SUMMARY and GLOSSARY

 

This is an attempt at an outline or summary of the online LONCAPA lab.  If it seems useful then the student can keep this page open as a guide. None of the material on this page is required reading.

 

There are

9 parts to the lab and the student should visit each part at least once

 

 

4 of the parts require answers either based on material you should master or results from the requested analysis

 

Problem

 

5 informational pages with assignments

 

  

 

 

One Excel spread sheet must be built as you work through the material

 

 

 

 

Contains the following work sheets

 

 

 

 

 

straight line

 

 

 

 

fit

 

 

 

 

non linear

 

 

 

 

non linear fit

 

 

 

 

logarithms

 

 

 

Lab parts

    P1 Introduction

information &

assignments

    P2 excel line plot

information &

assignments

  Problem>P3 find slope and intercept from line plot < (2 parts)

Answers to be submitted

  ProblemP4 Fit line (2 parts)

Answers to be submitted

    P5 Fit line

information &

assignments

    P6 Plot non linear

information &

assignments

  ProblemP7-Which function

Answers to be submitted

  BranchProblemP8 non linear fit

Answers to be submitted

    P9 logarithms

information &

assignments

 

 

 

 

Review your understanding of functions, variables and parameters

function

Relationship between quantities. How quantities depend on each other. 

variables

Measurable quantities that vary in an experiment.

parameters

Fixed quantities: coefficients in functions, physical constants (g), and other quantities that define functions (powers or exponents).

 

 

Review how you determine values for the quantities of interest in an experiment.  Here we want to highlight that some quantities are directly measured (length), some quantities are simple combinations of directly measured quantities (velocity= dist./time) and some quantities require a sophisticated analysis of the data (slope of a straight line fit  [x vs t] to find a velocity).

direct measurement

The process where a quantity of interest is measured by an instrument that provides the result.  An example is measuring length with a ruler.

indirect measurement

When several direct measurements and other indirect measurements are combined to yield the result.

reference

Using data from a book, publication or internet site. For example, using the value  g=9.8 as provided by your text book

Coffee filter experiment is a good illustration because the terminal velocity that one uses in the final analysis is determined by a somewhat complex analysis of the data from the falling filters while the masses of the filters are directly measured.

 

 

In looking at models for data sometimes we have a specific model that we are testing and other times we examine a more general model. Here again the coffee filter experiment is relevant. One model for how terminal velocity is reached allows for only one quantity to be adjusted (parameter C), while a more general model doesn’t require that the functional relationship be restricted to velocity squared so that there are two parameters that need to be determined (B, a).

 

 

Review of the straight line function using an EXCEL spread sheet.

slope

Straight line parameter that determines the tilt of the line, rise/run

intercept

Value of the function when evaluated at zero.

 

 

Change a line by manually adjusting slope and intercept to see how one can match a line to data.

manual fit

self adjusted data and line

 

 

Examine how to evaluate if the line matches the data

student based quality factor

your statement as to how one judges when the line best matches the data

 

 

crude chi squared or quality factor

somewhat intuitive definitionè A cumulative assessment of the difference between the data and the curve. The distance away from the curve is evaluated for each data point and an overall judgment made based on all these distances.

 

 

Fitting data using a straight line function.

 

 

general functions

polynomial functions

Sum of terms each term has a coefficient and the independent variable raised to an integer power.

exponential function

functions that involve e raised to a power that depends on the independent variable

 

 

General curve fitting:  Fit data to a function.

 

 

Logarithms