# 1.2: Experiment 1 - Measurements

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Measurements and the Irrational Number Pi

Learning Objectives

By the end of this lab, students should be able to:

• Accurately measure materials using a home made ruler.
• Select appropriate measuring device for each application.
• Select appropriate number of significant figures for each measurement.
• Convert between units or measurement using dimensional analysis.
• Differentiate between accurate and precise measurements in an aggregate set of data.
• Graph a set of data and determine the slope with Google sheets.

Prior Knowledge:

## Introduction

In this lab students will work in online groups of four using Zoom breakout groups while collaborating on a Google Doc, and will create scales based on the width of their pointer finger (PF) to determine the value of pi. Students will use the PF scale to create the additional scale of the Fist, which is equal to the width of 5 PF's. Once this scale is completed, students will then create a more precise scale, the deciFist scale, where each unit is 1/10th the length of the Fist scale. After creating these scales students will then find 5 circular objects around their house, measure the circumference and diameter, and then use Google Sheets to plot these measurements and determine the value of Pi.

• Week 1:  Students work in their group to design a protocol for building a ruler based on the width of your pointer finger. Then each student individually performs the experiment and plots their data in Google Sheets.
• Week 2: Students pool all of the class data, plot with Google Sheets, and work up their data and turn in individual worksheets.

Supplies:

In this lab you may need to obtain supplies, if you go to the store be sure to follow proper COVID-19 hygienic protocols, wear a mask, wash your hands thoroughly and maintain safe distance from fellow shoppers. Please review these protocols from the CDC.

• two strings or shoe laces that can be marked on
• red and blue markers
• ruler with metric units (cm)
• firm paper (thin cardboard from packaging can be used)
• scissors
• cell phone with camera
• laptop or computer with camera, speakers and microphone hooked up to internet
• scotch tape

## Protocols

### Week 1a: Worksheet

The document below is a preview only.

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### Week 1b: Experimental Design

Using Zoom breakout groups collaboratively work with your online group on the Google Doc in your Google Classroom called "Experiment 1: Measurements Design Proposal". You need to develop a protocol for building a ruler based on the width of your pointer finger.  As you will be measuring the circumference of a circular object, the "ruler" needs to be made of a flexible material, like a string or a power cord. You will make two different scales, both based on the same fundamental unit of length, which we will call a "Fist" as its 5 times the length of your pointer finger.

Note

Students need to make two scales, and upload a picture of the two scales to their worksheet in Google Classroom. These scales are based on the same unit of length (the length of 5 pointer fingers, which we will call the "Fist"), but have different precision. When making measurements students must report the correct number of significant digits (all certain values and the first "guestimate", section 1B.2.1.2 of your LibreText).

The document below is a preview only.

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### Week 1c: Graphing with Google Sheets

Video $$\PageIndex{1}$$: Tutorial on using Google sheets for linear graphs created by Bob Belford (https://youtu.be/muF0eJkN9CQ)

The Google Sheet below is a preview only.

### Week 2a: Graphing Group Data

You will now make 4 graphs and plot the data of all four classmates, but you must identify which data points are your own. That is, you can color code your data points, or use a different symbol.

 Graph 1: Use all students' data from the half PF scale and include the origin (0,0) Graph 2: Use all students' data from the half PF scale and do NOT include the origin (0,0) Graph 3: Use all students' data from the five PF scale and include the origin (0,0) Graph 4: Use all students' data from the five PF scale and do NOT include the origin (0,0)

The Google Sheet below is a preview only.

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Review Section 1B.5: Graphs and Graphing, and specifically go to the section on Graphing Linear Functions where there are step-by-step instructions on how to create a graph.

We know from section 1B.5 that the equation for a linear function is $y=mx+b$, where

m is called the slope of the line, which is the ratio of the change in y (the rise) to the change in x (the run). Since the line is linear, the slope is the same between any two points along the line.

b is called the y-intercept, which is the value of y when x=0.

If a linear function is based on an extensive property like the mass and volume of a substance, or the circumference and diameter of a circle, then the Y intercept (b) is zero (if on the scale zero means there is nothing), as if the mass of an object is zero, so is it's volume, or if the diameter of a circle is zero, then its circumference must also be zero.  So the above equation becomes  $y=mx$

This brings forth an interesting question that we wish you to discuss, should you include the point (0,0) in your graph?

### Week 2b: Converting

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