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TRANSCRIPT
UNIVERSITI MALAYSIA SARAWAK
FACULTY OF ENGINEERING DEPARMENT OF MECHANICAL AND
MANUFACTURING ENGINEERING
KNJ1241 MECHANICAL AND
MANUFACTURINGENGINEERING
LABORATORY2
LABORATORY MANUAL
TABLE OF CONTENT
Lab Code Title Page
SD1
SD2
SD3
SD4
SD5
SD6
SD7
SD8
SD9
SD10
Deflection of a Beam
Reaction of Continuous Beam
Reaction of Moment for a Fixed End Beam
Reaction of Propped Cantilever Beam
Torsion of Shaft
Flexure Stress
Relation between Angular Speed and Linear Speed
Compound Pendulum
Flywheel Apparatus
Belt Friction
1
5
9
13
17
21
25
29
35
39
Appendix
A
B
Safety First
Guidelines for Laboratory Report
43
44
KNJ1241 Engineering Laboratory 2 Faculty of Engineering Universiti Malaysia Sarawak
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TITLE :
SD1 – Deflection of a Beam
THEORY :
Deflection of a beam can be described by the degree of the displaced beam or the
displacement of the certain point on the beam under a load application. The deflection of
a beam depends on its length, its cross-sectional shape, the material, where the deflecting
force is applied, and how the beam is supported. The equations given here are for
homogenous, linearly elastic materials, and where the rotations of a beam are small.
Figure 1: Simply Supported Beam
The mid-span deflection of a simply supported beam loaded with a load W at mid-span is
given by;
δ = (1)
Rewriting,
E = Or,
E =
OBJECTIVE :
To establish the relationship between deflection and applied load and determine the
Young Modulus of the beam specimen from the deflection data.
WL3 48 EI
L
L/2
W
L3 48 I
× Slope of the load deflection curve
L3 W 48 I δ
KNJ1241 Engineering Laboratory 2 Faculty of Engineering Universiti Malaysia Sarawak
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APPARATUS :
A support frame, a pair of pinned support, a load hanger, dial gauge, beam specimen, set
of weights.
SAFETY PRECAUTIONS :
Beware of the loose heavy items such as weights and make sure apparatus is well
tightened.
PROCEDURE :
1. Measure width and depth of specimen and record the readings (take measurement at 3
locations and record the average reading)
2. Place the beam specimen between the clamping plates and fix the load hanger at the
mid-span of the beam.
3. Position the dial gauge at the mid-span of the beam to measure the resulting
deflection and set the dial gauge reading to zero. (1 div = 0.01 mm)
4. Place a suitable load on the load hanger then record the resulting dial gauge reading.
Increase the load on the load hanger and record all the result in the table 1.
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RESULTS :
1. Complete the required data
Span of tested beam, L = mm
Width of beam specimen, b = mm
Depth of beam specimen, d = mm
Moment of inertia of beam specimen, (bd3/12) = mm4
2. Tabulate the table below.
Table 1 : Deflection againts Applied Load
Applied Load
Experimental Deflection Theoretical Deflection
mm
Test 1 Test 2 Average Deflection
mm N div mm div mm
3. Using the tabulated data in the Table 1, plot the graph of load versus experimental
deflection. Draw the best fit curve through the plotted point and hence deduce the
relationship between the applied load and the resulting mid span deflection.
4. Calculate the Modulus of Elasticity using the slope of the graph obtained assuming a
linear relationship between load and deflection as shown below.
DISCUSSION :
1. Discuss the relationship between the load and the experimental deflection and
compare with the theoretical calculation.
2. What does the slope of the graph represents and how does it varies in relation to the
load position.
3. Calculate the Young Modulus from the result obtained and compared the result with
the reference.
4. Discuss the accuracy of the data.
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TITLE :
SD2 – Reaction of a Continuous Beam
THEORY :
Continuous beam is a beam which extends over three or more supports that joined
together. Therefore, the given load on one span will effect on the other spans. Hence the
reaction on the other support can be calculated based on the given load. Typical reactions
at the support of a continuous beam is as shown below
Figure 2: Reaction of Continuous Beam a
Figure 3: Reaction of Continuous Beam b
Figure 4: Reaction of Continuous Beam c
Different arrangement of span and load will give a different value of reaction at the
support. Choose only one from the examples for your experiment.
3W / 8
2L
7 W / 8 W / 4
L
W
L
22 W / 16 5W / 16 5W / 16 L L
W W
L/2 L/2
22 W / 32 3W / 32 13W / 32 L L
W
L/2
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OBJECTIVE :
To determine the reaction of a two-span continuous beam
APPARATUS :
A support frame, 3 nos. reaction support pier, 2 nos. load hanger, beam specimen, a meter
ruler, digital load reader, a set of weights.
SAFETY PRECAUTIONS :
Beware of the loose heavy items such as weights and make sure apparatus is well
tightened.
PROCEDURE :
1. Place the beam specimen between the two cylindrical pieces of each support.
Tightened the two screws at the top of each support with your fingers.
2. Fix the load hanger at the position where the beam is to be loaded.
3. Connect the load cell from the support pier to the display unit, each load cell
occupying one terminal on the display.
4. Beginning with channel 1 record the initial reading for each channel.
5. Place a suitable load on the load hanger and note the reading of each load cell. This
represents the reaction at each pier.
6. Increase the load on the load hanger and record the pier reactions.
7. Repeat step 8 for at least 5 load increments. (result on the display should be divided
by 5.7 as the offset because of the calibration problem)
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RESULTS :
1. Complete the required data
Left-Hand span of beam, LL = mm
Right-Hand span of beam, LR = mm
Distance of load from left-hand support, XL = mm
Distance of load from right-hand support, XR = mm
2. Tabulate the Reaction at the Support table below.
Table 2: Reaction At The Support
Load On LL Load On LR Support Reaction N N Left (N) Middle (N) Right (N)
3. Plot the graph of reaction against load for each support of the beam using the
tabulated data and draw the best-fit-curve through plotted points.
4. Using the slope of the graph, calculate the percentage error between the experimental
and theoretical reaction.
DISCUSSION :
1. Discuss the relationship between the reaction and load of each support of the beam.
2. How does the experimental reactions compare with the theoretical.
3. State the possible factors that might have influenced your results and possible means
of overcome it.
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TITLE :
SD3 – Reaction of Moment for a Fixed End Beam
THEORY :
Fixed end beam is a beam that is supported at both free ends and is restrained against
rotation and vertical movement. This will produce the moment reaction on the support.
Fixed End Beam is also known as built-in beam.
The fixed end moment of a fixed end beam is given by the following equations;
MFAB = - W * a * b2/ L2 (1)
MFBA = - W * a2 * b/ L2 (2)
Figure 5: Theory of Fixed End Beam
OBJECTIVES :
To determine the relationship between fixed end moment of a fixed end beam and the
applied loads.
APPARATUS :
Two supports that able to measure moment, beam specimen and set of weights.
SAFETY PRECAUTIONS :
Beware of the loose heavy items such as weights and make sure apparatus is well
tightened.
W
b
B A
MFA
MF
B
L
a
KNJ1241 Engineering Laboratory 2 Faculty of Engineering Universiti Malaysia Sarawak
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PROCEDURE :
1. Fixed the two supports tightly to the base with the distant between them equals to the
span of the beam. (refer the attachment)
2. Place the ends of the beam between the clamping plates of the supports and tightened
the two screws to fix the beam.
3. Pass the cord at the end of the aluminum rod over the pulley on the right of the left
support and the pulley on the left of the right support. (Refer to experimental setup
diagram)
4. Clipped the load hanger at the position where the beam is to be loaded.
5. Zero the dial gauge reading at both supports.
6. Load the beam by placing weights on the load hanger fixed to the beam.
7. Notice that at support A the aluminum rod has rotated in a clockwise direction while
at support B the aluminum rod has rotated in an anticlockwise direction. Note the
readings on both dial gauges.
8. Record the loads on the beam and at the end of the both cords.
9. Remove the loads from the load hangers and zero the dial gauges reading.
10. Place a higher load on the beam and repeat step 5 to step 9 for four more loadings.
(result on the display should be divided by 5.7 as the offset because of the calibration
problem)
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RESULTS :
1. Complete the required data
Beam Span = mm
Distance of load from support A = mm
Distance of load from support B = mm
2. Tabulate the obtained result in the following table.
Table 3 : Relation between the loads
Load On The Beam
N
Load on Pulley at Support A, HA
N
Load on Pulley at Support B, HB
N
3. Calculate and complete the following table.
Table 4 : Moment at the support against load on the beam
Load on Beam (W)
Fixed End Moment at Support A Nmm
Fixed End Moment at Support B Nmm
MF (Exp) = HA * 220
MF(Theory), refer equation 1
MF (Exp) = HB * 220
MF(Theory), refer equation 2
4. Using the data from the Table above plot the graph of fixed end moment versus load
for both supports and determine the slope of each graph.
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5. Calculate the percentage error using the slope obtained from the above graph.
For support A;
Theoretical slope = a * b2/ L2
Experimental slope is obtained from the graph
Percentage error = (slope theory – slope exp) * 100/ slope theory
For support B
Theoretical slope = a2 * b/ L2
Experimental slope is obtained from the graph
Percentage error = (slope theory – slope exp) * 100/ slope theory
DISCUSSION :
1. Discuss the relationship between the fixed end moment and load as well as the
reaction at the pinned support and load.
2. Describe the change in the magnitude of the fixed end moment and the reaction at the
fixed support if the load moves away from the pinned support.
3. Compare and discuss the empirical and theoretical calculation.
4. Comment on the accuracy of the result obtained in this experiment.
KNJ1241 Engineering Laboratory 2 Faculty of Engineering Universiti Malaysia Sarawak
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TITLE :
SD4 – Reaction of a Propped Cantilever Beam
THEORY :
Propped Cantilever Beam is a beam with a built in support at one side where there is no
rotation about or translation in the x, y, z direction. The other side of the beam is a point
support with no translation in the x, y, z direction but a rotation about the z direction.
The fixed end moment at the support of a propped cantilever beam is given by;
MF = - W * a * (L2 – a2) / (2L2) (1)
The reaction at the simple support is given by;
RA = W{ 1 - [(L-a)2 * (2L+a)] / (2*L3)} (2)
Figure 6: Theory of a Propped Cantilever Beam
OBJECTIVE :
To determine the fixed end moment and reaction at the supports of a propped cantilever
beam.
APPARATUS :
A support that able to measure moment and reaction, beam specimen and a set of
weights.
SAFETY PRECAUTIONS :
Beware of the loose heavy items such as weights and make sure apparatus is well
tightened.
L
MF W a
B A
KNJ1241 Engineering Laboratory 2 Faculty of Engineering Universiti Malaysia Sarawak
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PROCEDURE:
1. Please refer to attachment for experimental set up
2. Switch on the display unit to warm up the unit.
3. Fixed the two supports tightly to the base with the distant between them equals to the
span of the beam.
4. Check that the load cell is properly secured to the pivoting plate.
5. Place one end of the beam between the clamping plates of the moment support and
tightened the two screws to fixed the beam.
6. Place the other end of the beam with the load hanger.
7. Record the initial reading of the channel. (result on the display should be divided by
5.7 as the offset because of the calibration problem)
8. Place a suitable load on the load hanger and record the reading of the load cell.
9. Increase the load on the load hanger and record the pier reactions.
10. Repeat for a few more load increments
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RESULTS :
1. Complete the required data
Beam Span = mm
Distance of the load from support B, a = mm
Reaction at pinned support = R1
Reaction at fixed support = R2
Fixed end moment (Experimental) = (R2 * 55) Nmm
2. Complete the following table.
Table 5 : Support Reaction against Applied Loads
Load W, (N) Load Cell Reading
at Pinned Support, R1, (N)
Load Cell Reading at Fixed Support
R2, (N)
3. Calculate and complete the following table
Table 6 : Reaction and Moment against Applied Loads
Load On The
Beam, W, (N)
Reaction At Pinned
Support (N)
Reaction At Fixed
Support (N)
Fixed End Moment
(Nmm)
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4. Using the data from the Table above plot the graph of:
(a) Fixed end moment verses load
(b) Reaction at the fixed support versus load
5. Determine the slope of each graph
6. Calculate the theoretical fixed end moment and reactions for 1 N load.
7. Determine the percentage error.
DISCUSSION :
1. For a beam loaded with a single point load as above, discuss the the relationship
between the fixed end moment and load as well as the reaction at the pinned support
and load.
2. Describe the change in the magnitude of the fixed end moment and the reaction at
the fixed support if the load moves away from the pinned support.
3. Compare and discuss the empirical and theoretical calculation.
4. List the possible cause of errors.
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TITLE :
SD5 – Torsion of Shaft
THEORY :
Torsion is a straining action produced by couple moment that act normal to the axis of a
member. It is identified by a twisting deformation. When subjected only to torque, the
member is in pure torsion, which produces pure shear stresses. The shear properties of
materials are determined by a torsion test.
From the torsion theory the relationship between torque, section property, length,
material property, and angle of twist is given by,
T σ Gθ
J r L
Where T is the torque
r is the radius of the specimen where stress is to be determined
L is the length of the specimen
J is polar second moment of area of the section
G is the shear modulus of the material
σ is the stress at radius r
θ is the angle of twist in radian
From the above equation,
T Gθ
J L
Or
GJ
L
= =
=
T = x θ
(1)
(2)
(3)
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Since G,J and L are constant for a particular experiment, therefore equation 3 can be
written as follows;
T = constant x θ
By plotting the graph of torque verses the angle of twist, the value of the constant can be
determined from the slope of the graph.
OBJECTIVE :
To determine the relationship between the applied torque and the angle of twist and hence
obtain the shear modulus.
APPARATUS :
Torsion apparatus, test specimen.
SAFETY PRECAUTIONS :
Beware of the apparatus controller; please don’t overdo the experiment to avoid the
failure of the specimen.
PROCEDURE :
1. Attach the specimen to the socket of the torsion apparatus. Measure the length and
diameter of the specimen.
2. Tighten all the parts including the protractor to read the degree rotation.
3. Apply torque to the specimen by pressing the motor switch to ‘test’ position.
Increase the load by 1N and for each increment switch off the motor to allow readings
to be taken. Whenever the motor is not capable of twisting the specimen further turn
the motor controller knob just slightly to increase the motor speed.
4. Record the load cell and the protractor readings for each load increment. The reading
of digital protractor can be omitted.
5. This experiment is to be conducted in the linear range only, it is advisable that the
torsional stress should not exceed 0.3 the yield stress of the material.
(4)
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RESULTS :
1. Complete the required data
Length of spesimen = mm
Diameter of spesimen = mm
Polar moment of inertia. = mm
Torque arm, L = mm
2. Record and calculate all the data in the following table
Table 7 : Experimental Data
Load Cell Applied Torque
Nmm Angle Of Twist
(degree) Angle of Twist
(radian)
3. Plot the graph of applied torque, T (Nmm) versus the angle of twist, θ (radian). Draw
the best fit curve through the plotted points.
4. Determine the slope of the graph. This represents the average torque per unit angle
of twist. Find the value of G.
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DISCUSSION :
1. From the experimental data define the relationship between applied torque and angle
of twist.
2. How does the value of G obtained from the experiment compares with that normally
assumed in practice for the material being tested.
3. What are the possible sources of error in this experiment.
4. If the specimen is tested to failure describe the failure surface. Does it reflect the type
of material (brittle or ductile) being tested..
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TITLE :
SD6 – Flexure Stress
THEORY :
Flexural strength, also known as modulus of rupture, bend strength, or fracture strength, a
mechanical parameter for brittle material, is defined as a material's ability to resist
deformation under load. The transverse bending test is most frequently employed, in
which a rod specimen having either a circular or rectangular cross-section is bent until
fracture using a three point flexural test technique. The flexural strength represents the
highest stress experienced within the material at its moment of rupture. It is measured in
terms of stress, here given the symbol σ.
Figure 7: Simply Supported Beam
Calculations: Deflection formula for the load given above:
δδ
I
FLE
EI
FL
4848
33
==
A determination of the flexural stress yields:
( )41
LFFM
W
Mb
b
bb +==σ
L
F+F1
L/2
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When rectangular it is 12
3bhI = and
6
2bhWb =
When circular it is 64
4dI
π= and
32
3dWb
π=
δ = Deflection (mm.) E = Coefficient of Elasticity L = Span(mm.) I = Inertia Factor Mb = Moment of Flexure (Nmm) F1 = Load occasioned by weight of Load Device
(N) Wb = Resistance to Flexure (mm3) F = Load occasioned by additional weight (N) σb = Flexural Stress (N/mm2)
When E is calculated, the initial load caused by the load device has no significance since
the gauge has been set at zero with the device in place. However, when calculating
flexural stress, F1 is included.
OBJECTIVE :
To determine and compare the coefficient of elasticity for different materials.
APPARATUS :
Beam apparatus, beam specimen (steel, brass and aluminium), a set of weights.
SAFETY PRECAUTIONS :
Beware of the loose heavy items such as weights and make sure apparatus is well
tightened.
PROCEDURE :
1. Bolt the two supports to the support frame using the plate and bolt supplied with the
apparatus. The span is set at 500 mm and steel is employed
2. Mount load device and set the testing device.
3. Load with weights as shown in Table (shown in example) and read off the deflection.
(1 div = 0.01mm)
4. The test is repeated with test specimens of brass and aluminium.
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RESULTS:
1. Complete the required data
Beam Span, L = mm
Base length, b = mm
Height, h = mm
Weight load device, F1 = (N)
2. Complete the table with experimental results and calculate the coefficient of
Elasticity and the flexural stress.
Table 8 : Experimental Data
Material Load F (N)
Moment of Flexure
Mb (Nmm)
Flexural Stress
Deflection Coefficient of
Elasticity
σb
(N/mm2) δ
(mm) E
(N/mm2) Eave
(mm)
Steel
Brass
Aluminium
DISCUSSION :
1. Discuss the relationship between the Moment of flexure, Flexural Stress and
Coefficient of Elasticity with the increasing of loads.
2. Compare the Coefficient of Elasticity obtained with the theoretical value for each
material and discuss the results.
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TITLE :
SD7 - Relation between Angular and Linear Speeds
THEORY :
Linear velocity is the distance travelled in a straight line per unit time while Angular
velocity is the angle travelled per unit time. Angular velocity expressed in the form of
what angle is rotated in a certain amount of time.
This relationship can be viewed in Uniform Circular Motion. For Instances, if ones
watches bicycle going along it is clear that, because there is no slippage between the
wheels and the road, there is a direct relationship connecting the linear speed along the
road and the rate at which the wheels turn. Instantaneously the speed at right angles to the
radius at the point of contact should be the rate of rotation of that radius.
OBJECTIVE :
To find the relationship between the angular rotation of a stopped shaft and the linear
travel of weights carried by cords wound round the shaft.
APPARATUS :
Mounting Bracket, Bob Weights, Measure Tape or Ruler.
SAFETY PRECAUTIONS :
Beware of the loose heavy items such as weights and make sure apparatus is well
tightened.
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PROCEDURE :
1. Fix the apparatus in a vice or on a bench top so that the bob weights can travel at
least 950 mm towards the floor.
2. Release the top screw within the stepped shaft and turn the stepper shaft so that the
cords start to wind evenly and neatly onto the shaft. Wind the cord so that the three
bob weights are level, and just under the shaft. Insert the top screw so that the cords
do not unwind
3. Use the adjustable screws in the bob weights to adjust the heights of each weight so
that the undersides are the same distance above the floor when the stepped shaft is
against the stop screw. Record these heights in columns 2,4 and 6 in table 9, against
the 0 number of shaft turns.
4. Temporarily release the stop screw and let the stepped shaft turn one revolution as the
weights descend. Measure the new heights above the floor of the bob weights and
enter them in columns 2, 4 and 6 of table 1 against 1 number of shaft turns. Repeat
this for three more turns of the handle recording in table each time.
5. Measure the nominal diameter of the steps in the shaft after the cords are wound
completely off the shaft. It will be easier with most of the cord removed. Record these
diameters.
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RESULTS :
1. Record all the required data in the following table.
Table 9 : Bob weight travel against shaft rotation for different diameters
1 2 3 4 5 6 7 Shaft Dia. Ø25 mm shaft Ø50 mm shaft Ø75 mm shaft
No. of turns of shaft, N
Height above floor (mm)
Distance Moved
s (mm)
Height above floor (mm)
Distance Moved
s (mm)
Height above floor (mm)
Distance Moved
s (mm)
0 1 2 3 4
2. Plot distance moved by each bob weight against turns of the shaft graph. Calculate
the gradient of each straight line and divide the gradients by the nominal diameters, d
to find the ratio in each case.
3. Convert the distances and rotation to linear and angular speeds by assuming that the
four turns of the shaft take four second.
DISCUSSION :
1. Comment on general accuracy of the results and suggest any improvements to the
procedure, which would minimize errors.
2. Describe was the relationship between the linear speeds and the angular rotation?
3. Why should the rpm of a drilling machine be varied to suit the size of the drill?
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TITLE :
SD8 – Compound Pendulum
THEORY :
A compound pendulum, in its simplest form, consists of a rigid body suspended vertically
at a point which allows it to oscillate in small amplitude under the action of gravity.
Consider a bar suspended at point O and is free to oscillate.
Figure 8: A compound pendulum
O is the point of suspension
G is the centre of gravity
m is the mass of the body
θ is the angular displacement
α is the angular acceleration
I0 is the mass moment of inertia of the body
When the body is given a small displacement θ, the restoring moment about O to bring
the body back to its equilibrium position is given by:
Restoring moment, Mr = m×g×h sin θ (1)
Disturbing moment, Md = I0×α (2)
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Since θ is small, sin θ = θ, therefore;
m×g×h = I0 ×α
α = (m×g×h) / I0 (3)
Periodic time = 2π × √(�������� �/������� )
= 2π × √(�/�)
= 2π × √(��/��ℎ) (4)
Frequency of motion, n = 1/ (periodic time) (5)
From parallel axis theorem,
I0 = Ig + mh2 (6)
Ig = m k2 (7)
Where k is the radius of gyration.
OBJECTIVE :
To determine the frequency of motion of a compound pendulum , mass moment of inertia
and the radius of gyration.
APPARATUS :
A simple compound pendulum (rod and a cylindrical bob weights), a stop watch.
SAFETY PRECAUTIONS :
Beware of the loose heavy items such as weights and make sure apparatus is well
tightened.
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PROCEDURES :
A. Frequency of motion of the rod
1. If the bob weight is attached to the rod, remove it. Measure and record the diameter of
the rod.
2. Weigh and record the weight of the rod. Hang the rod at the point of suspension.
3. Hang the rod at the point of suspension. Measure and record the distance the point of
suspension from the end of the rod (close to the point of suspension) to obtain the
position of centre of gravity.
4. Displace the rod at a small angle and release the rod and start the stopwatch
simultaneously. Stop the watch after the rod has executed 5 cycles of oscillations.
Record this time in the Table provided.
5. Repeat step 5 for a few more times to get the average of time over 5 oscillations.
6. Remove the rod and hang it at a new point of suspension. Measure and record the
distance the point of suspension from the end of the rod (close to the point of
suspension).
7. Repeat step 3-6
B. Frequency of motion of the rod and bob weight
1. Take the bob weight and weight it. Record its weight
2. Measure and record the diameter of the bob weight to obtain the position of centre of
gravity.
3. Measure and record the thickness of the bob weight.
4. Decide the position of the bob weight on the rod and insert the rod through the hole in
the bob weight until the decided location. Tightened the screw on the bob weight against
the rod to hold the bob weight in position.
5. Measure the distance of the centre of gravity of the bob weight from the point of
suspension
6. Displace the rod at a small angle. Release the rod and start the stopwatch simultaneously.
7. Stop the watch after the rod has executed 5 cycles of oscillations.
8. Record the time in the Table provided.
9. Repeat step 6 to 8 for 10, 15 and 20 oscillations.
10. Repeat with a few more positions of the bob weight.
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RESULTS :
1. Record the required data.
Part A:
Diameter of the rod = mm
Weight of the rod = mm
Length of the rod = mm
Part B:
Weight of the bob weight = mm
Diameter of bob weight = mm
Thickness of bob weight = mm
2. Tabulate the data in the following table.
Table 10 : Time of readings of time over 5 oscillations
Distance of the point of suspension from the top
end of the rod, mm
Time Taken, s
1 2 3 Average
3. Plot the data of average time taken against the distance.
4. Tabulate the following table.
Table 11 : Average time versus number of oscillations
Distance to the bob
weight (mm)
Number of Oscillations 5 10 15 20
1 2 3 �̅ 1 2 3 �̅ 1 2 3 �̅ 1 2 3 �̅
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5. Plot the graph of average time (sec) versus number of oscillations (cycle)
6. Calculate the theoretical periodic time and hence the frequency of motion.
7. Calculate the mass moment of inertia about the point of suspension and radius of gyration
about axis passing through the centre of gravity.
DISCUSSION :
1. Describe your findings from the results obtained especially from the plotted graph.
2. Comment on general accuracy of the results and suggest any improvements to the
procedure, which would minimize errors.
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TITLE :
SD9 – Flywheel Apparatus
THEORY :
Most machinery has parts, which revolve on their rotational axis; for example, wheels,
shafts, electric motors, centrifugal pumps, etc. This rotary motion is subject to the same
basic laws as linear motion, but all the terms have to be transformed to comply with the
special conditions of rotation.
For example the second law of motion changes as follows :-
Force = Mass × Acceleration ( F = ma)
Force × Radius = Rotational Mass × Rotational Acceleration
Couple = Moment of Inertia × Angular Acceleration (C=Iα)
The couple, C is also referred to as the torque, being the turning force exerted. The
application of this alternative form of the second law is widespread and most important in
understanding the performance of rotating machinery.
Where it is necessary to start rotating machinery quickly the moment of inertia must be as
small as possible to permit fast acceleration with the maximum value of torque.
On the other hand, when a reciprocating engine is required to run at a uniform speed
regardless of the fluctuation in driving force as each cylinder delivers power it is common
practice to increase the overall moment of inertia by adding a flywheel to the engine
shaft. A further use of flywheel is to store rotational energy, which is recoverable as it
slow down, thereby making a large couple available for a short period.
OBJECTIVE :
To determine the relationship between the angular acceleration of a flywheel and the
torque producing the acceleration.
APPARATUS :
Flywheel apparatus, bob weights, timer
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SAFETY PRECAUTION :
Beware of the loose heavy items such as weights and make sure apparatus is well
tightened.
PROCEDURE :
1. Take the load hanger and pulling cord, and hook the end loop over the peg on the
flywheel shaft.
2. Wind up a definite number of turns; say 8, from the position where the cord falls off
the peg. This ensures that the driving torque due to a load on the hanger will act for a
set number of revolutions.
3. Wind up the pulling cord 8 turns and add a 10N load to the hanger. This load will
just allow the flywheel to rotate at a near constant angular velocity, and thus
overcome bearing function.
4. Hold the flywheel with one hand and a stopwatch in the other. The engraved mark
should be by the pointer at this stage.
5. Release the flywheel and start the watch. Count the revolutions with the aid of the
mark, using this to judge when to stop the watch as the set number of revolutions is
turned. The load hanger will fall onto the ground.
6. Repeat the above procedure adding load by increments of 1N. Keep on repeating the
experiment until at least six readings have been obtained. Try re-timing one or two
of the readings to see what the probable accuracy of the measurement is.
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RESULTS :
1. Tabulate the times for the different values of mass plus hanger and calculate 1/t2
Table 12 : Acceleration of a Flywheel
No. of turns N
Weight mg (N)
Time (t) (s.)
1
�� Effective Couple
(Nm) 0 1 2 3 4 5 6 7 8
2. Plot the experimental results on a graph of total load against 1/t2, and draw the best
fit straight line through the points.
3. The gradient of the line provides an average value for the relationship between the
driving force and the angular acceleration, and should be multiplied by the
appropriate factor to obtain the value of k (that is, the moment of inertia). The
intercept on the total axis gives the initial load for which there is zero acceleration;
this must be the load required to overcome the friction in the bearings of the flywheel
shaft. Deduct this from the total load for each result and hence calculate the effective
couple, which should be entered in the table.
4. Convert the distances and rotation to linear and angular speeds by assuming that the
four turns of the shaft take four second.
DISCUSSION :
1. Compare the experimental and theoretical values of the moment of inertia obtained
in the experiment. Note the variability of any re-measured results of time, and of the
deduced friction if the experiment was repeated. Comment on the accuracy of the
experiment.
2. The theory, which was being verified, assumed the angular acceleration was uniform.
Can the experiment test this assumption?
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TITLE :
SD10 – Belt Friction
THEORY :
The belt friction apparatus set as below will provide us some set of data including the
tension of the belt and the angle of contact. The coefficient of friction can be calculated
based on the data obtained.
Figure 9: Belt Friction apparatus
Let, T1 = Tension on the tight side
T2 = Tension on the slack side
θ = The angle of contact, ie. the angle subtended by the arc AB at the centre of
the driven pulley
µ = The coefficient of friction between the belt and the pulley
The ratio of the two tensions may be found by considering an elemental piece of the belt
MN subtending an angle dθ at the centre of the pulley
The various forces that keep the elemental piece in equilibrium are:
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(a) Tension T in the belt at M acting tangentially
(b) Tension T + dT in the belt at N acting tangentially
(c) Normal reaction R acting radially outward at P, where P is the mid point of
MN
(c) Friction force F = µR acting at right angle to R and in the opposite direction to
the motion of the pulley
The angle PCM = FMT = dθ/2
From the theory, we will obtain
R = T dθ (1)
R = dT / µ (2)
Equating (1) and (2) gives
T dθ = dT / µ
= µ dθ (3)
Intergrating Equation (3) gives
loge (T1 / T2) = µθ
or (T1 / T2) = eµθ (4)
The torque exerted on the driving pulley = (T1 – T2) * r1 (5)
For the this experiment T2 is the equal to the load applied at the hook end
T1 is obtained from equation (5)
By plotting the graph of loge (T1 / T2) versus θ the coefficient µ can be found.
OBJECTIVE :
To determine the coefficient of friction between belt and pulley
APPARATUS :
Belt friction apparatus, Set of Weights
SAFETY PRECAUTIONS :
Beware of the loose heavy items such as weights and make sure apparatus is well
tightened.
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PROCEDURE :
1. Decide and record the angle θ.
2. Screw the stud to the mounting hole corresponding to this angle.
3. Hang a load hanger at the hook end of the belt.
4. Wound a cord round the pulley to apply torque to the system.
5. Hang a load hanger at the free end of the cord.
6. Apply tension to the belt by applying load on the hanger.
7. Place small weights on the torque hanger and observed the pulley. If the pulley does
not move, remove the load from the hanger. Increase the load and place it again on
the hanger. Repeat until the load on the hanger is able to rotate the pulley.
8. To get a more accurate result, adjust the last load on the hanger that causes the pulley
to rotate (decrease the load) and record the smallest load that causes the rotation.
This is the load that provides the torque just sufficient to overcome friction of the
belt.
9. Record the tension in the belt and repeat step 8 to 11 for a few more load increment.
10. Choose another angle θ and repeat the experiment.
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RESULTS :
1. Record your observations for the load on belt and torque against angle.
Table 13 : Load on belt and torque hanger against angle
Stud Angle δ
Degrees
Angle of Contact, θ Degrees
Angle of Contact, θ Radian
Load on Belt, T2 (N)
Load on Torque Hanger, WT (N)
2. Plot the graph of T2 versus WT for each angle of contact.
3. Obtain the slope of each graph to obtain the average belt tension, T2 for each case.
4. Obtain the average values of T1 and T2 and fill the values in Table 2.
Table 14 : Average values of T1 and T2 against angle
Average T1 (N) Average T2 (N) Loge (T1/T2) Angle of Contact, θ, radian
5. Plot the graph of Loge (T1/T2) versus θ.
DISCUSSION :
1. Comment on the value of the coefficient of friction and the results.
2. How does the radius of the pulley affect the tensions in the belt?
3. How does the angle of contact affect the performance of the system?
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APPENDIX A
SAFETY FIRST
• Follow all instructions carefully.
• Appropriate clothing must be worn in the lab. No loose clothing or jewelry around
operating equipment. Do not wear open toe shoes or sandal in operating laboratories.
• Do not operate equipment or carry on experiments unless the instructor/technician is
present in the laboratory.
• Assure that necessary safety equipment is readily available and in usable condition.
• Become familiar with safety precautions and emergency procedures before
undertaking any laboratory work.
• All injuries, no matter how small, must be reported.
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APPENDIX B
GUIDELINES
• All laboratory works should be conducted within the period given.
• The laboratory rules and regulations apply throughout the lab sessions.
• Lab report should be submitted ONE (1) WEEK after every lab session.
• Attendance for every lab session is COMPULSORY. No mark will be given to any
report (s) submitted without attending the lab session (s).
• Reports must be written in the following format :-
� Formatting guidelines
– Font type & size : Times new roman, 12
– Spacing : 1.5 spacing
– Margin : left (1.5”), right (1.25”), top (1”) and
bottom (1”)
– Front Cover : Use Template Provided
– Tape binding
� Peers Evaluation Form – submit individually for every laboratory activity
weekly.
� Content guidelines
– Assessment Cover Page (only write the group name & signed by group’s
representative)
– Front Cover page
– Table of content
– Lab code & title of experiment
– Introduction / Theory
– Objectives
– Procedure
– Result
– Discussion
– Conclusion / recommendation
– References