

Note: Draw the diagram for the experimental set-up.











Aim: To find out stiffness and modulus of rigidity (shear modulus) for the

material of a closed coil helical spring under tensile loading conditions.

Apparatus used: Spring apparatus with closed coil helical spring, vernier

calliper, Steel scale, Hanger (1/2 kgf load), weights (1/2 kgf, 10 Nos), etc.

Theory:

Spring stiffness: spring stiffness is defined as the load applied per unit

elongation for a given spring material.

Elongation

d LoadApplie

fnessSpringStif =

dW

K =

Where K is the spring stiffness (N/m)

W is the Tensile load applied in Newton

d is the elongation in mete

(Inverse of slope of Final extension – Load curve )=Tanα = spring stiffness (K)

Modulus of Rigidity (Shear modulus):Modulus of rigidity or Shear modulus is

defined as the ration of Shear stress to shear strain.

nShearstrai

sShearstresulushear igidityorS Modulusofr =mod

( )f A F

G/

=

ø

F

W (Kgf)

Finalreading

of scale

(cm)

α







For a spring material

4

38

d

nWDG

d=

WhereG is the shear modulus of spring material (N/mm

2)

W is Load applied (N)

D is the mean coil diameter [(d1+d2)/2] in (mm)

d1 is the inner diameter of spring coil in (mm)

d2 is the outer diameter of spring coil`in (mm)

n is the effective number of turns = N+1

d is the net elongation of spring for load W in (mm)

d is the diameter of spring wire [(d1-d2)/2] in (mm)

Procedure:1. First of all find the least count of the vernier scale.

2. Note initial reading of vernier scale without external load.

3. Gradually apply the load 1kg at first time and note final reading

vernier scale.4. Now, increase the load with 1/2 kg increment and note final

reading of vernier scale.

5. Repeat the experiment for 10 readings.

6. Measure the internal and external diameters of spring with the

help of separate vernier calliper.

7. Count the no. of turns of the springs.8. Add (1/2turn for upper bound coil+1/2turn for lower bound

coil)= 1 to N to get effective number of turns (n).






Observations:

1. External diameter of spring d1 = mm

2. Internal diameter of spring d2 = mm

3. Number of turns (N) =

Final reading of vernier scale in(cm)

Springstiffness

(k) in

N/mm

S.No.

WeightApplied

(W) in Kgf

Initialreading of

vernier

scale in(cm) Ascending

order

Descending

order

Average

1.

2.

3.

4.

5.

6.7.

8.

9.

10.

Calculations:

Result:

Precautions:1. Keep the spring in proper tensile position before applying load.

2. Vernier scale should be free to move at main scale.

3. Weight should be apply gradually.4. Weights should be applied in ascending order and after that in

descending order

5. Parallax should be removed before taking vernier reading.6. Internal and external diameters of spring should be checked from

three or four different positions.

Sources of Error:

1. There may be friction between main scale and vernier scale.

2. Spring may be not in right tensile loading position.








Discussion:

Note: 1. Draw the diagram for experimental set-up.

2. Draw the graph between final reading of vernier scale at y-axisand Load applied at x-axis.

3. The standard value of Spring stiffness is 10 N/mm and Modulus of

rigidity for steel is 211 m/N0`18 ´






Applied Mechanics Laboratory



Instruction Sheet-2

Aim: To find the modulus of elasticity (Young’s modulus ) for a given material

of cantilever for concentrated load at free end.

Apparatus Used: Cantilever Apparatus, Fraction weight(5, 10, 20, 50, 100gmf),

Scale.

Theory : The cantilever beam with concentrated beam is shown in fig.

Cantilever with deflection( maxd ) at free end due to concentrated load (W)

L

b

d

w

L

maxd







The maximum deflection of beam at free is given by the formula

EI

WL

3

3

max =d

max

3

3 d I WL

E =

Where maxd = Maximum deflection at free end of cantilever (m)

W = Concentrated load at Free end (Newton)

L = Length of beam from support to the application of load

E = Modulus of elasticity (young’s modulus) for givenmaterial of cantilever (N/m

2)

I = Area-moment of Inertia of beam about neutral axis ( m4)

Moment of Inertia of Cantilever

12

3bd I =

Where I = Area-moment of Inertia of rectangular beam about N.A. (m4)

b = Width of x-section of rectangular beam (m)

d = Depth of x-section of rectangular beam (m)


100Pr % ´-= Idealvalueueacticalval Idealvalue Error

Procedure:

1. First of all set the length of beam and mark the position of

cantilever end as (initial reading of deflection).

2. Apply the load (50gmf hanger) at free end and note the final

reading of deflection

3. Repeat the experiment 10 times.

b

d N.A.

x x







Observations:

1. Length of beam from fixed end to point of application (L) = m

2. Width of beam (b) = m3. Depth (Thickness) of beam (d) = m

Deflection ( maxd ) (m)S.

No.

Load (W)

(Newton) Initial Final Net

Calculations:

Result:

Precautions:

1. Hold the cantilever with support carefully.

2. Note the reading of deflection after removing parallax.3. Do not apply heavy loads at end of beam.

4. Deflection should be noted at point of application of load to get

maximum deflection.5. Thickness should be measured either by vernier calliper ,

micrometer or screw gauge.

Sources of Error:

1. There may be positive or negative error in vernier calliper.

2. Point of application of load may be change.Discussion:

Note: 1. Draw the diagram for the experimental set up.

2. Draw the curve between Load (x-axis) and maximum deflection

(y-axis)

3. Experiment may be repeated for different length.4. Standard value of E for steel is 211 /0̀12 m N ´









Applied Mechanics Laboratory Instruction Sheet -5

Aim: To find out the coefficient of friction between flat pulley and rope withthe help of combined belt and rope friction apparatus using gradually

applied load.

Apparatus Used: Combined belt and rope friction apparatus , Rope , Weights

(500gmf, 1000gmf, 100gmf, 50gmf, 20gmf, 10gmf, etc.) and Hangers

(50gmf each).

Theory: For flat pulley and rope

mqeT T =

2

1

2

11

T

T Log e´=

qm

Where T1 = Tight side tension (gmf)

T2 = Slack side tension (gmf)µ = co-efficient of friction

q = Angle of Lap (radian)

W1 W2

T1 T2

pq =

Flat

Pulley

Rope

Weights

Angle

of Lap








Procedure:1. First of all put the rope on flat pulley.

2. Now put the hanger two sides of rope and make them at same

level.3. Increase load on one side till the rope just start to move

(impending motion).

4. Note the readings of T1 and T2 (T1>T2).5. Repeat the experiment 10 times for different values of T2.

Observations:

Angle of Lap pq =

S.No.

Tight sideTension(T1) (gmf)

Slack sideTension(T2) (gmf)

Co-efficient of friction ( m )

1. 2.

3. 4. 5. 6. 7. 8. 9. 10.

Calculations:

Result:

Precautions:1

1. Rope should be inextensible and weightless.

2. Tapping should be done gradually.

3. The ends of the rope should be at same level during experiment.

4. Weight should apply gradually at hanger.5. The range of weight which has to apply is (5gmf to 1000gmf).

Sources of Error:

1. Rope may be extensible.

2. Tapping may be uneven.












Discussion:

Note:1. Draw the diagram f or experimental set-up.

2. Draw the curve between T1 (Y-axis) and T2 (X-axis).

3. Draw the curve between m (Y-axis) and2

1

T

T (X-axis).

4. The value of m may lie between (0.2 to 0.3).














Applied Mechanics Laboratory Instruction Sheet 6

Aim: To determine Mechanical Advantage (M.A.), Velocity ratio (V.R.) andefficiency (h ) for a given Screw-Jack (single start thread) Apparatus.

Also determine the law of machine and plot curve for:

(i) Load vs Effort

(ii) Load vs Mechanical Advantage (M.A.)

(iii) Load vs Efficiency (h )

Apparatus Used: Screw efficiency apparatus, inextensible strings, weights{1/2

kgf (10 nos), 100gmf (2 nos), 50gmf (3nos), 20gmf(1nos), 10gmf(1nos)},

vernier calliper, Outside calliper, scale, etc.

Theory:Mechanical Advantage (M.A.) : Mechanical Advantage for a simple

machine is defined as the ratio of load lifted to the effort applied.

iedEffortAppl

LoadLiftedAdvantageMechanical =

P

W A M =..

Fig. (Simple pulley shows Load lifted and Effort applied)

Simple

Pulley

Load

Lifted

EffortApplied

xy

W

P








Velocity Ratio (V.R.) : Velocity ratio is defined as the ratio of distance

moved by effort to the distance moved by load.

LoadbymovedDistannce

efforbymovedDistannceRatio Velocity

®®®®®®

=

x

y.R .V =

Efficiency (h ): Efficiency of a simple machine is defined as the ratio of out-put( work obtained as load lifted) to the input (work done at

other end of pulley).

100Input

outputEfficiency ´=

100yP

xW´

´´

=h

100

xy

PW´=h

100RatioVelocity

AdvantageMechanical´

®®

=h

Law of Machine : is mathematically defined as for a simple machine.

CmWP +=

Where P is the effort applied (kgf)

W is load lifted (kgf)

m is the slope or co-efficient of friction

C is the co-efficient of friction for machine

For single start screw thread

p

D Ratio Velocity

´p=

Ideal Machine

Actual Machine

C

)m(Tan1-

Load (W)

Effort









For double start screw thread

p2

D Ratio Velocity

´p=

Where D is the diameter of effort wheel (mm)

P is the pitch of the screw thread (mm)

Pitch : is defined as the axial displacement of load in one completerotation of effort wheel.

Fig. : Screw Jack Apparatus

Effort pulley

Guide

Pulley

Screw

Threads

Lifted

Load

Effort

Applied

Base

Motion

Screw

Spindle

Arms

Pitch

MotionMotion

Load

Han er

Tap

here

Collar






Procedure:

1. Measure the pitch of the screw with vernier calliper.

2. Measure the diameter of effort pulley with outside calliper andmeter scale.

3. Wrap the thread around the effort pulley passing over the guide

pulley and put the effort hangers at the ends of threads.4. Place a known weight in the Load hanger with collar and start

hanging weights with the effort hanger gradually till the load

starts lifting.

5. Repeat the experiment at least 10 times with different weights

(Loads).

6. Calculate M.A., V.R. and % Efficiency.

Observations:

1. Diameter of Effort pulley =…….Cm2. Pitch of screw thread =……..Cm

3. Velocity Ratio =……..

S.

No.

Load Lifted

(kgf)

Effort Applied

(kgf)

Mechanical

Advantage (M.A.)

(%) Efficiency

( h )

1.

2.

3.4.

5.

6.

7.

8.

9.

10.

Calculations:

Result:









Precautions:1. Wrap the string properly around effort pulley.

2. There may be Positive or negative error in vernier calliper.

3. Reading of pitch should be taken carefully.4. It should be noted that whenever load lifted (means load

goes in upward direction), the effort should be applied in

downward direction.5. Tapping should be done gradually and at right place.

Sources of Error:

1. There may be slight friction in pulleys.

2. Strings may be extensible and weightless.

Discussion:

Note: 1. Draw the diagram for the experimental set-up.2. Draw various curves (Load W at x-axis) as indicated in Aim.















Aim: To locate the Centroid of given laminas

a. Sector of circle b. Trapezium c. Parallelogram d. Trianglee. Irregular Body .

Apparatus Used: Laminas (Sector of circle, Trapezium, Parallelogram,

Triangular and Irregular body), Inextensible strings, Plumb, Rigid

support, Paper (A-3 size) and Pencil for marking.

Theory: A body which has negligible mass and thickness is called lamina. The

Centroid of lamina is the point at which the whole area of lamina is

supposed to be concentrated.

For Sector of Circle :

S.

No.

Shape Areaxx y

Y

1. Circular Sector 2r´q

qq

3

sinr2 0

Fig. Circular sector

x

Y

q q

c

r

Origin(0,0) O

xX








For Trapezium :

S.

No.

Shape Areaxx yY

1. Trapezium ( ) hba2

1´+´ 0 ( )

ba

ba2

3

h

++

´

For Parallelogram:

S.

No.

Shape Areaxx

yY

1. Parallelogram hb ´ 2

h

a

b

h

Origin

O (0,0)

c

Y

x

x

Y

Origin

O (0,0)

b

hc

2

h

( )ba

ba2

3

h

++

´









For Triangle:

S.

No.

Shape Areaxx y

Y

1. Triangle hb2

1´´

3

h

Percentage Error may be calculated by following formula

100

F

FFError%

4

44 ´¢

-¢= ®

®®

Y

x

b

h

c

3

h

Origin

O (0,0)









For Irregular Lamina:

S.No.

Shape Areaxx y

Y

1. Irregular

Procedure :

1. Use different laminas wrap paper on them and suspend it from

point P with the help of a string.

2. Draw the line PP` by chalk or pencil on the lamina. PP` is the

extension of string line from P.3. Similarly hang the lamina from point Q and draw the line QQ`

on the lamina. The QQ` is the extension of string line from Q.4. The same procedure may be repeated by hanging the lamina

from point R.

5. The point at which the line PP`,QQ` and RR` cut gives theCentroid of the lamina.

6. Measure the distance of the Centroid from the point P`.

c

x

Y

P

P`

Q

Q`

R

R`

Origin

(0,0)










Observaions:

xx yY S.

No.Shape Area

Calcu-

-lated

Obse-

-rved.

Calcu-

-lated

Obse-

-rved.

%

Error

1. Circular Sector

2. Trapezium

3. Parallelogram

4. Triangle

5. Irregular Lamina

Result : The co-ordinates of Irregular lamina are =……………………

Precautions:

1. The line PP` and RR` should be marked accurately.2. The point of intersection of the lines should be located

accurately.

Discussion:

Note : 1. Draw the diagram for experimental set-up.

2. Attach paper of each lamina drawing.









Aim: To determine Mechanical Advantage (M.A.), Velocity ratio (V.R.) andefficiency ( h ) for given Single and double Purchase Winch-Crab

Apparatus. Also determine the law of machine and plot curve for:

(i) Load Vs Effort

(ii) Load Vs Mechanical Advantage (M.A.)

(iii) Load Vs Efficiency (h )

Apparatus Used: Single and double purchase Winch-Crab apparatus,

inextensible strings, weights{1/2 kgf (10 nos), 100gmf (2 nos), 50gmf

(3nos), 20gmf(1nos), 10gmf(1nos)}, Outside calliper, scale, etc.



iedEffortAppl


P

W A M =..


Simple

Pulley

Load Lifted

EffortApplied

xy

W

P












®®®®®®

=

x

y.R .V =



100Input


100yP

xW´

´´

=h

100

xy

PW´=h

100RatioVelocity

AdvantageMechanical´=h


CmWP +=

Where P is the effort applied (kgf)W is load lifted (kgf)

m is the slope or co-efficient of frictionC is the co-efficient of friction for machine

Ideal Machine

Actual Machine

C

)m(Tan1-

Load (W)

Effort









For single purchase Winch-Crab

The unit consists of two axles called the effort axle and load axle.

Both these axles are mounted on rigid supports called strands. The effort

axle carries a teethed wheel called pinion meshes with a big teethed wheel Spur gear.

Fig. : Single Purchase Winch-Crab

When the effort wheel completes one revolution, the distance moved

by the effort is D´p for one revolution of pinion, the number of

revolution undergone by the spur gear is2

1

T

T.

Therefore, the displacement of load is given by:

2

1

T

Td ´´p

Loadof ntDisplaceme

Effortof ntDisplaceme(V.R.)RatioVelocity =

Spur

Gear

Pinion

Load

D

d

1T

2T

Effort

Axle

Load Axle or Drum

Effort

Applied







2

1

T

Td

D(V.R.)R atioVelocity

´´p

´p=

d

D

T

T .R .V

1

2 ´=

Where D is the diameter of effort wheel (cm)

d is the diameter of Load drum (cm)T1 is number of teeth of Pinion

T2 is number of teeth of Spur gear

P

W A M =..

100

Ratio Velocity

Advantage Mechanical´=h

2

1

T

T

D

d

P

W´´=h

For Double purchase Winch-Crab

The system employs two pairs of gears for obtaining increased

velocity ratio. There are three axles. An effort axle , load axle and anintermediate axle. The effort axle carries a pinion which gears with the

spur wheel of the intermediate axle.The pinion of the intermediate axle meshes with the spur wheelmounted on the load axle.

When the effort wheel completes one revolution, the distance movedby the effort D´p .

The effort axle and pinion (T1) mounted on it also turn one

revolution. This pinion gear meshes with spur gear (T2) fixed onto theintermediate axle. The revolution made by one intermediate axle are =

2

1

T

T1´

The pinion (T3) mounted on the intermediate axle will also turn

through the same number of revolutions. This pinion meshes with spur

gear (T4) of the load axle.

Thus the revolution made by load axle and the load drum mounted

on it are =4

3

2

1

T

T

T

T1 ´´






Distance moved by the load = ÷÷ ø

öççè

æ ´´´´p

4

3

2

1

T

T

T

T1d

Loadof ntDisplaceme


4

3

2

1

T

T

T

Td

D(V.R.)RatioVelocity

´´´p

´p=

31

42

TTd

TTD(V.R.)RatioVelocity

´´´´

=

Where D is the diameter of effort wheel (cm)d is the diameter of Load drum (cm)

T1 is number of teeth of Pinion with effort wheel

T2 is number of teeth of Spur gear (intermediate axle)T3 is number of teeth of Pinion with intermediate axle

T4 is number of teeth of Spur gear with load drum

4T

D

Spur

Gear

Pinion

1T

2T

Spur

Gear

Load

d

Load Axle or Drum

Spur

Gear

2T

Pinion

3T

Effort

Applied








Fig. : Double Purchase Winch-Crab

P

W A M =..

100Ratio Velocity


4

3

2

1

T

T

T

T

D

d

P

W´´´=h

Procedure:

1. Make strings for load drum to move upward and effort to move

downward.

2. Apply known load (initially 0.5 kgf) at load hanger and apply

corresponding effort (50-150gmf) at effort hanger in order that

the effort wheel just move on slight tapping at bearing.

3. Note the readings of load and effort and repeat the experiment

for different loads ten times.

Observations:

For single purchase Winch-Crab

1. Circumference of Effort wheel ( D´p )= cm

2. Circumference of Load drum ( d´p ) = cm3. No. of teeth of pinion (T1) =

4. No. of teeth of Spur gear (T2) =

5. Velocity ratio ( d

D

T

T .R .V

1

2 ´=) =

S.

No.

Load Lifted

(kgf)

Effort Applied

(kgf)

Mechanical

Advantage (M.A.)

(%) Efficiency

( h )

1.

2.

3.

4.

5.

6.7.

8.

9.

10.








For double purchase Winch-Crab

1. Circumference of Effort wheel ( D´p )= cm

2. Circumference of Load drum ( d´p ) = cm

3. No. of teeth of pinion (effort wheel) (T1) =4. No. of teeth of Spur gear (intermediate axle) (T2) =

5. No. of teeth of pinion (intermediate axle) (T3) =

6. No. of teeth of Spur gear (Load drum) (T4) =

7.31

42

TTd

TTD(V.R.)RatioVelocity

´´´´

= =

S.No.

Load Lifted(kgf)

Effort Applied(kgf)

MechanicalAdvantage (M.A.)

(%) Efficiency

( h )

1.

2.

3.

4.5.

6.

7.

8.

9.

10.

Result:

Precautions:

1. Wrap the string properly around effort pulley.2. It should be noted that whenever load lifted (means load goes in

upward direction), the effort should be applied in downward

direction.3. Tapping should be done gradually and at right place.

Sources of Error:1. There may be slight friction in pulleys.


Discussion:


2. Draw various curves (Load W at x-axis) as indicated in Aim.










Aim: To determine Mechanical Advantage (M.A.), Velocity ratio (V.R.) andefficiency (h ) for given Single and double Start Worm and Worm Wheel

Apparatus. Also determine the law of machine and plot curve for:

(i) Load Vs Effort

(ii) Load Vs Mechanical Advantage (M.A.)

(iii) Load Vs Efficiency (h )

Apparatus Used: Single and double Start Worm and Worm Wheel apparatus,

inextensible strings, weights{1/2 kgf (10 nos), 100gmf (2 nos), 50gmf

(3nos), 20gmf(1nos), 10gmf(1nos)}, Outside calliper, scale, etc.



iedEffortAppl


P

W A M =..


Simple

Pulley

Load Lifted

EffortApplied

xy

W

P












®®®®®®

=

x

y.R .V =



100Input


100yP

xW´

´´

=h

100

xy

PW´=h

100RatioVelocity

AdvantageMechanical´=h


CmWP +=

Where P is the effort applied (kgf)W is load lifted (kgf)m is the slope or co-efficient of friction

C is the co-efficient of friction for machine

Ideal Machine

Actual Machine

C

)m(Tan1-

Load (W)

Effort









For single start worm and worm wheel

Single start worm and worm wheel consists of Worm with effort

pulley, Worm wheel with load drum . As worm rotates one rotation,

Worm-wheel advances single lead of its threads.

Loadof ntDisplaceme


D

Td

T

DVelocity =

´

´=

p

p d(V.R.)Ratio

D

Td RV .. =

Where D is the diameter of Load drum (cm)

d is the diameter of effort pulley (cm)T is number of teeth of Worm Wheel

P

W A M =..

100Ratio Velocity


Td

D

P

W ´=h

For Double start worm and worm wheel

Double start worm and worm wheel consists of worm with effort

pulley, Worm wheel with load drum . As worm rotates one rotation,Worm-wheel advances double lead of its threads.

Loadof ntDisplaceme


DTd

T

DVelocity

22

d(V.R.)Ratio =´´

´=p

p

D

Td RV

2 .. =







Where D is the diameter of Load drum (cm)

d is the diameter of effort pulley (cm)T is number of teeth of Worm Wheel

P

W A M =..

100Ratio Velocity

Advantage Mechanical

´=h

Td

D

P

W 2´=h

Procedure:

4. Make strings for load drum to move upward and effort to move

downward.

5. Apply known load (initially 0.5 kgf) at load hanger and apply

corresponding effort (50-150gmf) at effort hanger in order thatthe effort wheel just move on slight tapping at bearing.

6. Note the readings of load and effort and repeat the experiment

for different loads ten times.

Observations:

For single start worm and worm wheel

1. Circumference of Effort pulley ( d ´p ) = cm

2. Circumference of Load drum ( D´p ) = cm3. No. of teeth of Worm wheel (T) =

4. Velocity ratio ( D

Td RV .. = ) =

S.

No.

Load Lifted

(kgf)

Effort Applied

(kgf)

Mechanical

Advantage (M.A.)

(%) Efficiency (h )

1.

2.

3.

4.5.

6.

7.

8.

9.

10.








For double start worm and worm wheel

1. Circumference of Effort pulley ( d ´p ) = cm

2. Circumference of Load drum ( D´p ) = cm

3. No. of teeth of Worm wheel (T) =

4. Velocity ratio ( D

Td RV

2 .. = ) =

S.No.

Load Lifted(kgf)

Effort Applied(kgf)

MechanicalAdvantage (M.A.)

(%) Efficiency( h )

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Result:

Precautions:

1. Wrap the string properly around effort pulley.

2. It should be noted that whenever load lifted (means load goes inupward direction), the effort should be applied in downward

direction.3. Tapping should be done gradually and at right place.

Sources of Error:

3. There may be slight friction in pulleys.


Discussion:


2. Draw various curves (Load W at x-axis) as indicated in Aim.







Delhi Technological University(Govt. of NCT of Delhi) Shahbad daulatpur, Bawana Road, Delhi-42



List of Experiment

UG Classes, Branch: Mechanical Engineering

1. To verify law of moments of forces for a overhanging beam

carrying transversal load.

2. To find co-efficient of limiting friction between two surfaces

using inclined plane Apparatus.

A. Wood vs Wood

B. Wood vs Aluminium

C. Wood vs Brass

3. To verify the law of polygon of forces (Concurrent, Co-

planer forces which are in equilibrium ) with the help of

Universal Force Table Apparatus.

4. To determine the mass moment of Inertia of Fly-Wheel

using energy method.

5. To find the stiffness and modulus of rigidity (Shear modulus)

for the material of a closed coil helical spring under tensile

loading conditions.







6. To determine Mechanical Advantage (M.A.), Velocity ratio

(V.R.) and Efficiency (η) for a given Screw Efficiency

Apparatus. Also determine the law of machine and plot

graph for:

A. Load vs Mechanical Advantage (M.A.)

B. Load vs EffortC. Load vs Efficiency(η)

7. To find Centroid of given laminae by geometrical methods

using Centroid of laminae Apparatus.


(V.R.) and Efficiency (η) for given Single Purchase Wich-Crab and Double Purchase Winch-Crab Apparatus. Also

determine the law of machine and plot graph for:


B. Load vs Effort

C. Load vs Efficiency(η)

9. To determine Mechanical Advantage (M.A.), Velocity ratio(V.R.) and Efficiency (η) for given Single Start Worm &

Worm Wheel and Double Start Worm & Worm Wheel

Apparatus. Also determine the law of machine and plot

graph for:


B. Load vs Effort


10. To find the co-efficient of friction between flat pulley and

rope using Combined Rope and Belt Apparatus.







Delhi Technological University(Govt. of NCT of Delhi) Shahbad daulatpur, Bawana Road, Delhi-42



List of Experiment

UG Classes, Branch: ECE, COE, EE

1. To verify law of moments of forces for a overhanging beam

carrying transversal load.




3. To verify the forces transmitted by members of a Simple

Roof Truss using gradually applied loads.

4. To verify law of moments using Bell Crank Lever apparatus.



6. To find the stiffness and modulus of rigidity (Shear modulus)

for the material of a closed coil helical spring under tensile

loading conditions.







7. To find the modulus of elasticity (Young’s modulus) for a

given material of cantilever for concentrated load at free

end.

7. To perform shearing test for given material on

Tensometer and plot Load-elongation relationship.






Lab-Incharge’s Cabin

Please do not sit here

Lab-Incharge’s Cabin

Please do not sit here




List of ExperimentUG Classes, Branch: ME and AE




2. (a) To verify law of moments of forces for a overhanging

beam carrying transversal load.

(b) To verify law of moments using Bell Crank Lever

apparatus.



4. To locate the Centroid of given lamina using geometrical

method.

a. Triangle

b. Irregular Body .





(V.R.) and efficiency (h ) for a given Screw-Jack (single

start thread) Apparatus. Also determine the law of

machine and plot curve for:(i) Load vs Effort

(ii)Load vs Mechanical Advantage (M.A.)

(iii)Load vs Efficiency (h )

6. To verify the forces transmitted by members of a Simple

Roof Truss using gradually applied loads.

7. To determine the mass moment of Inertia of Fly-Wheel

using energy method.

8. To find co-efficient of limiting friction between two surfacesusing inclined plane Apparatus.

A. Wood vs Wood

B. Wood vs Aluminium

C. Wood vs Brass







1. To verify the law of polygon of forces (Concurrent,

Co-planer forces which are in equilibrium )

using Universal Force Table Apparatus.

2. To verify law of moments of forces for a simplysupported beam carrying transversal load.

3. To find the co-efficient of friction between flat

pulley and rope using Combined Rope and BeltApparatus.

4. To find the stiffness and modulus of rigidity

(Shear modulus) for the material of a closed coil

helical spring under tensile loading conditions.






5. To find the modulus of elasticity (Young’s

modulus) for a given material of cantilever for

concentrated load at free end.

6. To determine the mass moment of Inertia of Fly-

Wheel using energy method

7. To determine Mechanical Advantage (M.A.),

Velocity ratio (V.R.) and efficiency ( h ) for agiven Screw-Jack (single start thread)

Apparatus. Also determine the law of machine

and plot curve for:

(i) Load vs Effort



8. To verify law of moments using Bell Crank Lever

apparatus.








7. To find the modulus of elasticity (Young’s modulus) for a

given material of cantilever for concentrated load at free

end.

8. To perform shearing test for given material on

Tensometer and plot Load-elongation relationship.






1. To verify the law of polygon of forces (Concurrent,

Co-planer forces which are in equilibrium )

using Universal Force Table Apparatus.

2. To verify law of moments of forces for a simplysupported beam carrying transversal load.

3. To find the co-efficient of friction between flat

pulley and rope using Combined Rope and BeltApparatus.

4. To find the stiffness and modulus of rigidity

(Shear modulus) for the material of a closed coil

helical spring under tensile loading conditions.






5. To find the modulus of elasticity (Young’s

modulus) for a given material of cantilever for

concentrated load at free end.

6. To determine the mass moment of Inertia of Fly-

Wheel using energy method


Velocity ratio (V.R.) and efficiency ( h ) for agiven Screw-Jack (single start thread)

Apparatus. Also determine the law of machine

and plot curve for:

(i) Load vs Effort




Velocity ratio (V.R.) and Efficiency (η) for a

given Double Purchase Winch-Crab Apparatus.

Also determine the law of machine and plotgraph for:


B. Load vs Effort









9. To locate the Centroid of given lamina using

geometrical method.

a. Sector of circleb. Trapezium

c. Parallelogram

d. Triangle

e. Irregular Body

10.To verify law of moments using Bell Crank Lever apparatus.





Documents

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