Mechanical technology
• An understanding of the fundamental concepts, laws and analytic methods for the
solution of applied mechanics problems
Skills
• Proficiency in the use of mechanical technology, and the ability to evaluate and
appraise the results of practical experiments.
1 Abstract
• A self-contained summary of what you did and your main findings
and conclusions.
• Maximum length: 200 words. You should include a Word count
at the end of the abstract.
10
2 Results
• Full and complete table of experimental readings.
• Well-presented and fully labelled graphs.
10
10
3 Analysis of results
Discuss briefly:
Experiment 1
• Show the relationship between deflection and beam material.
• Comparison of experimental and theoretical values of Young’s
modulus (E) for brass, aluminium and mild steel
Experiment 2
• Estimate the inertia of the flywheel by treating it as a solid steel disc.
Full working should be shown.
• Critically analyse the tabulated data and comment on your graph and
results and compare the value with the textbook value for the all three
beam materials.
10
4 Discussion
• A critical discussion of the accuracy of the results, which includes a
description of the main sources of error/inaccuracy.
5
5 Quality of presentation of the report
The use of an appropriate technical style for the presentation of the
report.
5
Total marks for each report 50
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Part A: MOMENT OF INERTIA OF A FLYWHEEL
During the course of the experiment a set of weights were hung in turn on a piece of cord
from a pulley attached to the flywheel. The objects were allowed to fall under gravity from a
height of 1 metre, as described in the laboratory sheet. This was performed three times and
the data recorded is shown in the table below. The diameter of the spindle d (= 2r) was found
to be 38 mm (0.038 m).
Total weight
(including hanger)
(N)
1
st descent
time
(s)
2
nd descent
time
(s)
3
rd descent
time
(s)
3.2 29.69 34.60 34.60
6.0 24.25 24.28 25.22
8.5 19.60 19.70 19.95
11.0 17.60 17.06 17.29
13.5 15.12 15.65 15.12
Complete the following tasks:
• The flywheel dimensions are as follows: diameter = 390mm, mean thickness
= 30mm. Also, it is made of steel, with density 7850 kg/m3
. Use this
information to estimate the inertia, by considering the formula for the inertia
of a solid disc. This value should be used as an approximate validation of the
inertia derived.
• Critically analyse the tabulated data and use it to determine the inertia of the
flywheel and the frictional torque Tf. You should use Excel to calculate and
tabulate relevant values, and to plot Pxr versus α, as per the laboratory sheet.
NB: do not confuse weight with mass (a common mistake!)
Part B: STIFFNESS OF DIFFERENT MATERIALS
During the experiment, three beams of different materials (Aluminium, Brass and Steel), but
of the same dimensions (9.5 mm x 3 mm), were tested to find their material stiffness values.
All steps to perform the complete experiment are given in the laboratory instruction sheet.
Tables 1 to 3 were obtained after completing the experiment.
Complete the following tasks:
• Complete tables 1 to 3 and obtain the values for equation 48δI / L3
.
Page 5 of 13
• Plot your load and equation 48δI / L3
results on the chart paper (as shown in
Figure 1).
• Find the gradient of the chart.
• Critically analyse the tabulated data and comment on your graph and results
and compare the value with the textbook value for the all three beam
materials.
Beam Modulus
Load (m)
(g)
Load (W)
(N)
Deflection
(mm)
Deflection (δ)
(m)
48δI / L3
0 0 0
100 0.98 0.65
200 1.96 1.16
300 2.94 1.73
400 3.92 2.23
500 4.9 2.74
Material: Aluminium
Beam Size: b= 9.5 mm d= 3 mm I = 2.1375 x 10-11 m4
Table 1: Results table for Aluminium.
Beam Modulus
Load (m)
(g)
Load (W)
(N)
Deflection
(mm)
Deflection (δ)
(m)
48δI / L3
0 0 0
100 0.98 0.36
200 1.96 0.80
300 2.94 1.06
400 3.92 1.41
500 4.9 1.75
Material: Brass
Beam Size: b= 9.5 mm d= 3 mm I = 2.1375 x 10-11 m4
Table 2: Results table for Brass.
Beam Modulus
Page 6 of 13
Load (m)
(g)
Load (W)
(N)
Deflection
(mm)
Deflection (δ)
(m)
48δI / L3
0 0 0
100 0.98 0.19
200 1.96 0.42
300 2.94 0.58
400 3.92 0.78
500 4.9 0.98
Material: Steel
Beam Size: b= 9.5 mm d= 3 mm I = 2.1375 x 10-11 m4
Table 3: Results table for Steel.
Figure 1: Blank results chart.
Laboratory instructions
Page 7 of 13
TITLE
EAT103: MOMENT OF INERTIA OF A FLYWHEEL
OBJECT
To determine the moment of inertia of a flywheel by accelerating it with a falling mass.
THEORY
APPARATUS
m
d
a
P
P
mg
,
Page 8 of 13
Flywheel, variety of masses m attached to length of cord.
m = falling mass, kg
h = distance fallen by mass, m
t = time of fall of mass, s
d = diameter of spindle, m
r = radius of spindle, m (= d/2)
a = acceleration of mass, m/s2
= angular velocity of flywheel when mass reaches ground, rad/s
= angular acceleration of flywheel with mass falling, rad/s2
P = tension in cord, N
g = gravitational acceleration = 9.81 m/s2
METHOD
1. For a particular mass, time the rate of descent and measure the distance fallen.
2. Use the formula given below in conjunction with Excel to determine the moment of inertia of
the flywheel, by plotting the straight line described.
3. Repeat steps 1-3 for a number of different masses (try at least five values of m).
4. Estimate the inertia using the formula for the flywheel of a solid disc, to enable you to check
that your experimental results are of the correct order of magnitude.
Considering acceleration of the flywheel:
T I
d
T = I P − f =
2
------------------------------------- (1)
Where, Tf = friction torque due to bearings etc.
I = moment of inertia of flywheel and spindle
Newton’s 2nd law applied to falling mass: mg − P = ma ------- (2)
Page 9 of 13
From (s = ut + 0.5at2
), acceleration:
2
2
t
h
a = ------------------------ (3)
Thus: (3) into (2)
2
2
t
mh P = mg − ---------------------------------- (4)
From (v = u + at), and using the expression for acceleration a given by equation (3), the speed of
mass m when it hits ground is:
t
h
v
2
= ---------------------------- (5)
Since = v/r, from (5) the angular velocity of the flywheel when the mass hits ground is:
rt
2h
== --------------------------- (6)
Also, the angular acceleration of the flywheel as mass falls is:
t
= ---------------------------- (7)
Thus, (6) into (7)
t r
h
2
2
= --------------------------- (8)
Equation (1) can be re-written as follows:
y mx c
P r I Tf
= +
= +
--------------------- (9)
In other words, if we plot P r (y-axis) versus (x-axis), we should get a straight line, where the
gradient is I, the inertia of the flywheel, and the intercept with the y-axis is Tf, the friction torque.
P is calculated using equation (4), and is calculated using equation (8).
TITLE
Page 10 of 13
EAT103: Stiffness of materials
OBJECT
To achieve an understanding of the stiffness of different materials under load.
THEORY
Stiffness is an important property for many applications of materials. The stiffness of a
structure depends on both the properties of the material from which it is made and on the
geometry of the structure.
Theory: Deflection of a simply supported beam.
This formula applies to beams which are subjected to a central load acting at a right
angle to their length.
The equation for the deflection of a beam supported between two points is given by:
Δ =
𝑊𝐿
3
48𝐾
Where:
𝑊 = Load (N)
Δ = deflection (m)
L = Length (m)
K = Flexural rigidity constant
K may be calculated due to the second moment of area of the material I, and the value of
Young’s modulus E
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𝐾=𝐸.𝐼
Some standard values of (E) for the following materials:
Brass 105 Gpa
Aluminium 69 GPa
Mild Steel 200 GPa
Second moment of area (I) for solid and hollow beams:
For a solid beam of rectangular cross section:
𝐼 =
𝑏𝑑
3
12
The units of I are m4
APPARATUS
The ES4 apparatus uses an example of a very simple structure, a beam in three point
bending. The apparatus explores that beams of different material but identical dimensions
(and I value) deflect by different amounts for the same load, providing that their material
property (Young’s Modulus) affects deflection.
The apparatus is very simple to use, the operator places the specimen into the apparatus
and applies a load. A dial indicator measures the deflection of the specimen at the point
of loading.
The apparatus is simple and demonstrated in Figure 1.
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Figure 1: Experiment Setup
METHOD
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Experimental Procedure – Beam Modulus
1. Find the three beams of different materials (Aluminium, Brass and Steel) but of
the same dimensions (9.5 mm x 3 mm). The aluminium beam weight less than
the other two and the brass beam has a golden colour.
2. For each beam, use the Dial Calliper Gauge (supplied with the kid) to accurately
measure the beam dimensions (b and d). Calculate the I values for the beam and
note this and the other beam properties into your results table 1-3.
3. Fit the aluminium beam to the supports.
4. Adjust the Dial indicator and Wire ‘stirrup’ along to the middle of the beam (180
mm).
5. Set and zero the Dial indicator.
6. In increments of 100 g, add weights up to a maximum of 500 g. Each time you
add a weight. Tap the work panel to reduce the effects of friction. Record the
deflection at each weight increment.
7. Calculate the load in Newton and calculate the results of the equation shown in
the table 1.
8. Rearranging the equation in the form y = mx+c means that the gradient of a chart
of W against
48 δI
𝐿
3
will give the value of E.
9. Plot your load and equation results on the chart paper.
10.Find the gradient of the chart.
11.Compare the value with the textbook value for the beam material.
12. Repeat for the other two beams.
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