Fall2023 Data Analysis and Graphing Online-1
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University of Texas, San Antonio *
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1611
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Date
Apr 3, 2024
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Data Analysis and Graphing Lab Online
Name______Riley Jacob Villas___________ Course/Section_____PHY-1611-012______________________
Instructor____Hayley West__________________________
Introduction
The purpose of this exercise is to learn some basic techniques of data analysis: conversion of units, plotting data, finding the slope of a graph, determining the units of the slope, using the units of the slope to determine the physical quantity the slope represents, and calculating the percent error of your results.
Instructions for Graphing •
You are to use a graphing program such as Excel, or something similar to make your graphs.
•
Turn in all your graphs with this lab worksheet.
•
The graph needs to be titled as such, (First physical quantity vs Second physical quantity)
•
All graphs are to be plotted as y vs x.
•
The first physical quantity goes on the y – axis (Vertical).
•
The second physical quantity goes on the x – axis (Horizontal). •
Each axis needs to be labeled by its physical quantity and with its units. •
As an example, an axis representing displacement where the units of measurement are meters needs to be labeled as such: Displacement (m).
•
Add a trendline (also called a Best-Fit Line) on the graph itself.
•
Unless you are specifically told which trendline (best-Fit line) to use, use the one that best fits your data.
•
Do not choose the option that “connects the dots”. This is not a Best-Fit Line. A Best-Fit Line is a line the “best” fits all of the data points.
Exercise 1.
Table 1 show the data collected by a motion sensor for a ball, initially at rest, then allowed to freely fall straight downward. Table 1
Time, t(s)
Distance from the sensor (m)
t
2
(s
2
)
Displacement, Δ
y(m)
0
0.872
0
0
0
0.872
0
0
0.10
0.922
0.01
0.5
0.20
1.061
0.04
0.189
0.30
1.287
0.09
0.415
0.40
1.635
0.16
0.763
0.50
2.079
0.25
1.207
•
Fill in the t
2
, and the displacement columns. Remember that displacement is direct line length directed from the initial position to the current position. (8 points)
•
Plot displacement vs time (
Δ
y vs. t). This means that Δ
y is the ordinate (vertical axis) and t is the abscissa (horizontal axis). Do NOT
add a trendline to this graph. (6 points)
•
Plot Δ
y vs. t
2
. Apply a Best-Fit Line through the data points. Determine the value of the slope of this line, and its units. (10 points)
•
What physical quantity (velocity, acceleration, etc.) does the slope of this graph represent? (Note: you are NOT being asked to describe the relationship between displacement and the square of the time shown by the graph) Here is a hint: The magnitude of the displacement of a freely falling mass with the initial velocity of zero is given by (6 points)
Acceleration
•
From the value of your slope determine your experimental value for g. (6 points)
4.816 = g / 2 so g = 9.632
•
Find the percent error of the experimental value of g, using g = 9.81 m/s
2
as the accepted value. (2 points)
percent error = ((9.81 - 9.632) / 9.81) x 100 = 1.81%
Exercise 2.
Table 2 shows the acceleration of different masses on a level surface, with the same constant force being applied to each mass separately.
Table 2
Mass, m (g)
Acceleration, a (m/
s
2
)
Mass, m (kg)
1/m (kg
-1
)
50.
15.72
0.05
20
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50.
15.72
0.05
20
100.
8.37
0.1
10
200.
4.02
0.2
5
400.
1.98
0.4
2.5
800.
1.03
0.8
1.25
1,600
0.47
1.6
0.625
•
Complete the above data chart. Show some calculations to receive credit. (8 points)
50 / 1000 = 0.05
1 / 0.05 = 20
100 / 1000 = 0.1
1 / 0.1 = 10
200 / 1000 = 0.2
1 / 0.2 = 5
400 / 1000 = 0.4
1 / 0.4 = 2.5
800 / 1000 = 0.8
1 / 0.8 = 1.25
1600 / 1000 = 1.6
1 / 1.6 = 0.625
•
Plot a vs m, where mass is in kilograms. Do NOT
add a trendline to this graph. (10 points)
•
Plot a vs 1/m, where mass is in kilograms. Display the trendline on the graph. (10 points)
•
What is the value of the slope of the trendline, with its units? (4 points)
slope = (5 - 1.25) / (4.02 - 1.03) = 1.254 kg-1/m/s^2
•
What physical quantity does the slope represent? What is the correct name for combination of units the slope possesses? (4 points)
The physical quantity that the slope represents is force. The correct name for the combination of unites the slope possesses is a newton
Exercise 3.
The period of a pendulum T
is given by the following equation.
Where l is the length of the pendulum, and g
is the gravitational acceleration 9.81 m/s
2
. Table 3 shows the data of the period of a pendulum as a function of length.
Table 3
l(m)
T(s)
T
2
(s
2
)
0.200
0.910
0.8281
0.400
1.26
1.5876
0.600
1.58
2.4964
0.600
1.58
2.4964
0.800
1.80
3.24
1.00
2.08
4.3264
1.20
2.22
4.9284
•
Plot T vs. l.
Do NOT
add a trendline to this graph. (10 points)
•
Fill in the T
2
column. Show some work to receive credit. (10 points)
0.910^2 = 0.8281
1.26^2 = 1.5876
1.58^2 = 2.4964
1.8^2 = 3.24
•
Make a graph of T
2
vs. l.
Display the trendline on the graph. (10 points)
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•
What is the value of the slope, with its units? (6 points)
slope = (0.6 - 0.25) / (2.4964 - 1.0) = 0.24 kg-1/m/s^2