Lab3-Force Table.1

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University of Illinois, Urbana Champaign *

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Mechanical Engineering

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Jan 9, 2024

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PHY 131/221 Force Table (Vector Addition) (revised 4/26/08 J) Name:_ Bianca Marie delos Reyes Date:_ Sept 27 _ Lab Partners:__ Annie, Alina, Gabe Introduction : Vectors are central to modeling forces and their effect on the motion of objects. Using force tables you will be able to add vectors “experimentally”. Then you will add those same vectors graphically and using the component method as discussed in class. Do the results convince you that the component and graphical method accurately represent the addition of forces in nature? You have already encountered displacement and velocity vectors. What is a force vector? First of all what is a force? If you need a pen from a drawer in your desk you pull on the drawer to open it. To close your car door you push it until it closes. A basic definition of a force is a push or a pull. Force is also a vector, it has a magnitude and a direction. You are helping your friend rearrange the furniture in their living room. Your friend asks you to put the table in the corner. You start to push the table when you realize he didn’t say which corner. When you ask which corner he points. By pointing he has made your motion of pushing the table a vector. You apply a force in a specific direction. Force in this class is measured in Newtons [N]. A Newton is a [kg · m/s 2 ]. In this lab we will be looking at the force of gravity on a mass hanger and masses. The force of gravity will be calculated as, Fg = mg Watch your significant figures! As you will see in the lab we will be using pulleys to redirect the vertical Force of gravity (gravity always pulls toward the ground) in a horizontal direction. I. Experimental Vector Addition 1) In each part of the lab you will have 2 to 3 force vectors to add together. The magnitude of each force vector will depend the mass of the mass hanger and masses placed on it. If you need a mass of 200g take a 50g mass hanger and add 150g in mass disks to get 200g. Then measure them together on a mass balance to the correct number of significant figures. The labels on the masses are not usually accurate ! 2) To calculate the magnitude of the force vector multiply the mass by g = 9.80m/s 2 1

3) Place each pulley at the angle indicated in the Data Table. For example, for Part 1 place a pulley at 60° and 120°. Then take your ring with the strings attached and place it at the center of the table with the pin coming through the ring. Place a string over each pulley and hang the appropriate mass hanger from each string. Now you have your force vectors (magnitude mg and direction determined by the location of the pulley). 4) Now to find the resultant vector. Pull on the remaining string in different angles until you find an angle where the pin is directly in the center of the ring. Place a pulley at this angle and hang an empty mass at this angle from a string. Place additional masses on the hanger until the pin is at the center of the ring. You now have a system in equilibrium. The last hanger is called the equilibrant because it balances the system. 5) The resultant vector has the same magnitude as the Equilibrant, but points in the opposite direction. The Resultant angle will be θ R = |180° - θ Equilibrant |. To find the magnitude of the Resultant measure the equilibrant mass and multiply by g. II. Component Method 6) Take the force vectors in each part of the lab and calculate the resultant vector using the component method. How do your results compare with the results from the experimental addition? III. Graphical Method 7) Choose an appropriate scale (eg. 1mm = 1N, 1 cm = 1 N, ?), then add the vectors graphically in each part of the lab. How do your results compare with those from the experimental and component method? 2

Data Table Experimental Results Component Method Graphical Method Part 1 → m 1 = _0.2 F 1 = __1.96_ @ 60° (200g) → m 2 = __0.2__ F 2 = __1.96_ @ 120° (200g) → F R = _3.38982_ @ __270___ → F R = _3.39___ @ __90__ → F R = __3.39___ @ ___90___ Part 2 → m 1 = _0.25__ F 1 =__2.45_ @ 120° (250g) → m 2 = __0.2__ F 2 = __1.96__ @ 200° (200g) → F R = _3.3173_ @ _335__ → F R = __3.39__ @ _155___ → F R = 3.39__ @ _154.674___ Part 3 → m 1 = __0.15__ F 1 = __1.47___ @ 0° (150g) → m 2 = __0.2__ F 2 = _1.96__ @ 90° (200g) → F R = 2.794176 @ __235___ → F R = __2.45_ @ __53.13__ → F R = _2.45__ @ __53.13__ Part 4 → m 1 = _0.15 F 1 = ___1.47__ @ 50° (150g) → m 2 = _0.2_ F 2 = __1.96__@ 90° (200g) → m 3 = _0.25 F 3 = ___2.45__ @ 140° (250g) → F R = 4.857762 @ __280__ → F R = _4.752__ @ _101.3__ → F R = 4.753___ @ _101.3__ 3

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Questions: 1. Consider the three methods used to find the resultant vector, which method is the most accurate? Explain. Component method is the more accurate for obtaining result. When we use graphical method, there are a lot of sources of errors, some but not limited to, error in the protractor, error in the angle or reading, etc. Experimental method also has a lot of sources of errors especially random errors. 2. Give some possible sources of error for each method. Experimental Method: There could be a lot of sources of errors when we are doing experiments that are simply just inevitable. The instruments that were used for the lab could also be part of the sources of errors, the instrument could be faulty. Human errors are also a factor, we might have written the right specific amount of mass, or we might not have placed the string in the right place. Component Method: Since component method requires a good amount of adding components to get to the resultant force some possible errors could be due to wrong resolving of a vector and its additions. Angle also plays a big role, if the calculated angle is wrong the resolved component is wrong as well as the final answer. Graphical Method: Some errors could come from pencil width, error in the protractor, error in the angle of reading, error in the tracing, etc. 3. Will the magnitude of F R be the same in Part 1 if we subtract the two vectors, F 1 – F 2 , instead of adding them? Explain. No, the answer that you would get from subtracting F1 – F2 would be different from instead of adding F1 and F2. The angle of Fe would then change from its initial angle, 60, it would then be 180. The magnitude when you subtract F1 and F2 would be less than adding them up 4. In this experiment you used the table in a horizontal position. How would your results be different, if at all, were the table positioned vertically? Explain and justify your answers with an example including calculations. If the table used in vertical direction instead of horizontal position, we would then consider gravity in our calculation but in case of horizontal its getting cancelled by the normal reaction 4