10 Sep Name: _____________________________________ PHY 111: Remote Lab #1

Name: _____________________________________

 

 

PHY 111: Remote Lab #1

 

Data Analysis

 

 

Purpose:

 

To investigate how measurements are performed and analyzed in physics

 

 

Objectives:

 

· To describe the process of measurement

· To present data in tabular form

· To properly plot data in graphical form

· To analyze data in graphical form

· To determine the standard deviation of a set of measurements

· To calculate various forms of uncertainties

 

 

Materials & Resources

 

· Various disks

· String

· Scissors

· Meter stick and/or metric ruler

· Graph paper

· “Accurate masses and radii of normal stars: modern results and application”, Torres, Andersen, and Gimenez, Astron. Astrophys. Rev. 18, 67-126 (2010)

 

 

Introduction

 

How do physicists make and report measurements?

Very often, physicists deal with “quantities”, concepts that can be expressed in numerical form. Quantities may come from direct measurement or calculation; they may refer to everyday experiences or abstract notions, they may be expressed in words or symbols, but in the end must be based on numbers.

The emphasis on quantities is not arbitrary. We may have many notions (“theories” or “models”) to use to describe how nature operates, but it is impossible to test the validity of any particular notion without comparing it to nature – which is where quantities come in.

 

Part #1: Determination of  – calculation method

 

Before talking in detail about the meaning of the concept of “quantity”, let’s perform some measurements and analysis of one.

The number “pi” (or, in Greek, “”) is amongst the most important numbers in all of mathematics and physics. It is difficult to determine – for example, it is an “irrational” number, meaning it cannot be found by taking the ratio of two whole numbers. Yet that is its most simple definition – pi is the ratio of the circumference of a circle compared to its diameter. In equation form,

 

 

 

 

If we cannot simply calculate  as a ratio, what can we do instead? One approach is to approximate pi through measurements.

Here, we will take a series of measurements that will allow us to calculate a value for . Along the way, we will also discuss some issues that come up while making measurements and how we should report them.

 

1. Before we begin, how close to  do you think your measurements should be in order to be considered reliable? Within 1%? 5%? 10%? (There is no wrong answer, but