12.) Lab 121_ Rotational Static Equilibrium

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New Jersey Institute Of Technology *

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PHYS121

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Mechanical Engineering

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Feb 20, 2024

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Lab 121: Rotational Static Equilibrium A. Introduction: Theory & Objectives According to Newton's laws, an object is stagnant only if all the net forces equal zero. The same applies to torque, which as learned in the previous lab is the force in a circular motion. So to reiterate, an object will not rotate only when all the net torques are equal to zero. However, many times torque isn’t applied directly onto an object, it is applied on an angle. In such cases, the angle at which the torque is applied along the available path of motion is only valid. The equation below, thus entails how torque on an angle can be calculated. τ = ?𝐹?𝑖𝑛θ In this lab, we will explore how various forces applied at different regions and in different magnitudes will affect a strut. Obviously, we will be looking at the strut while it is static and will assign magnitudes to some unknown according to how the other forces impact the system. We will further change the conditions, to see how the unknown’s value changes. We will then further compare our calculations to experimentally found data and understand the mechanisms of torque in static equilibrium. B. Experimental Procedure 1. Set up the two weights on the loop and the string from the top of the stand. 2. Measure the distance from the intersection point to weight 1, weight 2, the point where the string is attached, and the total length. (Labeled them L1, L2, L3 and L4 respectively). 3. Make sure the whole board is at a zero angle and the gravitometer actually measures zero. 4. Given the masses of the two weights, theoretically find the force of tension of the strong. 5. Then press record, after zeroing unattached first, and measure the force of tension experimentally. 6. Record both of those values. 7. Next, move the bar to be at an angle, less than 90, above the horizontal. 8. Measure the angle between the stand, the bar, and the string and the bar. 9. With that given and the connect with, calculate the new theoretical force of tension. 10. Experimentally record the force of tension as well with the force sensors. 11. Lastly, repeat the same process as the previous adjustment but set it to angle below the horizontal. 12. Find the theoretical and experimental force as always.
C. Results: Data & Calculations Part 1: Weight of Rod = .1186 kg Length of strut = .555 m Θ 1 = 56 W 1 = .150 kg L 1 = 30.5 Θ 2 = 0 W 2 = .150 kg L 2 = 50.5 L 3 = 40.5 Calculated Force of Tension: Static Equilibrium - Torque down = Torque Up F w1 + F g + F w2 = F T (.150)(9.8)(.305) + (.1186)(9.8)(.2775) + (.150)(9.8)(.505) = F T (.405) F T = 3.74 N Experimental Force of Tension: F T = 4.2 N Part 2: Θ 1 = 76 W 1 = .150 kg L 1 = 30.5 Θ 2 = 20 W 2 = .150 kg L 2 = 50.5 L 3 = 40.5 Calculated Force of Tension: Static Equilibrium - Torque down = Torque Up F w1 + F g + F w2 = F T (.150)(9.8)(.305)cos(20) + (.1186)(9.8)(.2775)cos(20) + (.150)(9.8)(.505)cos(20) = F T (.405)sin(76) F T = 3.62 N Experimental Force of Tension: F T = 3.5 N Part 3: Θ 1 = 35.5 W 1 = .150 kg L 1 = 30.5 Θ 2 = 22.5 W 2 = .150 kg L 2 = 50.5
L 3 = 40.5 Calculated Force of Tension: Static Equilibrium - Torque down = Torque Up F w1 + F g + F w2 = F T (.150)(9.8)(.305)cos(-22.5) + (.1186)(9.8)(.2775)cos(-22.5) + (.150)(9.8)(.505)cos(-22.5) = F T (.405)sin(35.5) F T = 5.94 N Experimental Force of Tension: F T = 5.33 N In this lab, we did three different static equilibrium setups. They all had different variables which allowed us to explore the mathematical concepts of torque. For the first setup, the strut was placed at a 90-degree angle to the stand and was just straight. We were then able to analyze what force was acting on the strut and in accordance with what torques were acting on the strut. Then, we were able to actually solve to find the unknown force of the string and then compare it with an experimentally obtained value. By comparing them, we got to know if our calculations were around the same value and also found errors in our setup and instruments. Next, to make the task more challenging, we put the strut on an angle above the horizontal. By doing this, we had to account for the angle between the strut and any force that was being applied to calculate the torque. Yet because the gravimeter was used to measure, additional calculations were required. Finally, to make it a little bit more out of the box, we set the strut below the horizontal. By doing this we had the angles more absurd and forced ourselves to fully rely on our knowledge and concepts rather than the visual aids in front of us. We applied similar mathematics as part 2, to solve part 3. D. Discussion: Error Analysis/Questions 1.) Error Analysis - The error overall for this lab was quite small. For part 1, the error was about 10.95%, for part 2, the error was about 3.43% and for part 3, the error was about 11.44%. I think we have a relatively small error because the quantities that we are looking at in themselves are very small. Had we had this error for bigger numbers, then I think it would be something detrimental. However, I think this error mainly resulted from using the gravimeter. This instrument to measure angles, in my opinion, is very inaccurate. I felt like the angel kept on fluctuating as I was trying to read it. This error I think messed up our theoretical calculations and has offset them to a level. Additionally, because we were using a relatively older force sensor, I think it could have been erroneous as well. As a result, with these two influencing variables, I think we had a relatively okay error.
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E. Conclusion of Experiment In this lab, I learned a lot about how static equilibrium works. I know that for a n object to stay in motion all the upward and downward forces must cancel out. However, when it is regarding a rotating object, it is about all the torque. I found this idea very intriguing, and I think enjoyed setting up both sides of the equation to find the unknown. I love doing simple algebra like this and so to be able to set it up and solve it was satisfying. Additionally, I think I was just able to practice looking at problems and scenarios like this and be able to recognize and assign the various topics in play. When in doubt, I just moved the actual bar to see where it was going to double-check my thinking. I think this lab has helped me do equilibrium problems in class better.