Lab 121_ Rotational Static Equilibrium — Forces on a Strut

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New Jersey Institute Of Technology *

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111A

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Mechanical Engineering

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Dec 6, 2023

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Lab 121: Rotational Static Equilibrium — Forces on a Strut Physics 111A Section 014 Group H Instructor: Date of Experiment: 04/19/23 Date of Submission: 04/26/23

Equipment List: ● Lab Computer with Capstone software ● 850 Universal Interface ● Force Sensor ● Clamp for the force sensor ● Strut system ● 50 g wight hangers ● Super pulley with a rod ● Standard set of weights ● One-meter stick ● Protractors ● Electronic Balance Introduction: ● Objectives: In this lab I sought to obtain a better understanding of torque and the conditions for rotational static equilibrium. In addition, I determined the tension on the supporting string in a strut system by applying the conditions of rotational equilibrium in the system. ● Background: By definition, torque is a vector product of the distance and applied force. The magnitude of torque is: (1) τ = ?𝐹?𝑖𝑛θ When a body is in rotational static equilibrium like seen in Figure 1 below, the sum of all the torques which is net torque acting on the body about any point, O, must be zero:

(2) τ 𝑛𝑒? = ∑ τ = 0 This can also be described as the sum of all torques in counterclockwise direction must equal to the sum of all torques in the clockwise direction. Figure 1 Experimental Procedure/Setup: ● After setting up the equipment as seen in Figure 2, I logged onto the computer, connected the force sensor to the 850 Universal Interface and zeroed the force sensor while ensuring that there was no force on it. Figure 2

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Two angles can be seen in the setup: is the angle between the strut and the supporting θ 1 string and is the angle of inclination of the strut with respect to a horizontal line. For θ 2 Part 1, we measured the difference lengths seen in the figure below, recorded the weight of the aluminum rod and measured the two angle values. In this lab, W1 and W2 were given and with the help of the force sensor, I measured the tension of the supporting string necessary to maintain equilibrium in the system. I then moved on to the second and third part of this experiment in which I maintained all the same conditions from the first part except for both angles. In the diagram shown below, one can see the angles chosen for part two and three.

Results/Calculations:

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Error Analysis: Discussion/Analysis: ● After completion of this lab and calculating the data, I performed error analysis which resulted in 37%, 15.5%, and 21.1% errors between my calculated and measured values. I believe these errors can range from many reasons but the most probable reasons include incorrect readings of angles or lengths, algebra errors during the calculations themselves, or incorrect readings from the force sensor. In order to minimize this error in the future, the experiment can be done with better precision in order to avoid any small mistakes which can lead to these errors. Conclusion: ● In this lab, we were tasked with determining the torque using a system involving forces on a strut. The lab consisted of a complex system of strings, weights, and angles and us students were asked to set this system up and perform calculations and observations through three different trials. After completing the experiment, I believe we now have a better understanding of torque forces and how to calculate tensions of strings in these systems.