UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering DEPARTMENT OF ENGINEERING MECHANICS STATICS LABORATORY LAPORAN MAKMAL/LABORATORY REPORT Kod M/Pelajaran/ Subject Code Kod & Tajuk Ujikaji/ Code & Title of Experiment
ENGINEERING LABORATORY I
TOPIC 4: PRINCIPLE OF MOMENTS
Kod Kursus/ Course Code
1.
LUQMAN HAKIM B MOHD MASROR
2.
FUAD RIDZUAN B MOKHTAR ARIF AIMRAN B AHMAD NORASIKIN BT AB RANI
3. 4.
Tarikh Ujikaji / Date of Experiment Tarikh Hantar / Date of Submission
Seksyen /Section
BNJ17001
Kumpulan/Group Nama Pelajar/Name of Student Lecturer/Instructor/Tutor’ s Name Nama Ahli Kumpulan/ Group Members
BDA 17001
6 No. K.P / I.C No.
7 LUQMAN HAKIM B MOHD MASROR
No. Matrik
1.EN. MOHD NAZRUL BIN ROSLAN 2. No. Matrik
Penilaian / Assesment
AN12011 5
Teori / Theory
10 %
AN12011 3
Keputusan / Results
15 %
AN12012 9 AN12003 2
Pemerhatian / Observation Pengiraan / Calculation Perbincangan / Discussions Kesimpulan / Conclusion Rujukan / References JUMLAH / TOTAL
20 % 10 % 25 % 15 % 5 % 100 %
4 OCT 2012 11 OCT 2012
ULASAN PEMERIKSA/COMMENTS
COP DITERIMA/APPROVED STAMP
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering
COURSE INFORMATION COURSE TITLE: ENGINEERING LABORATORY I (BDA17001) TOPIC 4: PRINCIPLE OF MOMENTS
1. INTRODUCTION The principle of moments is frequently used in engineering and building work where forces have to be balanced to prevent any turning movement. It can be applied both to parallel forces and to oblique forces. If a body has several forces applied to it which have turning effects in opposite directions, the body will not turn if the total turning moment in each direction are equal. This is called Principle of moments. 2. OBJECTIVES The objective of this experiment is to verify the principle of moments for parallel and non-parallel forces.
3. LEARNING OUTCOMES At the end of this topic, the students will be able to display basic skills and knowledge of principle of moments using laboratory equipments, analyze observable data obtained from principle of moments experiment properly, work effectively in a group through laboratory experiment and presentation and demonstrate comprehension of the general ideas of the topic through written report that comply with specified standards.
4. THEORY A concept often used in mechanics is the principle of moments, which is sometimes referred to as a Varignon’s theorem since it was originally
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering developed by the French mathematician Varignon. The moment of a force indicates the tendency of a body to turn about an axis passing through a specific point. It was defined as, M = F x d (in Nm)
……………………… (1)
Which, F is the action of force; d, is the perpendicular distance between F and centre of moment. (Figure 1a/1b) The principle of moments states that the moment of a force about a point is equal to the sum of the moments of the forces components about the point. For a body in equilibrium or not rotate: The Moment Clockwise = The Moments Anti-Clockwise (Refer to Figure 1c). So, F1d1 - F2d2 = 0 F1 d 2 F2 d1
……………………………….. (2)
F
d
d1
F
d2
d F2
F1
Figure 1a
BDA17001-2012
Figure 1b
4
Figure 1c
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering 4.1 ADDITIONAL THEORY
BDA17001-2012
6
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering Varignon ’s theorem can be proven easily using vector cross product that is obey distributive law. For two-dimensional problems , we can use the principle of moments by resolving the force into its rectangular components and then determine the moment using a scalar analysis. The moment is a scalar quantity,
BDA17001-2012
8
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering 5. EQUIPMENTS Table 1: Principles of Moments Equipment List No.
Apparatus
Qty.
1 2 3 4 5 6 7 8
Panel board Pivot bar and stop ( EX5) Pulleys ( P12) Nuts Screw Weight hook ( P10) Cord approx (40cm long) Set of weights
1 2 4 6 5 1 1 1
6. PROCEDURES 1. Set up the panel board as shown in Figure 2. Ensure pivot bar is in balance and attached pulley using bolt and nut. 2.
Pivot bar Figure 2
Weight Hook
Pulley
Figure 2: Experiment Setup 3. Hang weight hooks from the end holes of the bar entering the hook from the back of the bar.(Refer Figure 3a). The weight of hooks each weight 0.1N. BDA17001-2012
10
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering 4. Add a 1.9N load to each hook to make the total of 2N. 5. Record the value of F 1 and F2. Then measure and record the distance d1 and d2. 6. Move the right hand weight hook to a hole nearer the pivot bar (Refer Figure 3b) and load it with just sufficient weighs to balance the bar in the level position. 7. Record the weight value F2 and the distance d2 8. Then, hang right hand weight hook (without weight) through pulley (refer Figure 3c). 9. Load the weight hook to balance the bar. 10. Record the weight value F2 and the perpendicular distance d2. 11. Set up the panel as shown in Figure 3d, repeat the procedure from 7 to 9 with the cord passing over the left hand pulley and attach to the lowest hole of the centre arm of the bar. 12. Fill in the Table 2
d1
d2
2N
2N
Figure 4.3a: Test 1
d1
BDA17001-2012
d2
12
2N
F2
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering
d1
Figure 3b: Test 2
2N d2
F2
Figure 3c: Test 3
BDA17001-2012
14
d1
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering
d2 2N F2
Figure 3d: Test 4
7. RESULT 1. Fill in the experimental result in the Table 2. 2. Plot a graph for
BDA17001-2012
F1 d 2 vs F2 d1
.
16
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering Table 2: Results Moment
Left Pivot Bar
Right Pivot Bar
Total
Ratio
Test
Figure 4.3a
Figure 4.3b
Figure 4.3c
Figure 4.3d
F1
d1
M1
F2
d2
M2
M1 - M 2
F1
d2
(N)
(m)
(Nm)
(N)
(m)
(Nm)
(Nm)
F2
d1
2.00
0.16
0.32
2.00
0.16
0.32
0.00
1.00
1.00
2.00
0.16
0.32
3.20
0.10
0.32
0.00
0.62
0.62
2.00
0.16
0.32
3.50
0.09
0.32
0.00
0.57
0.56
2.00
0.16
0.32
4.00
0.08
0.32
0.00
0.50
0.50
* Data sheet must approved by the instructor
BDA17001-2012
18
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering 8. CALCULATON 1. Calculate the Moment for Left Pivot Bar and Right Pivot Bar.
BDA17001-2012
20
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering
Moment for left pivot , M = F x d (in Nm) Figure 4.3 (a) 2N (0.16m) = 0.32 Nm Figure 4.3 (b) 2N (0.16m) = 0.32 Nm Figure 4.3 (c) 2N (0.16m) = 0.32 Nm Figure 4.3 (d) 2N (0.16m) = 0.32 Nm
Moment for right pivot Figure 4.3 (a) 2N (0.16m) = 0.32 Nm Figure 4.3 (b) 3.20N (0.10m) = 0.32 Nm Figure 4.3 (c) 3.5N (0.09m) = 0.32 Nm Figure 4.3 (d) 4N (0.08m) = 0.32 Nm
2. Calculate the ratio of forces and distance. BDA17001-2012
22
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering
Ratio of distance Figure 4.3 (a) 2 N ÷ 2 N = 1.00 Figure 4.3 (b) 2 N ÷ 3.20 N = 0.62 Figure 4.3 (c) 2 N ÷ 3.5 N = 0.57 Figure 4.3 (d) 2 N ÷ 4 N = 0.50
Ratio of distance Figure 4.3 (a) 0.16m ÷ 0.16m = 1 Figure 4.3 (b) 0.16m ÷ 0.1m = 0.62 Figure 4.3 (c) 0.16m ÷ 0.09m = 0.56 Figure 4.3 (d) 0.16m ÷ 0.08m = 0.50
9. OBSERVATIONS BDA17001-2012
24
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering For the test1, the distance of force for left pivot bar was equal to the distance for left pivot bar from the centre pivot bar. The force of F1 and F2 are equal, sop the total value of moment is equal to zero. Thus, it is in equilibrium. For test2, the F1 is maintain and small than F2 because the load require for right pivot is more than left pivot to balance the pivot bar. Thus, the ratios of force and distance small. The distance of right pivot was shorter than then distance of left pivot. All the experiment was success because the total moment equal to zero according to the theory. From my observation, the ratio of force equal to the ratio of distance. This experiment obey the principle of moment state that the moment of clockwise equal to the moment of anticlockwise.
BDA17001-2012
26
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering 10. DISCUSSIONS
1. Discuss the graph obtained. The graph obtain is decreasing graph. When the ratio of force smaller, then the ratio of distance will decrease. Thus, the force become larger as the distance decrease.
2. Discuss your opinion about the summation of moment from your experiment results. Value of moment increase as the force becomes larger and as the distance from force’s line of action increase. If the line of action of F2 is perpendicular to the distance that we let, d as shortest distance between these two lines , then the moment produced by F1 has size F1d (Nm). The total moment will be zero or equilibrium when the value moment of left pivot bar are equal to the value moment of right pivot bar. ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… BDA17001-2012
28
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering
3. If the moment is nonzero, what are the factors may influence the experiment. The factors may influence the experiment when the moment is nonzero obtain after experiment is the force of load that we set up not balance. Second, the pivot bar that we were set up not balance before we added the load. Then, the distance between the load and the centre of pivot bar not accurate because when we measure the distance, maybe there was an error. The angle of perpendicular distance not equal to 90 also can influence the moment obtain.
10.1 QUESTIONS 1. What is the principle of moment and how moments achieved? The principle of moment also known as Vargnon’s thorem. It state that the moment of a force about a point is equal to the sum of the moment of the force’s components about the point. Principle of moments is if an object is
balanced then the sum of the clockwise moments about a pivot is equal to the sum of the anticlockwise moments about the same pivot. The moment can achieve when the distance from the line of action of the force to the pivot was obtained and its perpendicular to the force. The moment depends on the size of the force, the direction of the force and the distance from the force to the hinge. ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… BDA17001-2012
30
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering
2. What does the principles of Moment state about the turning moments of forces acting on a body? It will produce a tendency for the body to rotate about a point that is not on the line of action of the force. It is called simply the moment. The larger the force or the longer the moment arm, the greater the moment or turning effect. If the force applied at an angle, θ ≠ 90, then it will be more difficult for turning occur. It moment arm will be zero since the line of action of force will intersects to the z-axis. As the result, the moment of force about z-axis is also zero and the turning moment of forces cannot occur.
3. How to determine the moment in three dimensions body?
The moment in three dimensions body can be determine using the formula of clockwise moments equal to anticlockwise moment. You need to consider the force of three dimension bodies. You also need consider the distance of the bodies. ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………
BDA17001-2012
32
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering
11. CONCLUSION Deduce conclusions from the experiment. Please comment on your experimental work in terms of achievement, problems faced throughout the experiment and suggest recommendation for improvements. Moment of a force depends on both the forces and the location of the point about which the moment evaluated. Moment of force is equal to the sum of the moment of the components of the force after we carried out the experiment. So, the principle of moment was achieved. The principle of moment for parallel and non-parallel forces was verified. During the experiment, the pivot bar is unbalance, so we should ensure the pivot bar is in balance before we added the load. The ratio of force and the ratio of distance must be equal after calculating them because the moment of clockwise equal to the moment of anti-clockwise. So, the graph of
F1 d 2 vs F2 d1
could be plot.
Lastly, when carrying the experiment, we should avoid the parallax error while measure the distance using a ruler.
12. REFERENCES
BDA17001-2012
34
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering -Http://En.Wikipedia.Org/Wiki/Moment_(Physics) -Http://Www.S-Cool.Co.Uk/A-Level/Physics/Moments-Couples-AndEquilibrium/Revise-It/The-Principle-Of-Moments -Engineering mechanics statics, Twelfth edition, R. C. Hibbeler
BDA17001-2012
36
