PHY 1951 Data Analysis and Graphing Online PDF

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Data Analysis and Graphing Lab

Name Stefany Pascua Course/Section PHY-1951-005 Physics for Scientist and Engineers 1 Laboratory Instructor Stephen Flowers 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 1. You are to use a graphing program such as Excel, or something similar to make your graphs. a. Turn in all your graphs with this lab worksheet. 2. The graph needs to be titled as such, (First physical quantity vs Second physical quantity) 3. All graphs are to be plotted as y vs x. a. The first physical quantity goes on the y – axis (Vertical). b. The second physical quantity goes on the x – axis (Horizontal). 4. Each axis needs to be labeled by its physical quantity and with its units. a. As an example, an axis representing displacement where the units of measurement are meters needs to be labeled as such: Displacement (m). 5. Add a trendline (also called a Best-Fit Line) on the graph itself. a. Unless you are specifically told which trendline (best-Fit line) to use, use the one that best fits your data.

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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) 0 0.10 0.20 0.30 0.40 0.50

Distance from the sensor (m) 0.872 0.922 1.061 1.287 1.635 2.079

t2(s2) 0 0.01 0.04 0.09 0.16 0.25

Displacement, Δy(m) 0 0.05 0.189 0.415 0.763 1.207

1. Fill in the t2, and the displacement columns. Remember that displacement is direct line length directed from the initial position to the current position. (8 points) 2. Plot displacement vs time (Δy vs. t). This means that Δy is the ordinate (vertical axis) and t is the abscissa (horizontal axis). (6 points)

3. Plot Δy vs. t2. Then draw a Best-Fit Line through the data points. Find the value of the slope of this line, and its units. (show calculation, and units together on the graph paper) (10 points)

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m= rise/run = y2 – y1/x2 – x1 0.763 - 0.189/0.16 - 0.04 = 4.82 The value of the slope of this line is 4.82 m/s2. 4. What physical quantity (velocity, acceleration, etc.) does the slope of this graph represent? (Please 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 1

of a freely falling mass with the initial velocity of zero is given by ∆𝑦 = 𝑔𝑡2 . (6 points) 2

The slope of this graph represents acceleration. 5. From the value of your slope determine your experimental value for g. (6 points) My experimental value for g is 9.6 m/s2. 6. Find the percent error of the experimental value of g, using g = 9.81 m/s2 as the accepted value. (2 points) The percent error of the experimental value of g is 2.1%.

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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) 50. 100. 200. 400. 800. 1,600

Acceleration, a(m/s2) 15.72 8.37 4.02 1.98 1.03 0.47

1/m (kg-1)

Mass, m(kg) 0.05 0.1 0.2 0.4 0.8 1.6

20 10 5 2.5 1.25 0.625

1. Complete the above data chart. Show some calculations to receive credit. (8 points) 50/1000 = 0.05 100/1000 = 0.1 200/1000 = 0.2 400/1000 = 0.4 800/1000 = 0.8 1600/1000 = 1.6 1/0.05 = 20 1/0.1 = 10 1/0.2 = 5 1/0.4 = 2.5 1/0.8 = 1.25 1/1.6 = 0.625 2. Plot a vs m, where mass is in kilograms. (10 points)

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3. Plot a vs 1/m, where mass is in kilograms. Make the trendline be displayed on the graph. (10 points)

4. What is the value of the slope of the trendline, with its units? (4 points) m= rise/run = y2 – y1/x2 – x1 5 – 1.25/4.02 - 1.03 = 1.26 The value of the slope of this line is 1.26 kg ⁻¹/m/s ². 5. What physical quantity does the slope represent? What is the correct name for combination of units the slope possesses? (4 points) The slope represents force, the correct name for combination of units the slope possesses is a newton. 5

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Exercise 3. The period of a pendulum T is given by the following equation. 𝑇 = 2𝜋√

𝑙 𝑔

Where l is the length of the pendulum, and g is the gravitational acceleration 9.81 m/s2. Table 3 shows the data of the period of a pendulum as a function of length.

Table 3 l(m) 0.200 0.400 0.600 0.800 1.00 1.20

T(s) 0.910 1.26 1.58 1.80 2.08 2.22

T2(s2) 0.8281 1.5876 2.4964 3.24 4.3264 4.9284

1. Plot T vs. l. (10 points)

2. Fill in the T2 column. Show some work to receive credit. (10 points) 0.910 * 0.910 = 0.8281 1.26 * 1.26 = 1.5876 1.58 * 1.58 = 2.4964 1.8 * 1.8 = 3.24 7

2.08 * 2.08 = 4.3264 2.22 * 2.22 = 4.9284 3. Make a graph of T2 vs. l. Display the trendline on the graph. (10 points)

4. What is the value of the slope, with its units? (6 points) m= rise/run = y2 – y1/x2 – x1 0.6– 0.25/2.4964 - 1 = 0.24 The value of the slope of this line is 0.24 kg ⁻¹/m/s ².

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