Lab 2 Formal Report

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Rio Salado Community College *

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111

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Mechanical Engineering

Date

Dec 6, 2023

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docx

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Oluwadamilola Esan PHY111 09/04/2023 Kinematic Graphs Purpose: How will learning how to use spark tapes help determine the velocity of two different objects? Materials :  Printer  Paper  Ruler  Pen or pencil  Tape  Scissors  2 different objects Procedures : 1. Preparation:  Set up a flat surface.  Label your equipment.  Prepare two tapes 2. Experimental Setup:  Place tape on the flat surface.  Ensure they are straight and secure.  Position the camera to capture the setup. 3. Data Collection:  Measure dot positions on both tapes at 0.1-second intervals from time zero. 4. Data Recording:  Record time (s) and dot positions (m) in your lab notebook. 5. Data Analysis:

 In Excel, create tables for Tape 1 and Tape 2 data (time in seconds, position in m).  Calculate approximate velocity (m/s) for each point  Calculate approximate accelerations using velocity changes. 6. Graphs:  Create position vs. time graphs for Tape 1 and Tape 2 (position vs. time).  Add titles and labels.  For Tape 1, use a linear trendline with the equation.  For Tape 2, use a power trendline with the equation. 7. Velocity vs. Time Graphs:  Create velocity vs. time graphs for both tapes (velocity vs. time).  Include titles and labels.  Add linear trendlines with equations. Photograph(s) of Experiment : Data : Tape 1 Data

TAPE 2 DATA Calculations and Graphs : To find average Velocity for Tape 1, we need to find out the velocities used. Two values from the data table are 0.0365m/s at 9 seconds and 0.012m/s at 4 seconds. The equation for average velocity is (V2-V1)/2 The time amounts are useless as we are only calculating average velocity for now. We add 0.0365 to 0.012 and we get 0.0377m. We then divide that value by two to get our average velocity which is 0.0189 m/s. To calculate average

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acceleration, we will be using the same numbers from our Tape 1 data set. First, calculate the change in velocity and change in time : Change in Velocity = V2 - V1 Change in Velocity = 0.0365 m/s - 0.012 m/s = 0.0245 m/s . Change in Time = T2 - T1 Change in Time = 9 seconds - 4 seconds = 5 seconds . Now, plug these values into the formula to calculate the average acceleration. Average Acceleration (a avg ) = (0.0245 m/s) / (5 seconds) . Average Acceleration (a avg ) = 0.0049 m/s² . So, the average acceleration of the object is 0.0049 meters per second squared (m/s²).

Results : Tape 1 Position Graph: Equation was 0.0189x - 0.0382, graph looked exponential. Tape 1 Velocity Graph: Equation was 0.0021x + 0.0061, graph looked exponential, two outliers at 11 and 12 seconds, however. Tape 2 Position Graph: Equation was 0.0512x – 0.1429, sudden jump in position from 7-8 seconds. Tape 2 Velocity Graph: Equation 0.0063x + 0.0141, can’t even tell what the graph looks like, but it looks like a proper scatter plot.

Conclusion : This is perhaps the most important section in the report because it includes your analysis of what happened in the investigation. The conclusion section should discuss all of the following:  Theory / Background : Acceleration is the rate of change of velocity of an object with respect to time. Velocity is the rate of change of displacement of an object with respect to time. Position vs time graphs are graphs that show how an object’s position changes over time. Spark timers are devices used to measure time intervals in physics experiments. Spark timers are often used to measure the acceleration due to gravity by timing how long it takes for an object to fall a certain distance. The traditional spark timer usually places spark dots on waxed tape as an object falls freely, but we used one made of paper. The distance between each two consecutive sparks increases due to the acceleration of the falling object. By measuring the distance between these marks, we can determine how much time has elapsed between them. This information can be used to calculate the velocity and acceleration of objects. The significance of the results obtained from this lab is that they provide a quantitative understanding of how an object’s velocity and acceleration change over time. This information can be used to make predictions about how objects will behave in different situations. For example, if we know the initial velocity and acceleration of an object, we can use this information to predict its future position and velocity at any point in time. When interpreting graphs, the slope and axis intercepts tell you about the relationship between the variables being measured. The slope of a line on a graph represents the rate at which one variable changes with respect to another variable. For example, on a position vs time graph, the slope represents the velocity of an object at that point in time. The axis intercepts represent the values of the variables when one or both are zero. I expected the Position v Time graphs to look as they did, but I’m not sure why the Velocity v Time graphs don’t look uniform, so they were lower quality than what I was expecting. I think my measurement could have been a bit more precise, because I was getting all sorts of weird numbers, and I also opted for using meters instead of centimeters for my data, so that could have led to math errors. Analysis Questions Response : Answer the following analysis questions:

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1. Use your data and graphs to determine the position of both objects after 5.0 seconds of travel. Show work. Tape 1- The equation is y = 0.0189x - 0.0382, where y represents position and x represents time in seconds. To find the position of the object after 5 seconds, we need to substitute x = 5 into the equation and solve for y: y = 0.0189(5) - 0.0382 y = 0.0945 - 0.0382 y = 0.0563 Tape 2- The equation is 0.0512x – 0.1429, where x represents time in seconds and the output of the equation represents position. To find the position of the object after 5 seconds, we need to substitute x = 5 into the equation and solve for the y: 0.0512(5) – 0.1429 = 0.1091. 2. How can you use the position graph for tape-1 to determine the velocity of the object? What is the velocity of the tape-1 object? You find the slope between two points (0.037-0.025)/(3-2)= velocity = 0.012 m/s 3. How can you use the velocity graph for tape-2 to determine the acceleration of the object? What is the acceleration of the tape-2 object? Find the velocity v time slope: (0.036 – 0.029)/(9-4)= 0.0014 m/s 2