DEPARTMENT OF ENGINEERING MECHANICS STATICS LABORATORY LAPORAN MAKMAL/LABORATORY REPORT

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1 Kod M/Pelajaran/ Subject Code Kod & Tajuk Ujikaji/ Code & Title of Experiment Kod Kursus/ Course Code Kumpulan/Group Nama Pelajar/Name of Student Lecturer/Instructor/Tutor s Name Nama Ahli Kumpulan/ Group Members DEPARTMENT OF ENGINEERING MECHANICS STATICS LABORATORY LAPORAN MAKMAL/LABORATORY REPORT ENGINEERING LABORATORY I BDA No. Matrik Penilaian / Assesment Seksyen /Section No. K.P / I.C No. No. Matrik 1. Teori / Theory 10 % 2. Keputusan / Results 15 % Tarikh Ujikaji / Date of Experiment Tarikh Hantar / Date of Submission ULASAN PEMERIKSA/COMMENTS Pemerhatian /Observation Pengiraan / Calculation Perbincangan / Discussions Kesimpulan / Conclusion 20 % 10 % 25 % 15 % Rujukan / References 5 % JUMLAH / TOTAL 100% COP DITERIMA/APPROVED STAMP

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3 COURSE INFORMATION COURSE TITLE: ENGINEERING LABORATORY I (BDA17001) TOPIC 1: EQUILIBRIUM OF FORCES 1. INTRODUCTION The parallelogram law gives the rule for vector addition of vectors A and B. The sum A+B of the vectors is obtained by placing those head to tail and drawing the vector from the free tail to the free head. The components form the sides of the parallelogram and the resultant is the diagonal. 2. OBJECTIVES The objective of this experiment is to test that when three non-parallel forces in the same plane are in equilibrium, their line of action meet at a point, and hence to show that the resultant of two forces can be found using the Parallelogram of Forces. 3. LEARNING OUTCOMES At the end of this topic, the students will be able to display basic skills and knowledge of equilibrium of forces using laboratory equipments, analyze observable data obtained from equilibrium of forces 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. EXPERIMENTAL THEORY When two forces act on a body in different directions in one plane, they are equivalent to single force (the resultant) acting somewhere in between them. An example of this is when a sledge is pulled by two horizontal ropes spread at an angle; the sledge will move in a direction between the ropes along the line of their resultant force. Until the sledge moves, it will pull back against the ropes with a single horizontal force equal and opposite to the resultant of the two ropes forces. It can be shown that when three such forces are balanced (that is, in equilibrium), their lines of action all meet at a point. Using this fact, the resultant of two forces in the same plane at an angle can be found by graphical method called the Parallelogram of Forces. To maintain equilibrium it is necessary and sufficient that the resultant force acting on a rigid body to be equal to zero. In terms of Newton s laws of motion, this is expressed mathematically as: F = 0 ; Where, F is the vector sum of all forces acting on the particle. When the body is subjected to a system of forces which all lie in the x-y plane, the forces can be resolved into their x and y components. Consequently, the conditions for equilibrium in two dimensions can be written in scalar form as: F X = 0 and F y = 0 Let s say that there are three forces namely 1 F r, 2 F r and 3 F r acts on a body as shown in Figure 1.

4 F2 F1 θ 2 θ 1 F 3 Figure 1: Free Body Diagram r r r For equilibrium, this equation must be equal to zero. Hence, F + F + F 0. r r r Therefore, F1 + F2 = F3. The sum of forces of x components, F1 F F x 2 = 0; F sinθ F 1 sinθ2 = sinθ = sinθ = = 2 (1) The sum of forces of y components, = ; F cosθ + F cosθ F 0 (2) F y 5. ADDITIONAL THEORY BDA

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6 6. EXPERIMENTAL EQUIPMENTS Table 1: Parallelogram of Forces Equipment List No. Apparatus Qty. 1 Diagram board with clips ( P 3 ) 1 2 Short Screws 2 3 Pulleys ( P12) 2 4 Knurled Nuts 4 5 Weight Hooks [0.1N] ( P10) 3 6 Set of Weights 0.05N, 0.1N, 0.5N, 1N, 2N 1 7 Ring with 3 cords attached 1 8 Protractor 1 9 Some sheets of plain paper 7. EXPERIMENTAL PROCEDURES 1. Prepare the mounting panel as shown in Figure Clip a sheet of paper to the diagram board. 3. Pass two of ring cords over the pulleys. Let the third cord hang directly downwards. 4. Attach all cords by 0.1 N weight hooks. 5. Attach the weight of 2.4N to the weight hook W 3 and the weight of 1.9N to the weight hook W 1 and W 2. Write in the weight supported by each cord W1, W2 and W3 (including 0.1N which is the weight of each weight hook). 6. Gently cause the system to bounce by jogging the CENTRE weight only and letting it settle freely in its equilibrium position. 7. Mark the position of the three cords with pencil dots on the paper. 8. Remove the paper and join up the dots representing the three cords. 9. Measure the angle reading of θ 1 andθ 2 using protractor. 10. Repeat step 5 and 9 while you adjust the weights of W2 by 0.1N increments until reached 2.5 N. Figure 2: Parallelogram of Forces Apparatus Setup BDA

7 8. OBSERVATIONS 9. RESULT 1. Fill in the experimental result in the Table Fill in the Table 3 using calculation method. (Please refer Law of cosines to get the angle) W 1 F1 sinθ 3. Plot the graph of = against 2 for both experimental and W2 F2 sinθ1 calculated results. 4. In each of your diagram, the lines representing the cord positions should be meets at the centre of the ring. Along the upper cord lines, mark off lengths OA and OB to represent the pull of weights W1 and W2 (Figure 3). Choose a suitable scale for this, (e.g. 50mm per N). Through A draw a line AC parallel to OB, and through B draw a line BC parallel to OA, to from the parallelogram OACB. Draw in the diagonal OC. This is the resultant force, F r of the vector F r and 1 F r Measure the length and direction of OC. BDA

8 Table 2: Experimental Results Weight Angle Angle Ratio No. W3 (N) W1 (N) W2 θ 1 θ 2 sinθ 1 sinθ 2 (N) sinθ2 sinθ 1 W 1 = W 2 F F * Data sheet must approved by the instructor. BDA

9 Table 3: Calculated Results Weight Angle Angle Ratio No. W3 (N) W1 (N) W2 θ 1 θ 2 sinθ 1 sinθ 2 (N) sinθ2 sinθ 1 W 1 = W 2 F F * Data sheet must approved by the instructor. BDA

10 10. SAMPLE OF CALCULATON BDA

11 11. DISCUSSIONS UNIVERSITI TUN HUSSEIN ONN MALAYSIA 1. Discuss the graphs obtained. 2. Discuss the parallelogram diagrams obtained. BDA

12 3. Make a comparison between experimental and calculated result. 12. QUESTIONS 1. Explain the parallelogram method to find the resultant of two parallel forces. BDA

13 2. What are the alternative methods that can be used to analyze the addition of two forces? BDA

14 13. 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. 14. REFERENCES BDA

15 Kod M/Pelajaran/ Subject Code Kod & Tajuk Ujikaji/ Code & Title of Experiment Kod Kursus/ Course Code Kumpulan/Group Nama Pelajar/Name of Student Lecturer/Instructor/Tutor s Name Nama Ahli Kumpulan/ Group Members DEPARTMENT OF ENGINEERING MECHANICS STATICS/DYNAMICS LABORATORY LAPORAN MAKMAL/LABORATORY REPORT No. Matrik ENGINEERING LABORATORY I Penilaian / Assesment BDA Seksyen /Section No. K.P / I.C No. No. Matrik 1. Teori / Theory 10 % Tarikh Ujikaji / Date of Experiment Tarikh Hantar / Date of Submission ULASAN PEMERIKSA/COMMENTS Keputusan / Results Pemerhatian /Observation Pengiraan / Calculation Perbincangan / Discussions Kesimpulan / Conclusion Rujukan / References 15 % 20 % 10 % 25 % 15 % 5 % JUMLAH / TOTAL 100% COP DITERIMA/APPROVED STAMP

16 COURSE INFORMATION COURSE TITLE: ENGINEERING LABORATORY I (BDA 17001) TOPIC 2: POLYGON OF FORCES 1. INTRODUCTION A set of forces whose resultant is zero can be depicted by drawing them end to end, so that they form a closed polygon; this is called a Polygon of Forces. If the polygon is not closed, there is a nonzero resultant force. 2. OBJECTIVES The objective of this experiment is to test that when four and more forces are in equilibrium at a point, they can be represented by a Polygon of Forces from which unknown forces can be found. 3. LEARNING OUTCOMES At the end of this topic, the students will be able to display basic skills and knowledge of polygon of forces using various laboratory equipments, analyze observable data obtained from polygon of forces 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 In the design of pin-jointed plane structures such as girders, bridges and roof trusses (see Figure 1), it is necessary to find the forces acting in each member so that the frame can be made strong enough to withstand the maximum loads exerted upon it. The Polygon of Forces is frequently employed to find such forces and deals with each joint in turn. This experiment could be regarded as one such joint on a structure, and it will be shown that in a system containing four or more forces, two unknowns can be found in magnitude or direction if the remaining information is known. The Polygon of Forces is an extension of the Triangle of Forces, and whereas Tri means 3, Poly means many. Figure 1: Roof Truss BDA

17 4.1 ADDITIONAL THEORY BDA

18 5. EQUIPMENTS Table 1: Polygon of Forces Equipment List No. Apparatus Qty. 1 Diagram Board & Clips 1 2 Short Screws 2 3 Pulleys 4 4 Knurled Nuts 6 5 Weight Hooks 5 6 Set of Weights 1 7 Ring with 5 cords attached 1 8 Some sheets of plain paper 1 6. PROCEDURES 6.1 TEST A 1. Secure the mounting panel as shown in Figure Clip a sheet of paper to the board (P21) and assemble with cords and weight hooks (P10) as shown. 3. Add weights to give total weights as shown in diagram. Write in the weight supported by each cord. Note: Total weight includes weight hook of 0.1N. 4. The fifth cord (required only in Test B) can be allowed to hang freely and will not affect Test A results. 5. Gently cause the system to bounce by jogging the free cord and let the four cords and the weights settle freely in its equilibrium position. 6. THEN MARK THE POSITION OF THE FOUR CORDS with pencil dots on the paper. 7. Remove the paper and join up the dots representing the cords. BDA

19 6.2 TEST B Figure 2: Experiment Apparatus Setup 1. Keeping the weight hooks and the weights as in Test A, attach a weight hook to the fifth cord and let it hang directly from the ring with a total weight of 1.1N (i.e. including hook). 2. Once again, bounce the system of jogging the centre weight only, and allow the ring, the five cords and weights to settle in its new equilibrium position, and THEN MARK THE POSITIONS OF THE FIVE CORDS with pencil dots on the paper. 3. Remove the paper and join up the dots on the paper. 7. RESULTS 7.1 TEST A 1. On your diagram sheet for Test A, mark the spaces between the cord lines with the letters A, B, C and D to give the Space Diagram (Figure 3). d W2 W3 D W4 C A B W1 Space Diagram a b c Force Diagram Figure 3: Space Diagram Figure 4: Force Diagram BDA

20 2. Draw a Force Diagram by first drawing scale lengths ab and bc to represent the forces W1 and W2 (Figure 4). Then through c and a, draw lines parallel to the directions of W3 and W4 (based only on direction angles of W3 and W4) to meet at d covering the whole circuit. The figure abcd is the force diagram, or Polygon of Forces, for the four forces W1, W2, W3 and W4. 3. MEASURE THE LENGTHS cd and da. There should be equivalent to the corresponding forces W3 and W TEST B 1. Draw the space diagram A, B, C, D, E to show the space positions of the five forces, W1, W2, W3, W4 and W5 (Figure 5). W3 W2 W4 D E C W5 B A Space Diagram W1 Figure 5: Test 2 Space Diagram 2. Draw a separate force diagram starting with scale lengths ab, bc and cd to represent the forces W1, W2 and W3. Complete the diagram by drawing lines parallel to the directions of W4 and W5 (based only on coordinate direction angles of W4 and W5), to give the point e. The figure 'abcde' is the force diagram, or Polygon of Forces, for the five weights W1, W2, W3, W4 and W5. 3. Measure lengths of de and ea and should be equivalent to the forces W4 and W5. Complete the Table 2 which describes the measurements. Table 2: Results The lengths of cd da de ea * Data sheet must approved by the instructor BDA

21 8. CALCULATION BDA

22 9. OBSERVATIONS BDA

23 10. DISCUSSIONS 1. Interpret the lengths of cd, da, de and ea in term of magnitude of the force vector (in N). Give your comment regarding the result. 2. From your results, discuss the method of using the Polygon of Forces for four or more forces in equilibrium at a point, say how many unknown forces can be found. Keep the following points in mind: a. What must be known about ALL the forces before the Space Diagram be drawn? b. How many of the force lines were NOT marked off in Force Diagram?... c. What do you notice about the arrows showing the direction of the forces in the Force Diagram? d. Can we find the direction of forces by this method if all other data given? BDA

24 10.2 QUESTIONS 1. What are the differences between the Triangles of Forces and Polygon of Forces? 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. BDA

25 12. REFERENCES BDA

26 Kod M/Pelajaran/ Subject Code Kod & Tajuk Ujikaji/ Code & Title of Experiment Kod Kursus/ Course Code Kumpulan/Group Nama Pelajar/Name of Student Lecturer/Instructor/Tutor s Name Nama Ahli Kumpulan/ Group Members DEPARTMENT OF ENGINEERING MECHANICS STATICS/DYNAMICS LABORATORY LAPORAN MAKMAL/LABORATORY REPORT No. Matrik ENGINEERING LABORATORY I Penilaian / Assesment BDA Seksyen /Section No. K.P / I.C No. No. Matrik 1. Teori / Theory 10 % Tarikh Ujikaji / Date of Experiment Tarikh Hantar / Date of Submission ULASAN PEMERIKSA/COMMENTS Keputusan / Results Pemerhatian /Observation Pengiraan / Calculation Perbincangan / Discussions Kesimpulan / Conclusion Rujukan / References 15 % 20 % 10 % 25 % 15 % 5 % JUMLAH / TOTAL 100% COP DITERIMA/APPROVED STAMP

27 COURSE INFORMATION COURSE TITLE: ENGINEERING LABORATORY I (BDA 17001) TOPIC 3: EQUILIBRIUM OF A RIGID BODY 1. INTRODUCTION Beams are structural members which offer resistance to bending due to applied loads. Most beams are long prismatic bars, and the loads are usually applied normal to the axes of the bars. Beams are undoubtedly the most important of all structural members, so it is important to understand the basic theory underlying their design. There are two types of beam which is beam has more one supports than needed to provide equilibrium is statically indeterminate and other one is beam supports reactions can calculated by the methods of static alone are called statically determinate. To determine the support reactions for a beam, the load deformation properties in addition to the equations of static equilibrium should be considered. This experiment will show that by applying Principle of Moment, the reactions of the beam at each support can be calculated. 2. OBJECTIVES The objective of this experiment is to show the totals of distributed load may be considered as equivalent concentrated load acting on the beam at the centre of gravity and the reactions of the support for the beam can be calculated by applying the principle of moments. 3. LEARNING OUTCOMES At the end of this topic, the students will be able to display basic skills and knowledge of equilibrium of rigid body using laboratory equipments, analyze observable data obtained from equilibrium of rigid body 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 beam is a horizontal member of a structure which rests on supports (often walls or columns) and spans an open space. If a beam rests on two supports without any fixing down devices, it is said to be SIMPLY SUPPORTED. If load is placed on the beam and covers a very short length of the beam, it is BDA

28 called a POINT or CONCENTRATED load, but if the load is spread over an appreciable length of the beam it is called a DISTRIBUTED load. If the supports are placed each end of a beam and the beam is symmetrically loaded, the weight carried at each support (called the REACTIONS) must be half the total weight on the beam, as this experiment will show. Beams which are not symmetrically loaded must still carry the total load at the supports, but the proportion of the total weight carried by each support will depend on the weight of each individual load and the position which is occupies along the beam. A beam may also be subjected to a moment load, M. Imagine that the beam from the left support and right support has a symmetrical load, so the beam supports load is: 1 2 Total of Distributed Loading It can be illustrated as below: Figure 1: Distributed Load 4.1 ADDITIONAL THEORY BDA

29 5. EQUIPMENTS Table 1: Beam Reactions Equipment List No. Apparatus Label Qty. 1 Beam assembly EX8 1 2 Spring P Nuts 3 4 Adjustable hooks P6 3 5 Lightweight hook 0.1N P Spring balances 10N P8 2 7 Load Set 2N, 5N P7 5 8 Weight hooks 20g P Distributed load EX8A 2 BDA

30 6. PROCEDURES 1. Secure the mounting panel in the vertical position as shown in Figure 2. P6 P6 P6 P7 P10 Figure 2: Equipment Setup 2. Adjust the centre hook until the hole in the centre of the beam lines up with the panel board hole. 3. Attach the spring balance to the upper holes at each end of the beam with their scales at the ends furthest from the beam and hang over the remaining two adjustable hooks. 4. Adjust the balance support hooks so that the large hole in the centre of the beam coincides with hole (Step 2) and the beam is horizontal. (Set the balance scales to zero). 5. Measure and record the weight of concentrated load EX8A by using digital scales. Change the unit from grams to Newton. 6. Set up the beam and load as shown in Figure 3.3a. 7. Place the load 5N to 0.1N weight hook as shown in Figure 3.3a. After that, record the reading of spring balances R a and R b. 8. Set up the beam and load as shown in Figure 3.3b until 3.3i. Then record the reading of spring balances R a and R b for each diagrams.. 9. Note: After each load is applied in the tests described above the hooks supporting the spring balances must be moved so that the beam returns to its original position, i.e. centre in line with hole (Step 2) and horizontal. The weight of beam will then be supported by the centre spring and the reactions on the spring balances will be due only to the load. BDA

31 6.1 TESTING FIGURES All dimensions are in millimetres (mm) and all weights are in Newton (N). 5.1 N EX 8A EX 8A RA Figure 3a RB RA Figure 3b RB EX 8A EX 8A RA Figure 3c RB RA Figure 3d RB EX 8A EX 8A EX 8A RA Figure 3f RB RA Figure 3g RB EX 8A EX 8A EX 8A EX 8A RA Figure 3h RB RA Figure 3i RB BDA

32 W 0.1 N Figure 4 Consider the beam loaded by the force W. This indicates a point load (Fig. 4) and is applied to the beam by adding weights to a weight hook and hooking into hole in the lower row of the beam. EX 8A Figure 5 Distributed load (Fig. 5) was applied to the beam by placing the groove over the top edge of the beam. R Figure 6 This indicates a reaction at a support (Fig. 6) and is measured with a spring balance hooked into the hole in the top row of the beam. 7. RESULTS 1. Record experimental result in Table Calculate the forces at support R a and R b theoretically for each test. [Show calculation method] 3. Calculate the total forces (R a + R b ) for both experimental and theoretically.[show calculation method] BDA

33 Weight of EX8A : N Table 2: Results Test Experimental value Calculated value (theory) Comparison Ra Rb Ra + Rb Ra Rb Ra + Rb Same / (N) (N) (N) (N) (N) (N) Not same Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7 Figure 3.8 * Data sheet must approved by the instructor BDA

34 8. CALCULATION BDA

35 9. OBSERVATIONS BDA

36 10. DISCUSSIONS 1. Discuss the value of R a, R b and (R a + R b ) obtained. 2. Compare experimental and theoretical value. If not same, why? 3. Explain how are the steps to study and analyze a beam. What must be known first before we study a beam? 10.2 QUESTIONS 1. What is the principle used to obtain the value of R a and R b? 2. If the weight of the beam was an important factor to be considered, how would you include it in a calculation? BDA

37 3. What type of load would be carried by the beam supporting the roof if a heavy snow fall lay on a flat roof? 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 improvement BDA

38 12. REFERENCES BDA

39 Kod M/Pelajaran/ Subject Code Kod & Tajuk Ujikaji/ Code & Title of Experiment Kod Kursus/ Course Code Kumpulan/Group Nama Pelajar/Name of Student Lecturer/Instructor/Tutor s Name Nama Ahli Kumpulan/ Group Members DEPARTMENT OF ENGINEERING MECHANICS STATICS LABORATORY LAPORAN MAKMAL/LABORATORY REPORT ENGINEERING LABORATORY I BDA No. Matrik Penilaian / Assesment Seksyen /Section No. K.P / I.C No. No. Matrik 1. Teori / Theory 10 % 2. Keputusan / Results 15 % Tarikh Ujikaji / Date of Experiment Tarikh Hantar / Date of Submission ULASAN PEMERIKSA/COMMENTS Pemerhatian /Observation Pengiraan / Calculation Perbincangan / Discussions Kesimpulan / Conclusion 20 % 10 % 25 % 15 % Rujukan / References 5 % JUMLAH / TOTAL 100% COP DITERIMA/APPROVED STAMP

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41 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 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.

42 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, F 1 d 1 - F 2 d 2 = 0 F1 d = 2.. (2) F2 d1 F F d1 d2 d d F1 F2 Figure 1a Figure 1b Figure 1c BDA

43 4.1 ADDITIONAL THEORY BDA

44 5. EQUIPMENTS UNIVERSITI TUN HUSSEIN ONN MALAYSIA Table 1: Principles of Moments Equipment List No. Apparatus Qty. 1 Panel board 1 2 Pivot bar and stop ( EX5) 2 3 Pulleys ( P12) 4 4 Nuts 6 5 Screw 5 6 Weight hook ( P10) 1 7 Cord approx (40cm long) 1 8 Set of weights 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 BDA

45 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. 4. Add a 1.9N load to each hook to make the total of 2N. 5. Record the value of F 1 and F 2. Then measure and record the distance d 1 and d 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 F 2 and the distance d 2 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 F 2 and the perpendicular distance d 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 d 1 d 2 2N 2N Figure 4.3a: Test 1 BDA

46 d 1 d 2 2N F 2 Figure 3b: Test 2 d 1 2N d 2 F 2 Figure 3c: Test 3 BDA

47 d 1 d 2 2N F 2 Figure 3d: Test 4 7. RESULT 1. Fill in the experimental result in the Table 2. F1 d2 2. Plot a graph for vs F2 d 1. BDA

48 Table 2: Results Moment Test Left Pivot Bar Right Pivot Bar Total Ratio F 1 (N) d 1 (m) M 1 (Nm) F 2 (N) d 2 (m) M 2 (Nm) M 1 - M 2 (Nm) F 1 F 2 d 2 d 1 Figure 4.3a Figure 4.3b Figure 4.3c Figure 4.3d * Data sheet must approved by the instructor BDA

49 8. CALCULATON 1. Calculate the Moment for Left Pivot Bar and Right Pivot Bar. BDA

50 2. Calculate the ratio of forces and distance. BDA

51 9. OBSERVATIONS BDA

52 10. DISCUSSIONS 1. Discuss the graph obtained. 2. Discuss your opinion about the summation of moment from your experiment results. BDA

53 3. If the moment is nonzero, what are the factors may influence the experiment QUESTIONS 1. What is the principle of moment and how moments achieved? BDA

54 2. What does the principles of Moment state about the turning moments of forces acting on a body? 3. How to determine the moment in three dimensions body? BDA

55 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. 12. REFERENCES BDA

56 Kod M/Pelajaran/ Subject Code Kod & Tajuk Ujikaji/ Code & Title of Experiment Kod Kursus/ Course Code Kumpulan/Group Nama Pelajar/Name of Student Lecturer/Instructor/Tutor s Name Nama Ahli Kumpulan/ Group Members DEPARTMENT OF ENGINEERING MECHANICS STATICS LABORATORY LAPORAN MAKMAL/LABORATORY REPORT ENGINEERING LABORATORY I BDA No. Matrik Penilaian / Assesment Seksyen /Section No. K.P / I.C No. No. Matrik 1. Teori / Theory 10 % 2. Keputusan / Results 15 % Tarikh Ujikaji / Date of Experiment Tarikh Hantar / Date of Submission ULASAN PEMERIKSA/COMMENTS Pemerhatian /Observation Pengiraan / Calculation Perbincangan / Discussions Kesimpulan / Conclusion 20 % 10 % 25 % 15 % Rujukan / References 5 % JUMLAH / TOTAL 100% COP DITERIMA/APPROVED STAMP

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58 COURSE INFORMATION COURSE TITLE: ENGINEERING LABORATORY I (BDA17001) TOPIC 5: FRICTION ON THE INCLINED PLANE 1. INTRODUCTION Friction can be defined as a force of resistance acting on a body that prevents or retards slipping of the body relative to a second body or surface with which it is in contact. This force always act tangent to the surface at points of contact with other bodies. This friction force is opposite to the existing motion of the body relative to these points. 2. OBJECTIVES The objective of this experiment is to investigate friction on the inclined plane and to show that a force (applied parallel to the plane) required to slide a block up the plane, is equal to W ( inclination of plane. sin α + µ cosθ ), where α is an angle of 3. LEARNING OUTCOMES At the end of this topic, the students will be able to display basic skills and knowledge of friction on the inclined plane using laboratory equipments, analyze observable data obtained from friction on the inclined plane 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 When a block is placed on an incline, the tendency is for the block to slide down the plane. If the angle of inclination is small the block is prevented from slipping by the friction between the surfaces. As the angle is increased, the force exerted down the plane due to the weight of the block also increases, but the force pressing the surfaces together will decrease. At the angle of friction, the force acting down the plane just to overcome the friction and sliding takes place. This could be described as in Figure 5.1.

59 The sum of forces (parallel to the inclined plane), F = 0 Where, Thus, P = S+ F (1) S= W sinθ R= W cosθ F = µ R= µ W cosθ P = W sinθ + µ W cosθ (2) P : the force that required to overcome the friction to pull a block up the plane S : the force acting down the plane due to the weight. R : the force pressing down the surfaces together causing friction. F : the friction force The coefficient of friction, µ : From Equation (1): If P= 0; S = F = µ R W sinθ = µ W cosθ sinθ µ = = tanθ (3) cosθ Where, θ : is the angle of inclination of plane and µ is the coefficient of friction. S P θ F θ θ W R Figure 5.1: Friction on the inclined plane diagram BDA

60 4.1 ADDITIONAL THEORY BDA

61 5. EQUIPMENTS UNIVERSITI TUN HUSSEIN ONN MALAYSIA Table 5.1: Friction on Inclined Plane Equipment list No. Apparatus Qty. 1 Plane Assembly 1 2 Friction Block with Cord 1 3 Knurled Nuts 2 4 Plumb Bob & Line 1 5 Weight Hook 1 6 Set of Weight N Spring Balance 1 8 Set of Trigonometrically Table Figure 5.2: Friction on the inclined plane diagram BDA

62 6. PROCEDURES TEST 1 (Find the coefficient of friction) 1. Secure the mounting panel as shown in Figure 5.2. Hang the plumb line over the protractor centre screw. Weigh the block for three (3) times and record its average weight. 2. Use metal surface of the block placed in contact with the wooden surface of the plane. 3. Place the block at the right hand end of the plane and tilt the plane until the block slides down the plane with uniform speed. 4. Give the block a starting push to overcome static friction. 5. When the correct angle has been obtained, measure the angle at the protractor recorded against the plumb line. 6. Record this angle which is the Angle of Friction (φ ) for steel against wood. TEST 2 1. Do not alter the angle of plane which is now at angle of friction, φ. 2. Place the block at the left hand end of the plane and place the cord over the pulley. 3. Attach the weight hook to the end of the cord and apply weights until the block slides up the plane with slow uniform speed. 4. Once again, give the block a light starting push to overcome static friction. 5. Record this weight (including the weight hook of 0.1N). TEST 3, 4, 5, 6 and 7 1. Repeat as for Test 2 for angles of 0, 10, 20, 30 and 45. BDA

63 7. RESULT UNIVERSITI TUN HUSSEIN ONN MALAYSIA 1. Complete the Table 5.2. TABLE 3: Data Results. Test No. The angle of inclination of plane, θ The applied force P by P by Experiment Calculation Comparison Same / Different φ = * Data sheet must approved by the instructor BDA

64 8. CALCULATON UNIVERSITI TUN HUSSEIN ONN MALAYSIA 1. Calculate the Coefficient of Friction by using equation (3) for Test 1 BDA

65 2. In the case of angle of plane s inclination, θ equal to 0, calculate the value of the coefficient of the friction, µ and the weight of block, W. BDA

66 3. Calculate the value of P for each angle including (P) at the angle of Friction (ϕ ). BDA

67 9. OBSERVATIONS BDA

68 10. DISCUSSIONS 1. Discuss the values of P obtained by experiment and calculation. Compare those values with the force (S) acting down the plane. 2. Suggest some reasons why there are differences occur between the values of P by experiment and P by calculation. BDA

69 3. State the differences between friction on the horizontal plane and friction on the inclined plane QUESTIONS 1. What is the connection between the Angle of Friction and the Coefficient of Friction? BDA

70 2. Give two (2) engineering applications showing the significance of the friction on the inclined plane. 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. BDA

71 12. REFERENCES BDA