3 STUDY OF FRICTION - WEEK 10 3.1 INTRODUCTION The purpose of this lab is to experimentally demonstrate static friction and when this force due to static friction is overcome.

In this experiment we will compare different levels of static friction at different angles of inclined plane. There are two parts to this experiment, first, determining the forces to balance a block on the incline and the second to determine the angle of inclination just before the block tends to move (impending motion). We will compare whether friction is affected by the size and/or material of the block. Similar to previous labs you will use theory to determine what the forces and angles should be before or during the experiment. Objectives 1. Compare theoretically and experimentally derived values for F₁, the force acting on different materials parallel to the plane of inclination. 2. Calculate the static friction coefficient. 3. Determine coefficient for different size blocks. 4. Determine coefficient for different material blocks. 3.2 MATERIAL AND METHODS 3.2.1 Apparatus Description This lab is performed with blocks placed on an inclined slope and attached to a dynamometer apparatus. The blocks vary in size (you must measure geometry each block) and material (you must measure the weight of each block). The inclined slope setup can be moved up and down to change the angle to the horizontal, there is a protractor on the side that allows you measure this angle. The dynamometer is a simple tool that can measure the force exerted by the black that is attached. The force the block exerts on the dynamometer will change depending on the incline of the slope. From the force reading and angle of incline you can measure calculate the coefficient of friction. 3.2.2 Experimental Procedure 3.2.2.1 Part 1: Calculate the Force measured by the dynamometer (F₁) The force exerted by the weight of the block (of varying material) can be divided into a force F₁ along the plane and a force F₂ normal to the plane. The force along the plane goes in parallel to the same plane and the force normal to the same plane goes in perpendicular to the plane, Figure 6. Before carrying out the experiment it is important to review the theory and equations of how to calculate the normal force (F₂). The absolute forces are: OJMulvihill S α F₁ A h G F₂ Figure 6: Experiment 1 free body diagram. F₁ = G. sin x F₂ = G. cos x Sept 2023 V_3.2 This experiment confirms these two relationships. The two forces F₁ and F₂ are measured for the different angles of inclination ∞ using the dynamometer. G is the force exerted by the block placed on the setup (measure weight and convert to load value). It is possible to change the angle of inclination of the plane. Such that: The force along the plane is therefore given by: COS X = And the force normal to the plane is given by: h sin x = - S 2 [₁-4) S = G./1/2 S And force perpendicular to the plane equal to: F₁ = G.- F₂ = G. 1. OJMulvihill Procedure 1. Attach the dynamometer to the inclined plane hanging it to the pulley. Attach the block (any material or size) to the dynamometer. Ensure that the wire dragging the block is strictly parallel to the plane (no angle of the string). 2. Take note of the weight of the block (G), hanging it to the hook of the dynamometer. Set the dynamometer on the plane hanging it to the hook. 3. Measure the height, h of the ends of the inclined plane in respect to the plane of the table. 4. Measure the length, s of the inclined plane (s = hypotenuse). 5. Read on the dynamometer the value of the parallel force (F₁) necessary to balance the weight, G of the block. SI 6. Repeat the test changing the type of block (wood to PVC), in this case G will change. 7. Repeat the test changing the height, in this case & s of the inclined plane will change. 8. Report results in a table similar to table 5 below. Create a graph of the data if appropriate. 2 3.2.2.2 Part 2: Calculation of the Static Friction Coefficient In this part of the experiment, we want to demonstrate that you can calculate the coefficient of friction by knowing the angle at which the block just about moves down the inclined plane. First, we need to know the theory to prove this. As previously mentioned, a body on an inclined plane of weight G is subjected to a force along the plane (parallel to the plane) equal to: F₁ = G. sin x F2 = G. cos x This dependence on the inclination angle ∞ can be used to determine the coefficient of friction, μ of the body. The inclination angle of the plane is incremented by moving the plane until the body starts sliding i.e. the force F₁ along the plane and the static friction force F are in balance. In this experiment, the tangential to the inclination angle is determined by the height, h of the holding structure and the distance from the point in which the plane is hinged measured at the base, s as in Figure 7: 10 Sept 2023 V_3.2 a Therefore: S F₁ From the balance of the forces F₁ = F therefore: h OJMulvihill Figure 7: Experiment 2 free body diagram. h F₁ tan x=-= S F₂ The static friction force is generally proportional to the force F2₂ along the plane: F = μ. F₂ F₁ = μ. F₂ h μ== S F=μF₂ G F₂ Procedure 1. Remove the dynamometer and replace with a longer string/wire. 2. Set the smaller wood block on the inclined plane and set the inclined plane flat so that the wood block stays still. 3. Slowly increase the angle of the inclined plane until the block starts descending. Go slow! 4. Lock in this position using the clamp. 5. Measure the height, h at which the wooden block starts moving and calculate the value of the static friction coefficient, μ using the equations above. 6. Repeat the operation using the larger wooden block on the inclined plane. Repeat the operation using the smaller PVC block on the inclined plane as well as the different sized blocks. 7. Create a results table similar to table 6 below. Create a graph of the data if appropriate. 3.3 RESULTS The results section should only contain facts and experimental data. There should be no opinion or observations, this is reserved for the conclusions section. Here, you should describe the tables and figures based on what they contain rather than what the data shows. 3.3.1 Part 1: Calculate the Force measured by the dynamometer (F₁) The results discussion will show the results of your dynamometer for each scenario (different blocks and different inclines) compared to the values you attained from your respective calculations. This first show that there is agreement between the dynamometer reading and your calculations. Furthermore, you want to demonstrate that when changing both the weight of the block or the angle of incline is going to change the force F₁. 11 Sept 2023 V_3.2 Table 5: Results for inclined plane. Block Material Block (kg) Wood PVC Mass s (m) 3.3.2 Part 2: Calculation of the Static Friction Coefficient Here you will detail the experimental and theoretical results for each Table 6: Results for the calculation of the static friction coefficient. Block Material Block Mass Block Width (m) (kg) Block Length (m) Wood Wood (large) PVC PVC (large) h (m) OJMulvihill A (m²) 12 G (N) s (m) F₁ (N) h (m) 3.4 CONCLUSIONS As always please demonstrate concisely and cleanly the experimental and theoretical results of each part of the experiment. This section will allow you discuss and comment on anything from the experiment. Is the balancing force F₁ higher or lower than the weight G? In other words, is the inclined plane an advantageous machine? With the same weight, does the force F₁ change with the height? Considering the results in the table, and the limits of the experimental errors, is it possible to find a relation between the four measured variables? Mention some practical applications of the inclined plane. For part 2 comment on the effect of size and material on the coefficient of friction. μ 3.5 LAB REPORT - EXTRA INFO (PLEASE READ REPORT TEMPLATE) 1. Report to be written in a Microsoft Word document. Figures are to be created in Microsoft Excel using the data acquired. 2. Part 1: MUST include: one table of results (table 1), photos, and conclusions 3. Part 2: MUST include: table 2 data, photos (for each load), one figure (figure 1) and conclusions Sept 2023 V_3.2 4 REPORT TEMPLATE - FOR Each Lab REPORT INSTRUCTIONS The following document is a template on how to complete a report for each lab or demo. This document is generalized so each lab and demo will have more specific info in the lab manual (at end of each experiment section). Below you will find a template that MUST be used for all reports as part of this module. Follow the instructions below: 1. The coversheet (see page below) MUST be on the front of all reports - you will find an version on the SULIS site. This coversheet must be signed by all members of the group. To do this, please print out a table like below and fill with your names IDs and signatures, and date of signing - electronic signatures are recommended. The signature is an agreement that all information used is of your own and that each member of the group accepts that the grades are the same for all members. If this is not completed then the report will be given a 0 mark. Please include your group name in the coversheet e.g. Group 2B-5. NAME (BLOCK CAPITALS Student ID OJMulvihill Signature 2. Below the coversheet template are the headings that MUST be used for each report. Introduction - highlight the purpose of the experiment and objectives a. b. Materials and Methods - detail the experimental setup and the procedure used. C. Results - here contains the data and the figures as well as information related to the experiment process d. Conclusions - demonstrate your understanding of the experiment and summarise the findings. 3. This template document goes into further detail on each heading and what is expected. However, you are encouraged to bring in as much detail as possible within the maximum word count. 4. NEVER copy the words or data from the lab manual or this document or from any source. All reports go through plagiarism software and 0 marks will be given if there is evidence of plagarism. 5. Formatting of tables and figures are open but please use at least 11pt and standard font (arial, calbri, or Times New Roman). Spacing at 1.0 or 1.15. Margins no greater than 2.54 cm on any side. 6. Please do not use borders around the page. Please spell check before submitting. 7. Marks are given for DATE ALL Signed a. your ability to demonstrate the purpose and objective of the experiment b. the correctness and presentation of the data C. the correctness and presentation of the figures d. your calculation of the results and/or analysis of the results e. your interpretation of the results, key findings and relation to real-world 13 Sept 2023 V_3.2