Lab 3 - Exploring Constant Acceleration

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University of New England *

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3401

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Mechanical Engineering

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Apr 3, 2024

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Lab Assignment Sheet Exploring Constant Acceleration (Week 3) Model or Topic Explored: We will be looking at the constant acceleration particle model using the IOLab unit. We will be using some of the basic features of the ‘wheel’ on the IOLab unit along with the accelerometer to explore displacement, velocity, and acceleration. Please refer to the pre-lab video for instructions. All answers and graphs may be added electronically. Name: Tanyitaku Tanyi  Date: 2/07/2024 Constants:  Initial Velocity  Slope of surface Measurables:  Position “Ry”  Time •  Instantaneous Velocity “Vy”  Acceleration PHYS 1010 – page 1

Lab Assignment Sheet Observables:  IO Lab Unit  Rolling down incline  Starting from rest with increase in acceleration Problem Statement:  How does position depend on time for constant acceleration? Prediction: I anticipate that velocity will exhibit a linear dependence on position, while also showing a linear correlation with time. Additionally, the position is expected to demonstrate a linear relationship with time. . The graph will be a linear relationship (y=mx+b) with the slope being positive and equal to constant acceleration. PHYS 1010 – page 2

Lab Assignment Sheet Experiment Procedure ( list of steps with some detail): I. Gather the required laboratory equipment. II. Position a book under the ottoman to create an inclined surface. III. Utilize the IOLab to gather and record data. IV. Initiate the IOLab's motion from the top of the incline, allowing it to roll down the plane while recording the data into Excel. V. Generate a graph plotting position against time using the collected data from the IOLab device, and apply a trendline with its corresponding equation. VI. Repeat the process for the velocity versus time graph, recording the data in Excel. VII. Create diagrammatic representations of the graphs, incorporating trendlines and equations. VIII. Repeat the experiment, this time commencing the motion of the IOLab from the bottom of the incline and pushing it upward to record the data. Tools and Diagram of Apparatus: [In this section, please paste at least two digital photographs. One with you and your sign containing your name and the date of your experiment, and at least one more of you with the items used in your experiment (preferably while doing the experiment).] PHYS 1010 – page 3

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Lab Assignment Sheet Precautions and caveats: We must take precautions to ensure that the IOLab remains secure on the incline to prevent inaccurate data recording. Additionally, we should avoid setting the slope too steep, as it could limit the amount of data we can collect. Data Table with Units: Constant acceleration it the Y+ direction 1) Position vs. Time PHYS 1010 – page 4

Lab Assignment Sheet 2._) Velocity vs. Time 3) Velocity Squared vs Position PHYS 1010 – page 5

Lab Assignment Sheet 4) -Y Direction Data Data Graphs: [In this section, you may paste graphs that you have generated in MS Excel.] +Y Direction Graphs 1. Position vs. Time PHYS 1010 – page 6

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Lab Assignment Sheet 2.) Velocity vs. Time 3.) Velocity2 vs. Position PHYS 1010 – page 7

Lab Assignment Sheet -Y Direction Graphs 1. Position vs. Time 2) Velocity vs. Time 3). Velocity2 vs. Position PHYS 1010 – page 8

Lab Assignment Sheet Math Model(s): [Digital pictures or MS Word Equation Editor could be included if the equations cannot be easily typed.] +Y Direction Graphs: Position vs. Time y = 0.4805x2 + 0.1133x + 0.0234 Velocity vs. Time y = 0.8683x + 0.1564 Velocity Squared vs. Position y = 1.7122x - 0.0089 +Y Direction Graphs: PHYS 1010 – page 9

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Lab Assignment Sheet Position vs. Time y = -0.458x2 + 1.2658x - 0.0428 Velocity vs. Time y = -0.9511x + 1.3265 Velocity Squared vs. Position y = -1.787x + 1.2816 Diagrammatic Model: [Digital pictures or diagrams created within MS Word would be included here.] A. Position B. Acceleration C. Velocity PHYS 1010 – page 10

Lab Assignment Sheet A. Position B. Acceleration C. Velocity Verbal Representation: A. In the +Y direction section of the lab, distinct data tables are utilized for position vs. time, velocity vs. time, and velocity squared vs. position. The position vs. time graph displays an upward-facing parabola with a positive slope, confirming our initial prediction. Similarly, the velocity vs. time graph exhibits a linear relationship with a positive slope, further validating our prediction. Upon comparing the position and velocity graphs, it is evident that the velocity graph's slope is approximately twice that of the position graph. Our schematic model represents blue dots denoting positions along the y-axis, while colored arrows indicate velocity, starting small and gradually increasing with time. Acceleration is illustrated by uniform-sized colored arrows, reflecting constant acceleration. PHYS 1010 – page 11

Lab Assignment Sheet B). In the -Y direction segment of the lab, I opted to consolidate all the data into a single chart for the position vs. time, velocity vs. time, and velocity squared vs. position graphs. Our position graph exhibited a parabolic shape with a negative slope, while the velocity graph displayed a linear relationship with a negative slope as well. The slope of the position graph will yield velocity, whereas the slope of the velocity graph will provide average acceleration. Our schematic model illustrates blue dots representing position along the y-axis. Velocity is depicted by colored arrows, starting small and gradually increasing in size until reaching the peak of the parabola, where velocity hits zero before decreasing back to zero. Acceleration is represented by uniformly sized colored arrows, indicating constant acceleration. PHYS 1010 – page 12

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