ENGINEERING MECHANICS LABORATORY

MECHANICAL ENGINEERING DEPARTMENT

B.I.T. SINDRI

Index sheet of Laboratory Manual

S.No. TITLE/ CONTENT TITLE CODE

General Instructions -

1 BAND FRICTION EM1

2 FLYWHEEL EM2

3 SIMPLE MACHINE (SCREW JACK) EM3

4 SPRING EM4

5 YOUNG’S MODULUS OF

ELASTICITY

EM5

6 LIMITING FRICTION EM6

GENERAL INSTRUCTIONS

1. The students will come to the laboratory classes after consulting the rotation chart

available in the laboratory and for the particular experiment they have to perform.

2. The laboratory journals have to be written and completed during laboratory period and

submit there. For this students should come to the laboratory classes along with the loose

sheets, sketch sheets, graph sheets, and journal cover. The calculation if any should be

done in the class and curves if required should be drawn on the graph sheets in the

laboratory class and submit along with the laboratory journals. For write up of the

journals the student may write and bring (a), & (b) of the following items from the hostel

and rest should be completed in the laboratory class prior to the submission of the journal

on the same date.

a) Object and date.

b) Theory.

c) Sample calculations and Results.

d) Conclusion and comments

e) Practical application.

Any corrections and clarifications can be discussed with the teacher.

3. Under normal circumstances the students will not be permitted to take the journals to the

hostel after laboratory hours. In case, students are unable to complete the journals during

the lab. period, the completed journals can be submitted afterwards (i.e. any other day as

earliest as possible) at the cost of proportionate marks deduction.

4. The distribution of marks of the lab sessionals will be as follows:

(a) Teacher’s Assessment 10 Marks

(b) Attendance and submission 05 Marks

(c) End semester Exam (Viva – Voce) 10 Marks

If student/s absent himself/herself/ themselves from the class he/ she /they will be

. marked absent and marks allotted for the attendance will be deducted. Proportionate

. marks will be deducted for late submission and submission of incomplete journals.

5. If, due to power failure or any official reasons a particular class of batch/s could not be

held, the turn will be allowed by the teacher himself when the students, teachers and

laboratory are free, as regular turn without disturbing the original chart. However, if any

batch/s are absent due to their own reasons and a particular class is not held up, the same

will be allowed in make up turn at the end of the session by proper and timely

notification to the student. The total numbers of makeup turns allowed however, can not

exceed two.

6. If any student is absent in the end semester Exam (Viva-Voce) then he/she will be

marked zero in viva –voce and his/her all other marks will be submitted . No extra viva

will be held.

7. The students are requested to note the above rules carefully. Ignorance of the above rules

will in no case be accepted as excuse for any lapse on the part of the students.

Prof.(Dr.) S.C.Roy, Prof. Narendra Pratap,

H.O.D. Mechanical Engineering Department, Professor incharge,

B.I.T. SINDRI. Engineering Mechanics Laboratory.

1. TITLE: BAND FRICTION (EM1)

OBJECT: Determination of coefficient of friction between belt material (leather) and pulley

material (cast iron) using the relationship between tension on the two sides of belt and the angle

of lap.

SYSTEM:

First pulley (fixed) is on a regular wooden board centrally with a lever arrangement.

Second pulley (free) is at the tangential area of the same wooden board (fixed and free pulleys

are placed on the same plane of the wooden board). Fixed load (T2 = 1.5kgf) is applied at the

slack side of the belt.

PRIMARY VARIABLE:

a) Angle of Lap. θ.

b) Tension on the tight side, T1

(these terms has usual significance)

THEORY:

The relationship between tension on the two sides of rope or belt and the angle of lap:

(T1/T2) = 𝒆𝝁𝜽.𝒄𝒐𝒔𝒆𝒄𝜶

Where, T1 = tension in tight side,

T2 = tension in slack side,

μ = coefficient of sliding friction,

θ = angle of lap, in radians,

𝛼 = semi- groove angle.

EXPERIMENTAL PROCEDURE:

1. Set the angle of lap at 1800

2. Put the constant weight (T2 = 1.5 kgf) on the slack side,

3. Add weight (T1) and tight side till the pulley just starts to rotate clockwise direction (i.e.,

T1 starts to moves down)

4. Note down the reading of ‘T1’ for T2 = 1.5 kgf & θ = 1800

Repeat the procedure for the lap angles 1600, 140

0, 120

0 ,100

0 ,80

0 ,60

0 & 40

0 for

constant T2 = 1.5 kgf and note down the corresponding value of ‘ T1 ‘.

GRAPHS: Draw graphs between ,

a. (T1) vs. θ

b. In (T1 ) vs. θ

And determine the value of ‘μ’ &’ T2’ from graph

GRAPH FOR T1 vs θ GRAPH FOR ln T1 vs θ

TABLE:

S.No. Angle of

lap θ( in

degrees)

Slack

side T2

(in kg)

Tight side T1 (in kg ) ln T1 ln T2 μ = {ln T1 – ln T2 }/

(θcosecα) Increasing Decreasing Mean

T1

T2

Lap Angle

θ

T1 T1> T2

C.I. Pulley

Semi Groove Angle

Flat Belt

X

X

X

T1 (in kg)

Y

T2 = 1.5 kg(in kg)

ө (in radian)

Slope = tanθ=∆Y/∆X= μ T1 (in kg)

O

Y

l n T2

ө (in radian)

∆Y

X O

∆X

ln T1

Note:- write about ,

1. conclusions & comments,

2. its place of application.

2. TITLE: FLYWHEEL (EM2)

OBJECT: Determination of Polar Mass Moment of Inertia of the flywheel (rotating mass) using

the relationship between angular velocity and kinetic energy.

SYSTEM: Flywheel keyed to a shaft, mounted with the help of bearings (one at each end of the

shaft) with the shaft axis horizontal and free to rotate. The system (Flywheel keyed to shaft,

mounted with bearings) rests on a bracket fixed to the wall. The Flywheel can be imparted

angular velocity with the help of string wound over the shaft with the help of a peg (i.e. one end

of the string is hooked to the peg and then wound over the shaft) and then weight can be hooked

at other end.

PRIMARY VARIABLE: The angular velocity of the flywheel is the dependent variable.

Different angular velocities may be imparted by allowing different weights (here, weight, W =

0.5 kgf, 1.0 kgf, 1.5 kgf, 2.0 kgf, 2.5 kgf) attached to the free end of the wound string to fall

through. The difference in the height of the fall should be measured between the C.G. of weight

in the starting position and the C.G. when it just touches the ground. The techniques not only

allow imparting different velocities but also enable to measure the value of angular velocity

imparted and also to measure the kinetic energy given to flywheel. Let the time of the fall be ‘t1’

in second (s) , the height of fall be ‘h’ in meter (m) and falling to be equal to ‘mg’ in Newton (N)

, assuming that the bearing friction of the shaft remaining constant as weight falls. Hence the

weight will fall with uniform acceleration. Thus the final linear velocity of falling weight will be

given by,

v = 2h/t1, Where, h = 1.54 m

angular velocity given to shaft on which the string is wound will be given by, 2v/d,

where, ‘d’ is the diameter of the shaft in meter (m) , d=0.029m

also using principle of conservation of energy,

m g h = (1/2) mv2

+ θ1Ef + (1/2)Iω2

Where, θ1 = angle turned in the time ‘t1’ seconds,

Ef = energy dissipated in the bearing per radian of the flywheel

If Ef assumed independent of angular velocity , the value can be determined in terms of the K. E.

given to the total angle turned by the flywheel (from rest to rest in radians in the time ‘t2’

seconds).

Then, K.E. = (1/2)Iω2 = [mgh – mv

2 /2] (1- t1/t2)

GRAPH:

a. K.E. vs. ω

b. K.E. vs. ω2

Y Y

O O

GRAPH FOR K.E. Vs. ω GRAPH FOR K.E.Vs. ω2

TABLE:

Sl. No. Load in

Kg (W)

Time in

Second

(t1)

Time in

Second

(t2)

v = 2h/t1 ω = 2v/d

rad/sec.

ω2

K.E.

(Joule)

I

Kg-m2

Note:- Write about,

1. Conclusions & comments.

2. Its place of application.

3. TITLE: SIMPLE MACHINE, (SCREW JACK) (EM3)

OBJECT: Determination of law of machine and variation of efficiency of simple machine

(Screw Jack).

THEORY:

a. Mechanical Advantage (M.A.) = Load/Effort

or, M.A. = W/P

b. Velocity ratio = (velocity with which effort moves down)/ (velocity with which

load moves in upward direction)

or, ( V.R.) = (Distance moved down by effort in one rotation)/

(distance moved up by load in that rotation)

= X/Y

= π D/L, where, D = diameter of wheel = 7.2””.

L = lead of screw = ¼ ”

= np ,

K.E. (in

Joules )

ω ( rad / sec)

K.E. (in

Joules )

X X

ω2 ( rad / sec)

2

∆Y

∆X

Slope = tan θ = ∆Y/∆X = I/2

where, p = pitch of screw

n = 1, for single start thread,

= 2,for double start thread,

= [π (7.2”) ] / (1/4 ”) , for single start thread

= 4π (7.2”)

Or, V.R. = 4𝝅D = costant

c. Efficiency = output /input

= (W × Y) / (P × X)

= (W/P) / (X/Y)

= (Mechanical Advantage) / (Velocity Ratio)

= (M.A.) /(V.R.)

or, % Efficiency = [(M.A.) / (V.R.)] ×100

PROCEDURE:

a. Determine the value of effort (P0) when there is no load (i.e. W = 0),

b. Take the reading of effort (P) for every corresponding value of ,

W = 0.5 kgf, 1.0 kgf, 1.5 kgf, 2.0 kgf, 2.5 kgf, 3.0 kgf

(the final reading of the effort will be the mean of the reading that is taken

i) when the load is added, and

ii) when the load is removed one by one till 0.5 kgf)

GRAPH:

a) Load vs. Effort, determines the Law of Machine

b) Load vs. (% Efficiency).

GRAPH FOR Load vs. Effort.

%η= {1/tan θx V. R)}x 100

Slope = tan θ = ∆Y/∆X = 1/2

Effort P (in gm)

Y

C = intercept

Load W (in gm)

∆Y

X

O

∆X

P = W tan θ + C

θ

………………………………………

GRAPH FOR η Load Vs. Load

Sl.No. Load in

gm (W)

Effort in gm (P) M.A.= W/P V.R. = 4π D %η = M.A. /V.R. X 100

Inc Dec Mean

Note :- Write about,

1. conclusions & comments,

2. its place of application

4. TITLE: SPRING (EM4) OBJECT: Determination of stiffness of springs (Tensile Spring & Compression Spring).

SYSTEM:

An Iron frame with main scale and venier scale (venier scale, on a block that can slide in

the frame), rigidly fixed with the wall, so that the springs can be put under tension and

compression with the application of load (W).

Load (W) is applied using hook arrangement to measure deflection (δ) in the spring.

THEORY:

W = kδ

Where, δ = deflection, in cm or m

k = stiffness of the spring, in kgf/cm or N/m (1kgf = 9.81N)

W = load applied , in kgf or N

For a given W,

δ = 64𝑊 𝑅3𝑛

𝐺𝑑4

Where, W = load applied,

R = mean radius of the coil,

n = number of turns in the spring,

G = Modulus of Rigidity (represents the material of wire)

d = diameter of the wire,

Since only W and δ will change, K = W/δ,

%η

Y

Load W (in gm)

X O

PROCEDURE:

a. Note down the initial scale reading (ISR) at W = 0 kgf,

b. Take the final scale reading (FSR) to find the value of deflection

(δ = FSR – ISR) corresponding to the load (W) applied for,

W = 0.5 kgf, 1.0 kgf, 1.5 kgf, 2.0 kgf, 2.5 kgf, 3.0 kgf

c. The final reading of the deflection (δ) will be the mean of the reading that is

taken,

i) When the load (W) is added, and ,

ii) When the load (W) is removed one by one till 0.5 kgf,

GRAPH:

Draw graph for both the springs separately,

W vs. δ, and find the slope in order to find ‘k’ from graph,

GRAPH FOR load vs. deflection

S. No. Load (W)

(in kg)

Deflection δ (in Inches) Mean X

2.54 (in

cm)

Actual – δ

(in cm)

K = W/ Actual

δ (in Kg/Cm) Increasing Decreasing Mean

Note: - Write about,

1. conclusions & comments,

2. its place of application.

∆Y

∆X

W(in kg)

Y

X

𝛿 (in cm)

5. TITLE: YOUNG’S MOUDULES OF ELASTICITY (EM5)

OBJECT: Determination of Young’s Modulus of Elasticity for the material of wire (Copper

wire).

SYSTEM:

A wire (Copper wire) fixed at the top and loaded at the bottom. An extensometer fitted at the

bottom on a block [(cast iron block) suspended with the help of two supporting wire (Copper

wire)] and connected to the wire for experimentation to measure the deflection occurred due to

load applied.

THEORY:

Within elastic limit when a wire is axially loaded the stress (longitudinal) produced in it is

proportional to the corresponding strain (longitudinal)

Young’s Modules of Elasticity, E = Stress/strain

Or, E = σ / ε

Where, E = Young’s Modulus of Elasticity, in Kgf/cm2

σ = W /A, in kgf/cm2

ε = δl /L,

W = load applied in kgf, (here, W = 1kgf, 2 kgf, ……. 7 kgf)

A = cross-sectional area, in cm2, (where, d= 0.172cm)

δl = change in length of the wire, in cm.

L = total length of the wire, in cm, or, L = 225cm.

PROCEDURE:

a. set the dial gauge to zero reading,

b. read least count of extensometer from the dial gauge, (least count = 0.001cm)

c. the final reading of the elongation (δI) will be the mean of the reading that is

taken,

iii) When the load (W) is added, and,

iv) When the load (W) is removed one till 1.0 kgf.

Table:

S. No. Load

W

in kg

Extension δl =

Extension

X L.C.

(L.C. =

0.001cm)

Stress

W/A

(Kg/cm2)

Strain

δl / L

E =

Stress /

strain

(kg/cm2)

Inc Dec Mean

GRAPH:

Draw graph for,

a. W vs δl,

find slope and multiply by ‘L/A’ to slope to find ‘E’

b. σ vs. ε ,

find slope (i.e. ‘E’ from graph).

6. TITLE: LIMITING FRICTION (EM6)

OBJECT: Determine of co-efficient of limiting friction between,

(i) Cast Iron & Brass,

(ii) Cast Iron and Ebonite.

SYSTEM:

A box having rectangular base of given material and weight is pulled

by an external force with the help of the string passing over a

frictional less pulley and slides on another horizontal plane surface of

different material.

∆Y

∆X

W in kg

Y

X δl (in cm)

Y

O

θ X

Strain

∆Y

∆X

GRAPH FOR Stress Vs. Strain

E = Slope

Stress θ

O

O GRAPH FOR W Vs. δl

E = Slope x (L/A)

Table:

S. No. Load

W

in kg

Extension δl = Extension

x L.C.

(L.C. =

0.001cm)

Stress

W/A

(Kg/cm2)

Strain

δl / L

E = Stress

/ strain

(kg/cm2)

Inc Dec Mean

Note:- Write about,

1. Conclusion & comments,

2. Its place of application.

THEORY:

μ = P/W.

Variable which affects the limiting friction,

(a) pair of materials in contact,

(b) Weight of the sliding body,

(c) nature of the surface (roughness)

PROCEDURE:

(a) Select a pair of material surface and area of contact

(b) Take the reading of effort (F) applied on the pan for corresponding

load (W) applied on the surface (i.e., surface which can slide )

when it starts sliding .

(c) Take at least five observation for each pair of materials for

W = 0.2 kgf, 0.4 kgf, 0.6 kgf, 0.8 kgf, & 1 kgf.

F = μR

GRAPH:

Draw graph for ,

(a) F Vs. R, find slope in order to find ‘μ’ from

the graph for each pair of surface

GRAPH FOR F Vs.

Sl.No. Applied Load (W) = R External Force ( F) μ = F /R

wt. of

Box

wt. on

Box

Total

= R

wt. of

Pan

wt. on

pan

Total =

F

Slope = tan θ = ∆Y/∆X = μ

θ ∆X

∆Y

F

(in

gm)

Y

X

O R (in gm)

Note:- Write about,

3. Conclusion & comments,

4. Its place of application.