edited Phys1 Lab2

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New York University *

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UA11

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Mechanical_engineering

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May 14, 2024

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pdf

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Lab #2: Motion II PHYS-UA11
Objective and Description In this lab, we are able to analyze the relationship between position ( x ), velocity ( v ), acceleration ( a ) and time ( t ) in a physical sense. This is accomplished through the aid of the Capstone database, which this lab allows us to become even more familiar with. As in the previous motion lab, the black motion sensor that uses sound waves to detect the distance of an object was used. By attaching an index card to two different gliders, the motion sensor was able to track the motion of the index card as the glider traveled down an inclined air track as a function of time. Both the incline, 𝜽 , and the size of the glider were manipulated in the experiment. Theory There are several theories that are applied in the functioning and understanding of the experiment. For instance, we could make assumptions about what our graph should look like based on the knowledge of the mathematical relationship of the values. It is known that velocity is the derivative of position and acceleration is the derivative of velocity and therefore the second derivative of position. If acceleration is constant the following equations can be obtained from the integrations: x=x 0 + v 0 t + ½at 2 v=v 0 + at Furthermore, if friction is neglected, we are able to use Newton’s second law to predict that the acceleration of the glider is g •sin 𝜽 . This comes from the fact that 𝚺 F X =ma x . Since there is no friction, the x component of gravity is the only force acting upon the glider. Since mg x =mg•sin 𝜽 :
Procedure My partner and I followed the procedure in the write-up fairly closely, since it was mostly straight forward. However, a few minor differences did arise as the experiment was being conducted. For one, when initially leveling the track, we noticed that it was nearly impossible to get the glider at a state of not moving at all. Rather, we leveled it to where the glider was moving back and forth very slightly, which my instructor clarified is normal. Additionally, when switching from y 1 to y 2 , the initial graphs produced did not demonstrate a constant acceleration. My partner and I needed to realign the sensor with the track in order to fix this source of error. We also needed to make sure the index card was stable secure or else it’s movement would cause sharp changes in the acceleration curve. Finally, we found that smoothing out the acceleration curve anywhere from 7-11 units was a sufficient amount to get an accurate read without oversmoothing. Data and Calculations Part I Key Symbol Unit Value y 1 =thickness of thinner block m 0.0191m y 2 =thickness of thicker block m 0.0371m r=length of track m 1.2857m 𝜽 1 =angle formed by r and y 1 rad see calculation below 𝜽 2 =angle formed by r and y 2 rad see calculation below m 1 =smaller, yellow glider m 2 =larger, red glider a=acceleration (m/s 2 ), m=slope of velocity graph, n=power function is raised to Table 1.1
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