Lab 9 Report

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Leeward Community College *

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MISC

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Mechanical Engineering

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Feb 20, 2024

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Lab 9 Report Static Equilibrium

Objective The objectives of this lab are to: ● To determine the unknown masses to a lever ● To compute the sum of the forces and torques acting on a system Materials ● Fishing string (souji) ● Wooden Chopsticks ● 20 Pennies ● Clear Scotch Tape ● Ruler ● Wooden Back Scratcher (rod) ● 2 Wooden Stools (rod rested on) ● Mystery Item (Wooden Clothes Pin) Theory Explain the theory of the lab. In this lab, torque and static equilibrium are the main forces that were used. Torque is the rational force and is used in which the component of the force is perpendicular to the distance. When the object is not moving and completely balanced it is in static equilibrium. Static equilibrium was found in the different levers using the different pennyweights and varying distances from the penny center to the fulcrum using that as the rotation point. Using the different weights the rod would be unbalanced causing the penny stack to move closer to the fulcrum (Class 2 Lever) until the rod balanced evenly and the torques balanced out (Class 1 Lever). Method Type a short paragraph describing what you did in the lab. Emphasize why you did the lab the way you did, not a blow-by-blow procedure. Include at least one diagram or picture of the setup. In this lab, we reused the chopstick attached to a string from the last lab. We taped two pennies to one side of the chopstick. On the other side, we taped 3, 4, 5, and 6 pennies while changing the distance of the pennies to the center of the rod. We made sure it was balanced by making the chopstick straight and using static equilibrium. Then, we calculated the weight of the pennies and measured the distance between the middle of the pennies and the string. Using this, we were able to find the torque of both sides. We repeated the same steps and slid the pennies back and forth across the chopstick until static equilibrium was reached with the different penny weights. We also repeated the same procedure for our

mystery items. After the experiment, we noticed that if it is balanced then the torques would be similar to each other. Data *Provided Penny Bundles For Calculations* Penny bundle Mass (g) 2 pennies 5 g 3 pennies 7.5 g 4 pennies 10 g 5 pennies 12.5 g 6 pennies 15 g

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PART 1: Class 1 Lever W 1 = m 1 g (2 pennies) [N] Lever arm 1=r 1 [cm] Torque 1 =r 1 *W 1 [cmN] W 2 = m 2 g (3,4,5,6 pennies) [N] Lever arm 2=r 2 [cm] Torque 2 =r 2 *W 2 [cmN] 49.05 N 9 cm 441.45 cmN 73.58 N 6 cm 441.48 cmN 49.05 N 9 cm 441.45 cmN 98.10 N 4.50 cm 441.45 cmN 49.05 N 9 cm 441.45 cmN 122.63 N 3.60 cm 441.47 cmN 49.05 N 9 cm 441.45 cmN 147.15 N 3 cm 441.45 cmN PART 2: Unknown Mass (Mystery Item) m 1 (2 pennies) [g] Lever arm 1=r 1 [cm] Lever arm 2=r 2 [cm] Unknow n mass = r 1 m 1 /r 2 [g] 5 g 5.50 cm 10 cm 2.75 g 5 g 9.25 cm 7.25 cm 6.38 g Actual mass (if possible): 2.75 g & 9.08 g

Calculations Draw a free body diagram of the rod. Show a sample computation of an “unknown” mass from your data. Unknown mass = r 1 m 1 /r 2 = (5.5 cm)(5 g) / (10 cm) = (27.5 g x cm) / (10 cm) = 2.75 g Analysis 1. List the sources of uncertainty, the value of the uncertainty (if possible), and indicate whether they are random or systematic. [ Example: ruler distance, random: +/- 0.2 cm ] The uncertainties throughout the experiment were the measurements for example when measuring the distance between the center of the chopstick and the center of the pennies it wasn’t always exact, that would be off by a millimeter or two. Due to the placement of the pennies it would be difficult to find the exact center of the penny causing an estimation of the distance to be made like +/- 0.1cm (ruler) or +/- 0.2cm (center of penny). This caused random

uncertainty within our experiment due to the measurements we got. There were no systematic uncertainties as we used the same type of pennies with the same weight. 2. Estimate your uncertainty (margin of error) by finding the percent uncertainty in your SMALLEST distance measurement. Percent uncertainty = (uncertainty in measurement)/measurement *100%. [ Example: Suppose your smallest measurement is 5 cm and your uncertainty in distance measurements is 0.2 cm. 0.2 cm/5 cm*100% = 4% ] - (0.2 / 3) * 100 = 6.7% Conclusion Did you fulfill all of the objectives of the lab? Were you successful in proving or disproving your hypotheses? Explain how you have achieved these things.. The objectives of this lab was to determine unknown masses to a lever and to compute the sum of the forces and torques acting on a system. We were able to achieve all the objectives because we were successfully able to find the unknown masses of both the mystery item, which was a wooden clothespin and also find the mass of the rod (chopstick). Based on the data shown above, we were also able to compute and show the forces and torques that were acting on the system that we made for the experiment and showed that the torques were equal to each other while changing the masses and the lever arms. The hypothesis that we were trying to prove in this lab was that if we slide the pennies back and forth on the chopstick, then we would be able to find the distance from the center of the chopstick to the center of the pennies to be balanced. Because based on the calculations we make, we will be able to find the forces for the torques to be equal. The way that we were able to achieve these things was by using static equilibrium. We used static equilibrium because we needed to make sure that our lever was not moving and at the same time, we were using a class one lever, where the load and the effort are on opposite sides of the fulcrum. To accomplish our class one lever, we used a backscratcher as a rod to hold our chopstick (lever arm) and pennies. Then, we kept adding pennies to our second lever arm in order to see if the torques for both lever arms were going to equal each other, and they did. We also then repeated the process to figure out the unknown masses and got data from this experiment that our group was satisfied with. Overall, we are very satisfied with how our experiment turned out, even though there were some random errors throughout, and setting up the actual experiment took awhile, we were able to successfully fulfill the objectives and fulfill our hypothesis.

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Questions 1. How would your equation for Part II have changed if you moved the fulcrum (the string holding up the rod) so that it was NOT at the center of mass? [You might want to check out the introduction!] a. Draw a free body diagram of the situation. b. If the fulcrum was moved 1 cm to one side, predict the lever arm you would have gotten in Part I, row 1 (2 pennies and 3 pennies). Move the fulcrum towards the 3 pennies side. Keep the lever arm the same for the 2 penny bundle. You will need the mass of the rod from Part II to solve this. - (9 * 5) + (1 * 2.75) - (5 * 7.5) = 10.25 - (10 * 5) + (1 * 2.75) - (5 * 7.5) = 15.25 - (9 * 5) + (1 * 2.75) - (6 * 7.5) = 2.75 2. How does your guess for the mass of the rod from Lab 8 compare to the actual value you found in this lab? - The way that our estimate for the mass of the rod from Lab 8 compares to the actual value found in the lab is that according to the given for the previous lab, it is said that the rod is approximately 3 g. Based on the data that was given above for figuring out the unknown mass of the rod, we got 2.75 g, which was close to the given approximation. Yes, there were some uncertainties when we were trying to find the unknown mass, but if we round the value, it is equal to the given value in the previous lab which was 3 g.