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Engineering Mechanics (ENT 113)
Laboratory Module
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Northern Malaysia University College of Engineering
LABORATORY MODULE
ENT 113/4
Engineering Mechanics
LAB
(NO.)
(TITLE)
GROUP
:
NAME
:
MATRIC NO. :
DATE
:
LECTURER
: DR. MERDANG SEMBIRING
MR AHMAD FAIZAL SALLEH
TEACHING ENGINEER
: MISS ADILAH HASHIM
MISS ROBIYANTI ADOLLAH
TECHNICIAN
: MR MOHD NIZAM HASHIM
MR ANUAR AHMAD
Received by: ___________________________________________ Date: __________
Engineering Mechanics (ENT 113)
Laboratory Module
LAB 1
Resolution of a Force into Non Parallel Forces
1. Objective
To demonstrate that one force can be resolved into two forces whose lines of action
intersect.
2. Equipment
1. Demonstration board for physics
2. Torsion dynamometer, 2 N/4 N
3. Scale for demonstration board
4. Weight holder for slotted weights
5. Slotted weight, 10 g, black
6. Slotted weight, 10 g, silver
7. Slotted weight, 50 g, black
8. Slotted weight, 50 g, silver
9. Protractor disk, magnet held
10. Fish line, 0.5 m of
11. White board pen, water soluble
3. Procedure
1. Place one of dynamometer onto the demonstration board and adjust it.
2. Attach a small loop made of fish line to the hook of the weight holder.
3. Hang the weight holder with slotted weights (2 x 10 g, 1 x 50 g) on the
dynamometer
4. Read and record the force (F1) indicated on the dynamometer.
5. Place the second dynamometer onto the demonstration board, adjust it.
6. Hook its traction cord to the point of application of force (F2).
7. Shift the two dynamometers in such a manner that their traction cords enclose an
arbitrary angle between them.
8. Place the protractor disk such that its centre is behind the point of application of
the forces.
9. Read the values indicated by the dynamometer for F1, and F2.
10. Determine the angles α1, and α2 which F1 and F2 enclose with the perpendicular
on the protractor disk.
11. Record the results in Table 1.
12. Change the position of the dynamometers several times, and determine the
respective quantities F1 and F2 as well as the corresponding angles α1 and α2
(include the case where α1 + α2 = 90°).
13. (Note: ensure before each measurement that the point of action of the forces
coincides with the centre of the protractor disk.)
14. Record the measured values in Table 1.
Engineering Mechanics (ENT 113)
Laboratory Module
Figure 1
Remove the two dynamometers. With the aid of the protractor disk and the scale
construct the force parallelogram with the white board pen for one of the investigated
cases on the demonstration board (Fig. 2).
Figure 2
Engineering Mechanics (ENT 113)
Laboratory Module
The sum of the magnitudes of F1 and F2 is always larger than the magnitude of the force
which is to be resolved. The larger the angle enclosed by the forces (α1 + α2 ) the larger
their sum is.
In any case F1 and F2 result in the same action as the force F .They are termed the
components of F.
F1 and F2 can be determined by drawing their lines of action and the force F; thus
constructing a force parallelogram, whose diagonal is formed by F. The components F1
and F2 form the sides of the parallelogram.
A force can be resolved into components whose lines of action intersect in the point of
application of the force. The components can be determined by construction or
calculation.
Remarks
In this experiment the weight holder with slotted weights has been selected to preset a
force which is then resolved into its components. A helical spring which has been
displaced by a certain distance is also appropriate for pre-setting the force. In this case the
position of the protractor disk whose centre marks the end of the extended spring may not
be changed.
It is advisable to have the students simultaneously construct the same force parallelogram
in their notebooks and drawing it on the demonstration board.
The special case in which α1 + α2 = 90° was selected so that the students could check
their results with a sample calculation even without knowledge of trigonometry.
An additional task could be a graphical check of the remaining measurements.
Recording an exact series of measurements is not absolutely necessary. One can also
restrict the experiment to a single measurement of F1 , F2 , α1 and α2 and determine the
force parallelogram by quadrupling the values. In this case, one should however
demonstrate qualitatively that the components enclose arbitrary angles and as a result can
have differing magnitudes.
4. Results
F = _________N
Table 1
F1(N)
F2(N)
α1(°)
α2(°)
Investigated all the cases using free body diagram
F1 + F2(N)
α1 + α2(°)
Engineering Mechanics (ENT 113)
Laboratory Module
Example:
F = 1.3 N
F2
F1
1.06N
51°
58°
1.14N
F1 = 1.06 N
F2 = 1.14 N
α1 = 58°
α2 = 51°
F1 + F2 = 2.20
1.3N
α1 + α2 = 109°
F1 + F2 ≥ F
F
5. Discussion
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6. Conclusion
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Engineering Mechanics (ENT 113)
Laboratory Module
LAB 2a
Helical Spring
1. Objective
Show that Hooke's law is valid in the loading of a helical spring and that the extension of
the springs is a function of the acting force and of the hardness of the springs.
2. Introduction
This equipment is used for measurement of the spring extension under the acting of force.
The length of the spring will change in direct proportion to the force acting on it. The
magnitude of force exerted on a linear elastic spring which has a stiffness (k) and is
deformed (elongated) a distance (s), measured from its unloaded position.
3. Equipment and Set up
3.1 Equipment
1. Demonstration board for physics
2. Hook on fixing magnet
3. Torsion dynamometer, 2 N/4 N
4. Scale for demonstration board
5. Weight holder for slotted weights
6. Helical spring, 3 N/m
7. Helical spring, 20 N/m
3.2 Set up
1. Position the hook on the fixing magnet near the upper edge of the demonstration
board and hang the soft helical spring with 3 N/m onto it.
2. Place the dynamometer directly below the helical spring; hook its traction cord
onto the helical spring; turn the dynamometer in such a manner that the line is as
short as possible and that the spring is slightly preloaded.
3. Position the scale on the demonstration board such that the lower end of the
spring is at the same height as the zero mark of the scale.
4. Set the pointer of the dynamometer to zero, and secure the scale (Fig. 1).
Engineering Mechanics (ENT 113)
Laboratory Module
Fig. 1 : Position of the hook
and the soft helical spring.
4. Procedure
1. Move the dynamometer downward until it indicates 0.2 N; measure the resulting
extension s and record it in Table 1.
2. Increase the tractive force in further steps of 0.2 N each. (When the dynamometer
has reached the lower edge of the demonstration board, turn the dynamometer
slightly, if necessary, and thus wind up the cord until a value of F = 0.8 N is
reached.) Measure the respective extension and note it in Table 1.
3. In a corresponding manner, perform the experiment with the hard helical spring
with 20 N/m (until F = 1 .2 N), and
4. Record the measured values in Table 2.
Engineering Mechanics (ENT 113)
Laboratory Module
5. Results
a. Soft Spring
Table : Soft spring
SAV
F (N)
S1
S2
(cm)
SAV
(m)
F/S AV (N/M)
SAV
(m)
F/S AV (N/M)
S3
0.2
0.4
0.6
0.8
b.Hard Spring.
Table : Hard spring
SAV
F (N)
S1
S2
(cm)
S3
0.2
0.4
0.6
0.8
1
1.2
6. Discussion & Evolution/Exercises
The graph of the measured values (Fig. 2) is a straight line in each case. Therefore, the
following is true:
F ~S
D=F/s
Question.
What the relationship F ~ s and D = F/s
Engineering Mechanics (ENT 113)
Laboratory Module
Plot graph, (F/s )1 vs S1, , (F/s )2 vs S2, , (F/s )av vs Sav, ,
s
F
7. Conclusion
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Engineering Mechanics (ENT 113)
Laboratory Module
LAB 2b
Bending A Leaf Spring
1. Objective
To investigate the bending behavior of a leaf spring under the conditions that the point of
application and the direction of the force remain the same. In addition, demonstrate that
the action of the force I is greatest when the force acts perpendicularly to the leaf spring.
2. Introduction
This apparatus is for measurement of the leaf springs deformation under the acting of
force in few of direction, but the leaf of spring always remains centre on the protractor
disk (s = constant). We can see that the action of the force I is greatest when the force
acts perpendicularly to the leaf spring.
3. Equipment and Set up
3.1. Equipment
Demonstration board for physics
Clamp on fixing magnet
Torsion dynamometer, 2 N/4 N
Scale for demonstration board
Pointers for demonstration board,
2 out of
Protractor disk, magnet held
Leaf spring, 300 mm x 15 mm
White board pen, water soluble
3.2 Set-up
Place the clamp on fixing magnet onto the demonstration board and clamp the leaf spring
into a horizontal position with it. Position the two pointers in such a manner that their
lateral edges are at the same height as the horizontally positioned leaf spring (Fig. 1).
Place and adjust the dynamometer in such a manner that its traction cord is vertical.
4. Procedure
1. Move the dynamometer vertically downwards until it indicates a force of 0.1 N.
2. With the white board pen mark the point on the board above which the end of the
leaf spring is located.
3. Move the dynamometer further downwards and in each case shift it slightly to the
side (so that the traction cord always remains vertical), and proceed in 0.1-N steps
as above. Remove the dynamometer and with the aid of the scale determine the
(vertical) distances s between the points marked with the white board pen and the
lower edge of the scale.
Engineering Mechanics (ENT 113)
Laboratory Module
4. Record the values for s in Table 1.
5. Position the dynamometer on the lower part of the demonstration board is such a
manner that the traction cord remains vertical, and a force of 0.8 N is indicated
(Fig. 2). Place the protractor disk such that its centre is directly behind the end of
the leaf spring.
Fig. 2 : Position of the dynamometer
Now shift the dynamometer progressively in the horizontal plane (to the right and left;
and, if necessary, move it slightly vertically in such a manner that the traction cord forms
an angle of approximately 30°, 45° with the vertical line and the end of the leaf spring
always remains centred on the protractor disk (s = constant). Measure the required force
in each case and note the values for the horizontal traction cord and the traction cord
perpendicular to the bent spring
Engineering Mechanics (ENT 113)
Laboratory Module
5. Results
Table 1
F (N)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
θ1 = 30°
θ1 = 40°
θ1 = 50°
6. Discussion & Evolution / Exercises
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Plot graph, (F/s ) vsS 1, , (F/s ) vs S 2, , (F/s ) vs S 3
s
F
7. Conclusion
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Engineering Mechanics (ENT 113)
Laboratory Module
LAB 3a
EQUILIBRIUM OF A BEAM 2 FORCES
General description
This apparatus is for measurement of support reactions of a simple beam or cantilever in
equilibrium under different loads. The beam is supported by two weighing machine or
load cell supports which indicate reaction. The tops of supports have knife edges fixed on
to the pan to transfer forces to the weighing machines. Load hangers with various weights
are hung at any points on beam between both supports. In case of a cantilever, a spring
balance is connected to one end of beam and one support stays between both ends of the
beam. The load hanger with weights is hung at the end of cantilevered segment.
Objectives
To compare the experimental reactions to the theoretical reactions of simple support and
cantilevered beams.
Equipments
Test beam
Weighing machine
Spring balance
load hanger
weight
Figure 1
Engineering Mechanics (ENT 113)
Laboratory Module
According to figure 1 , equations of equilibrium must be applied. These equations can be
expressed:
Here ∑Fx and ∑Fy represent the algebraic sums of the x and. y components of all the
forces acting on the body, and ∑Mo represents the algebraic sum of the moments of all
these force components about an axis perpendicular to the x-y plane and passing through
point 0. Refer to figure l, sum of moments of all for about point (1) obtains
Test Procedure
1. Place 1000 mm long simple beam on tops of two weighing machine.
2. Adjust spacing between supports to a required lengthen 1000 mm.
3. Adjust both supports to measure that the tops are in the same level.
4. Place two load hangers at x1=200 mm and x2 = 400 mm( fixed ) from point 1 and the
extension 100 mm for each point until 800mm. Record in Table 1.
5. Adjust the scale reading of both supports to be zero.
6. Place W=500 g load on both hangers and adjust the tops of both supports to be in the
same level and record both scale readings.
7. Place load hanger and a required weight at the end of extension.
8. Record both scale readings.
Engineering Mechanics (ENT 113)
Laboratory Module
Table 1
W = 500 g
No
.
x1
(mm)
M1
(Nm)
Measured
x2
(mm)
M2
(Nm)
Theoretical
RL(g) RR(g) RL(g) RL(g)
%
Difference
RL
RR
1
2
3
4
5
OBSERVATIONS
Do the experimental results verify the theory? If there are discrepancies in the measured
values ∑Fx and ∑Fy , compared by theoretical which experimental method appears to be
more reliable?
Conclusions :
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Engineering Mechanics (ENT 113)
Laboratory Module
LAB 3b
EQUILIBRIUM OF A BEAM 3 FORCES
Test Procedure
1. Place 1000 mm long simple beam on tops of two spring.
2. Adjust spacing between supports to a required lengthen 1000 mm.
3. Adjust both spring to measure that the tops are in the same level.
4. Place three load hangers at x1=200 mm, x2 = 450 mm and x3 = 700 mm from the
left point, respectively.
5. Adjust the scale reading of both springs to be zero.
6. Place 500 g load on all hangers and adjust the tops of both springs to be in the same
level and record both scale readings, increased 100 g each point until 1 kg. Record in
Table 2
X3
X2
X1
W1
W2
R1
W3
R2
L
Engineering Mechanics (ENT 113)
Laboratory Module
Table 2
Measured
W
(kg)
0.5
0.7
0.9
1.1
1.3
1.5
WT
(kg)
M1
(Nm)
M2
(Nm)
M3
(Nm)
R1
(kg)
R2
(kg)
Theoretical
RT
(N)
R1
(kg)
R2
(kg)
RT
(N)
%
Difference
RT
OBSERVATIONS
Do the experimental results verify the theory? If there are discrepancies in the measured
values ∑Fx and ∑Fy , compared by theoretical which experimental method appears to be
more reliable?
Conclusions :
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Engineering Mechanics (ENT 113)
Laboratory Module
LAB 4
FRICTION ON AN INCLINED STEEL PLANE
a. FRICTION BETWEEN TWO SURFACES
1. Objective
The objects of this experiment are to show that friction is proportional to the normal
force, and to determine the coefficient of friction between various materials and a steel
plane.
2. Procedure
1. Firstly make sure the surfaces used in this work must be cleaned for the
experiment and kept free from corrosion when not in use.
2. The adjustable steel plane is to be positioned on a firm bench so that the load on
the hanger passes the edge of the bench as it descends.
3. Clamp the plane in the 0o position and use a spirit level to set the plane truly
horizontal by adjusting the three levelling feet.
4. All the trays to be used must be weighed and their masses recorded.
Part 1
1. Place the tray on the horizontal steel channel at the end remote from the pulley.
2. Attach the towing cord and arrange it over the pulley with the load hanger
suspended. Add load to the hanger until the tray will continue to slide at roughly
constant velocity after being given a slight push to start it moving.
3. Record this load in table Exp. 1 and Exp. 2
Engineering Mechanics (ENT 113)
Laboratory Module
Part 2
1. Repeat the above procedure with four increments of 5 N placed in the tray.
2. With as many trays as are available used in turn gently add weights to the load
hanger until the stationary tray plus a 5 N load suddenly moves.
3. Record the load as the static friction hanger load in table Exp 1. and Exp. 2
4. Then, while each tray is in use, repeat the initial procedure of Part 1 (tray still
with 5 N load).
5. Record the results in table Exp. 1 and Exp. 2
Results
Table Exp.1
Mass of tray =
Tray load
(N)
0
5
Normal force N
(N)
kg.
Sliding force F
(N)
Ratio F/N
(N)
Repeat the above procedure with four increments of 5 N placed in the tray.
Table Exp.2
Friction coefficients on a steel surface
Tray
Material Mass
(kg)
Static Friction
Total
Coefficient
Force
(N)
Sliding Friction
Total
Coefficient
Force
(N)
The block of wood is an example of a non-isotropic material as the natural growth creates
structure in three axes (radial, tangential and longitudinal). Depending on how the block
is oriented to the grain of the wood so the surfaces may vary. Hence it is worth
measuring the static and sliding friction on the three sides. Further to this, measure the
areas of contact and then repeat the sliding friction experiment with a 15 N load on the
block to see if the area of contact has any effect.
Engineering Mechanics (ENT 113)
Laboratory Module
RESULTS:
EXPERIMENT 1
Material
Mass
(kg)
Weight
(N)
Brass
Aluminium
Brake material
Part 1.
a. Brass
Table 1a
Tray load
(N)
0
5
10
15
20
Normal force N
(N)
Sliding force F
(N)
Ratio F/N
(N)
b. Aluminium
Table 1b
Tray load
(N)
0
5
10
15
20
Normal force N
(N)
Sliding force F
(N)
Ratio F/N
(N)
c. Brake material
Table 1c
Tray load
(N)
0
5
10
15
20
Normal force N
(N)
Sliding force F
(N)
Ratio F/N
(N)
Engineering Mechanics (ENT 113)
Laboratory Module
Part 2.
Table 1.2
Tray
+ 10 N
Material
a
Weight
(kg)
Static Friction
b
Total
Force
(N)
c
Coefficient
(b/a)
Sliding Friction
d
Total
Force
(N)
e
Coefficient
(d/a)
Brass
Aluminium
Brake
Material
Convert the mass of each tray into its weight multiplying kg x 9.81 to give Newtons. The
normal force is then the weight of the tray plus any added load. The sliding force is the
sum of the hanger and its added load. Plot the results of Part 1 on a graph of sliding force
against normal force. Complete table 2 in a similar way.
Comment on the difference between static and sliding friction.
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Engineering Mechanics (ENT 113)
Laboratory Module
b. FRICTION ANGLES ON A STEEL PLANE
Objective
The objective of this experiment is first to find the angle of friction of various materials
on a steel plane. The second object is to verify that the force required parallel to an
inclined plane to move a body up the plane corresponds to the friction coefficient (or
angle) already found.
Procedure
1. Firstly make sure the surfaces used in this work must be cleaned for the
experiment and kept free from corrosion when not in use.
2. The adjustable steel plane is to be positioned on a firm bench so that the load
on the hanger passes the edge of the bench as it descends.
3. Clamp the plane in the 0o position and use a spirit level to set the plane truly
horizontal by adjusting the three levelling feet.
4. All the trays to be used must be weighed and their masses recorded
5. Clamp the plane at 100 inclination.
6. Place the tray at the lower end and put the towing cord and load hanger in
position to pull the tray up the plane.
7. Add load to the hanger until the tray, given a slight push, slides slowly up the
plane.
8. Repeat the procedure with a 10 N weight in the tray. Record the results in
Table 1.
*Repeat the above at angles of inclination 200, 300 and 400 for as many trays as are
available. ( tufnol, nylon and wood )
The equation of equilibrium of a body on an inclined plane. At the moment
of sliding, or at uniform velocity, the friction force must be equal to the component of the
weight acting down the plane. If the coefficient of friction is m then
.Wcos = Wsin
which leads to the concept of the angle of friction  since
 = tan
Engineering Mechanics (ENT 113)
Laboratory Module
and if there are any values for the coefficients of friction from the previous experiment on
a horizontal plane compare the results.
The theory from which is developed is an extension of the above. In this case the net
force acting up the plane must be equal and opposite to the friction force.
This can be rearranged either in terms of P or . As the experiment is essentially about
the coefficient of friction that determines the choice.
To complete table ( 1a, 1b and 1c ) convert the mass of the tray to its weight and add any
extra load. Finally average the coefficients of friction for comparison with previous
values.
Results:
Material
Mass
(kg)
Weight
(N)
Tufnol
Nylon
Wood
Table 1a ( tufnol tray ): Friction angles on steel plane
Angle of
Plane

(0)
10
20
30
40
Weight
of Tray
W
(N)
Towing
Force
P
(N)
a.
Normal
Force
Wcost
(N)
b.
Sliding
Force
P - Wsin
Friction
Coefficient
 =b/a
Friction
Angle
tan-1
(0)
Engineering Mechanics (ENT 113)
Angle of
Plane

(0)
Weight
of Tray
W
(N)
Towing
Force
P
(N)
Laboratory Module
Table 1b ( nylon tray )
a.
b.
Friction
Normal
Sliding
Coefficient
Force
Force
 =b/a
Wcost P - Wsin
(N)
Friction
Angle
tan-1
(0)
10
20
30
40
Table 1c ( wood tray )
Angle of
Plane

(0)
Weight
of Tray
W
(N)
Towing
Force
P
(N)
a.
Normal
Force
Wcost
(N)
b.
Sliding
Force
P - Wsin
(N)
Friction
Coefficient
 =b/a
Friction
Angle
tan-1
(0)
10
20
30
40
Observations
Do the experimental results verify the theory? If there are discrepancies in the measured
values of friction coefficients, which experimental method appears to be more reliable?
Finally average the coefficients of friction for comparison with previous values
Engineering Mechanics (ENT 113)
Laboratory Module
Conclusions :
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LAB 5
Moment Of Inertia
1. Objective
To study of angular acceleration as a function of the moment from which angle of
rotation and angular velocity as a function of time can be derived.
2. Equipment
Aluminium disk with a three step pulley and bull’s eye level
 Diameter : 350 mm
 Angular scale = 1 degree
 Pointer angle = 15 degree or 0.2618 rad.
 Radius of Pulley = i) 20.0mm
ii) 35.0mm
 Air bearing with stand.
The top of the disk is painted in black and white angular stripe of 7.5° to facilitate the
angle count of the experiment
 GA 121 Release mechanism as per attached catalog
 GA 110 Blower as per attached catalog
 GA 123 Precision pulley as per attached catalog
 GE 210 Light barrier as per attached catalog.
 GE 102 Power supply as per attached catalog
 Air hose, 1 ea 1.5 m with clamp.
 Air hose adapter, 1 ea.
Engineering Mechanics (ENT 113)






Laboratory Module
GE 240 Capacity as per attached catalog
Weight 20 pcs., 1 g ea (Weight hanger is 1g)
Electrical wire : 2 ea
GA 014 Tripod base 1 ea per attached catalog
GA016 Round base 1 ea per attached catalog
GA 022 Table clamp 2 ea as per attached catalog
3. Theory
Rotation of a frictionless disk follows Newton’s law i.e.
T
=I α
Where: T
= Moment
I
= Moment of inertia of the disk
α
= Angular acceleration
………….. (1)
Relationship between angular velocity and displacement
Where:
ϖ
=
θ
t
= Angle of rotation (angular displacement) for the disk
= Time taken to pass θ
ϖ
= Average Angular velocity
θ/t
………….. (2)
(Motion Equation)
Assuming acceleration is constant
ϖ = ( ωo + ω1) / 2
; ω1 = Instantaneous Velocity;
ωo = Initial Velocity;……….. (3)
ωo = 0
In our experiment Method 1,
ϖ = (1 / 2) ω1
∴
Substituting ϖ into Eq (2),
ω1
= 2θ / t
………….. (4)
Relationship between angular acceleration and displacement
Given
θ
= ωo
t + (1 / 2)α t 2
(Motion Equation)
….……….. (5)
In our experiment Method 1, ωo = 0
θ
= (1 / 2) α t 2
When a graph of θ is plotted against (1 / 2)
………….. (6)
t 2 , the slope of the graph is α .
Engineering Mechanics (ENT 113)
Laboratory Module
Measurement of ϖ
We obtain ϖ directly from the measurement using the equipment.
If Δt is time for the rotation of the pointer which is obtained from the light barrier.
ϖ2
= Δθ
/Δt
where
……….. (7)
Δθ = 15° or 0.2618 rad, the width of the disc pointer; and
Δ t = t2, reading obtained using Experiment Method 2
Measurement of I
For this experiment, the disk is floated on a thin layer of air from the blower. The rotation is considered
frictionless.
T = Wr
……….. (8)
W = Weight (including hanger weight) through a frictionless pulley.
r = Radius of the pulley a above the disk
(r = 20, 35 mm)
From Eq (1) and Eq (8),
Thus
Where:
Wr
= Iα
I
= Wr / α
……….. (9)
Please note that all θ readings should be converted to radians for the purpose of our experiments. The
conversion factor is
1 Degree
=
4. Equipment Set Up
π / 180
radians
……….. (10)
Engineering Mechanics (ENT 113)
1.
2.
3.
Laboratory Module
The light barrier is installed on the tripod base on a table.
The blower air outlet is connected to the air bearing air inlet
Adjust the air bearing tripod footing until the disk is horizontal by observing the bull’s eye level
on the disk pulley.
4. Install the release mechanism on a round base such that the release pin blocks the disk pointer
rotation
5. Install the light barrier such that the disk pointer interrupts the light signal barrier.
6. Connect the wirings as per Figure 3.
7. Install the release mechanism such that the release pin blocks the disk pointer at a selected angle θ
from the light barrier. The release mechanism should be placed such that when the disc is released
to turn, the turning of the disc and hence the angle θ, is measured in the direction from the light
barrier to the beginning of the disc pointer.
8. Wrap the chord around the disk pulley several times. The direction of winding (clockwise or
anticlockwise) depends on the position of the release mechanism (See point 4.7 above)
9. Install the precision pulley such that the chord from the disk pulley passes over the precision
pulley horizontally and the chord hangs down just outside the bench/table with a weight hanger.
10. Turn on the blower and increase the blower speed until the disk can freely turn on the air bearing.
Engineering Mechanics (ENT 113)
Laboratory Module
The release mechanism consists of a shutter type button which activates the pin and is connected to the
light gate to facilitate the start and stop of the appropriate timer function.
To Lock
Press the shutter lock button fully until it clicks.
To Release
Press the shutter release button to release the shutter and pin.
Adjustment
The shutter release can be also used to make minor adjustments to ensure the shutter button functions
accordingly. Turnit clockwise or anti-clockwise to ensure the shutter button can be locked and released.
5. Procedure
5.1 Method 1 → Measurement of θ as a function of time, t1
This experiment assumes an initial velocity value, ωo = 0 as the measurement starts from a still-standing
disc.
1. Position the disk pointer at a selected angle e.g. 30° from the light barrier and lock the disk in
position by the release mechanism pin and record the angle θ.
2. Put a weight on the weight hanger e.g. 10 g and record the total weight W and the radius r of the
disk pulley used as per 4.8.
3. Start the blower and ensure that the disc is free to turn.
4. Turn the selector switch on the light gate to
and press reset.
5. Release the disk pointer and the disk will start to rotate. The timer should also begin counting.
6. As soon as the whole of the disc pointer clears the pin, press the shutter button to lock it again.
This is to ensure that the timer button will function correctly.
7. When the start of the pointer passes the light barrier, the timer will stop.
8. Record t1.
9. Repeat steps 5.1.1 to 5.1.8 for other θ at 30° increment each time.
10. Repeat step 5.1.9 at other weights e.g., at 10 g increment or using another disk pulley(different
radius).
11. Calculate ω for the corresponding θ using Eq (4)
12. Plot a graph of θ vs (1 / 2) t12 (Graph 1). The slope will give you α.
5.2 Method 2 → Measurement of ω as a function of time,t2
This experiment measures the average velocity, ϖ. The angular displacement, Δθ, is constant, i.e., 15°.
The different starting points are to coincide with the ω readings obtained in Method 1 above.
1. Position the disk pointer at a selected angle e.g. 30° from the light barrier and lock the disk in
position by the release mechanism pin and record the angle θ.
2. Put a weight on the weight hanger e.g. 10 g and record the total weight W and the radius r of the
disk pulley used as per 4.8
3. Start the blower and ensure that the disc is free to turn.
4.
5.
6.
7.
8.
Turn the selector switch on the light gate to
and press reset.
Release the disk pointer and the disk will start to rotate.
When the start of the pointer passes the light barrier, the timer will start and it will stop as soon as
the pointer leaves the light barrier.
Record t2.
Repeat steps 5.2.1 to 5.2.8 for other θ at 30° increment each time. Use the same θ readings as used
in Method 1.
Engineering Mechanics (ENT 113)
9.
Laboratory Module
Repeat step 5.2.9 at other weights e.g., at 10 g increment or using another disk pulley (different
radius)
10. Calculate ϖ from Eq (8) for a selected θ
5.3 ωo can be calculated using the following method:
From Eq (3), use ϖ from 5.2.11 and the corresponding ω (as calculated in 5.1.11) value for the selected θ
E.g.,: At θ = 60° or 1.047 rads , ∆ θ = 15° or 0.262
ϖ
= Δθ / Δt
=0.262 / 0.162
= 1.617 rad/s
(Disk pointer)
Also from Method 1,
At θ = 60° or 1.047 rads
ω1
∴ ωo
=2θ1 / t1
, At θ = 60° or 1.047 rads
=2 (1.047) / 1.348
=1.55
= 2 ϖ - ω1
=2(1.617) – 1.55
= 1.684 rad/s
5.4 Calculate I using Eq (9)
= Wr / α
I
6. Results
ME202 MOMENT AND ANGULAR MOMENT
Weight of hanger and weight = 20 g
Disk pulley radius
= 20 mm
Θ
deg
30o
60o
90o
120o
150o
180o
Θ
rad
Δt
s
t1
s
t2
s
t1 / 2
s
(1/2) t1
s
2
Calculated Value
α=
ω1 =
2Θ / t12
2Θ / t1
rad/s2
rad/s
Engineering Mechanics (ENT 113)
Laboratory Module
Weight of hanger and weight = 20 g
Disk pulley radius
= 35 mm
Θ
deg
Θ
rad
Δt
s
t1
s
t2
s
t1 / 2
s
(1/2) t1
s
2
30o
60o
90o
120o
150o
180o
Graph 1 : θ vs (1 / 2) t12
(1 / 2) t12
Θ
Calculated Value
α=
ω1 =
2Θ / t12
2Θ / t1
rad/s2
rad/s
Engineering Mechanics (ENT 113)
Laboratory Module
7. Discussion
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8. Conclusion
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Engineering Mechanics (ENT 113)
Laboratory Module
LAB 6
WORK DONE BY A VARIABLE FORCE
(TANGENTIAL AND VERTICAL EFFORT)
a. WORK DONE BY A VARIABLE FORCE
( TANGENTIAL EFFORT )
Introduction
The measurement of work is always the product of a force and the distance through
which the force acts. If the force is acting at right angles to a radial member of constant
length R then the circular path traced by the force is the distance moved and is measured
by R8 (8 in radians). For a variable force the work done is then
U ΣFR θ
==
The Izod testing machine for brittle fracture is an example of this, the energy being
generated by a swinging pendulum with a heavy bob.
The experiment apparatus has some resemblance to the Izod machine, but is really
designed to relate the effort applied in raising the pendulum arm to the potential energy
by the weight at the end of the arm.
Engineering Mechanics (ENT 113)
Laboratory Module
List of Parts
1. HFC7 and HFC6 Main Unit.
2. Spring Balance Support.
3. 0.5 N x 100 mm Hanger.
4. Sheathed Hanger.
5. 150 mm x l N Hanger.
6. Cord.
7. 1 m Ruler
Apparatus
A vertical board supported by a base plate has a 350 mm pendulum arm pivoted at the top
right hand corner. At the free end of the pendulum there is a spring balance attached at
right angles in the plane perpendicular to 1he pendulum pivot, and also a loose clevis in
which a load hanger can be hung. Fixed about the pivot axis is a 90° protractor with the
zero vertically below the pivot. The pendulum arm is notched in order to show the
angular position of the centre line of the pendulum on the protractor. A large screw eye in
the outer end of the spring balance. enables it to be pulled tangentially by hand.
Objective
The object of the experiment is to compare the work done by the tangential effort in
raising the pendulum with the gain in potential energy of the loaded pendulum.
Procedure
1. Stand the apparatus on a firm level surface.
2. Check the pendulum arm swings freely.
3. Place the load hanger on the pendulum end and lift the arm up to 90° by pulling
on the spring balance tangentially to the arm. Note any "zero load" reading of the
balance.
4. Place a 10N load on the hanger and pull the spring balance to turn the arm
through 10° from the vertical.
5. Record the balance reading in Table 1.
6. Continue turning the arm by 10° increments up to 90° (horizontal), recording the
balance readings at each step.
7. Repeat the whole procedure with loads of 10, 20, 30 and 40 N.
Engineering Mechanics (ENT 113)
Laboratory Module
Table 1
Tangential Effort for a Loaded Pendulum
Angle from Vertical
0
()
Effort in N for added load of
10N
20N
30N
40N
10
20
30
40
50
60
70
80
90
It may have been found that there are some erratic readings because of the difficulty in
pulling the spring balance both axially and in a tangential direction. Hence the first stage
is to plot all the experimental results on one graph of spring balance effort against the
added load on the hanger. As at anyone angle the effort must be linearly proportional to
the load the graph must yield a family of nine straight lines with a common origin.
Bearing in mind that the self weight of the pendulum and load hanger is the same
throughout the experiment, this suggests that the common origin for zero effort will be a
negative value on the added load axis. In fact the negative intercept should correspond to
the "zero load" reading made at the start of the procedure. Hence draw in the nine straight
lines for the angular positions 10° by 10° to 90° of the pendulum arm, making the
common origin a definite point.
Conlusions:
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Engineering Mechanics (ENT 113)
Laboratory Module
b. WORK DONE BY A VARIABLE FORCE
( VERTICAL EFFORT )
Introduction
The idea that work can be measured as the product of the active force and the distance it
moves in its line of action is fairly simple. Where a lever is used to lift a given load, the
effort is a constant and it is easy to calculate the work.
However, there are also cases where the load is constant while the effort varies owing to
the mechanism in use, as for example with a car engine. The principle is still the same,
that is:
Work done = Force x Distance moved
U = Fs
where F is the force component acting in the direction of s. The computation of U must
now take account of the variation in F, and it can be expressed mathematically as:
U = ∫F.ds
or
Σ F.ds
The summation is frequently transformed into calculation of the area and under a graph
of F plotted against s.
Engineering Mechanics (ENT 113)
Laboratory Module
Apparatus
The apparatus supplied is a simple lifting mechanism with obvious non-linear
characteristics. A suspension cord carrying a loaded trolley (weight 0.9 N) at mid-span is
tensioned by passing the cord over a pulley at one end and down to a weight hanger. As
the vertical effort is increased the tensioned cord will move to a new equilibrium position
lifting the loaded trolley. The pulleys of the trolley and end support have ball bearings to
minimize friction. The base of the board on which the apparatus is mounted provides a
reference plane for measuring the heights of the load and effort.
Objective
The object of this experiment is to calculate the work done by a variable effort and to
compare it with the work done in lifting the load.
Procedure
1. Set up the apparatus by passing the nylon cord through the load trolley, over the
end pulley and down to the weight hanger.
2. Place 5 N weight on the trolley hanger.
3. Add weights to the effort hanger until the load is held in equilibrium at its lowest
possible position.
4. Record the added load plus 1 N (hanger) for the effort and the heights above the
baseboard of the bottom edge of the load and effort.
5. Increase the effort by an increment of 0.2 N and allow the suspension system to
find a new position of equilibrium.
6. Note the new values of effort and heights.
7. Repeat this to obtain a good range of readings, say up to ten, recording the
readings in Table 1.
8. Plot graph total Effort, F ( N ) by height of Effort ( s2 )mm
Table 1
Load
Height
S1
(mm)
Work
done
W(S1 – S0)
(N.mm)
Total
F
(N)
Average
per
Increment
Fav
(N)
Effort
Distance
Work
moved
Total work
Height
done per
per
done
S2
increment increment
LFav.ds2
(mm)
Fav.ds2
(N.mm)
d s2
(N.mm)
(mm)
Engineering Mechanics (ENT 113)
Laboratory Module
Complete Table 1 as follows to obtain the cumulative work done on the load. The
average effort is half the sum of the current value and the preceding effort. The distance
moved per increment is the difference between the current height and the preceding
height. This leads to the work done by the increasing effort per increment and thence to
the cumulative total of that work.
Conlusions:
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