lab$1-$using Exel

INSTRUCTIONS

An object on a frictionless air track is measured to have the following instantaneous

velocities at various times, as recorded in the table below:

time $($sec$)1\mathrm{.}001\mathrm{.}502\mathrm{.}002\mathrm{.}503\mathrm{.}003\mathrm{.}504\mathrm{.}004\mathrm{.}505\mathrm{.}005\mathrm{.}506\mathrm{.}00$

Velocity $($m$/$s$)30\mathrm{.}625\mathrm{.}420\mathrm{.}715\mathrm{.}410\mathrm{.}65\mathrm{.}80\mathrm{.}7-3\mathrm{.}9-8\mathrm{.}8-13\mathrm{.}8-18\mathrm{.}7$

$($a$)$ Plot this data with t on the horizontal axis and v on the vertical

axis. Be sure you label the graph and the axes properly, including units.

$($b$)$ Decide whether a straight$-$line $$curve$$ is appropriate, and if so$,$ fit a straight

line using a trend line.

$($c$)$ From your graph, find the initial velocity $($i$.$e$.,$ the y$-$intercept$)$ and m $($i$.$e$.,$ the slope$),$ where

is the velocity at t $=0.$ To do this, you might need to extend your straight

line somewhat to the left. This is called extrapolation, where we assume that the

behavior prior to t $=1\mathrm{.}0$ sec is similar to the behavior after t $=1\mathrm{.}0$ sec$.($Please

note that such an assumption is not always justified.$).$ Note also that you can solve your trend line equation.

$($d$)$ What physical quantity does the slope m correspond to$?$ Give a reason for your

answer.

How to plot graphs using Excel

Using Excel for Graphing

Getting Started

This tutorial will lead you through the steps to creating a graph and performing linear regression analysis using an

Excel spreadsheet. The techniques presented here can be used to analyze practically any set of data you

will encounter in your introductory physics lab.

To begin, open Excel from the Start menu on your PC $($Start $>$ Programs $>$ Microsoft Excel$).$ A blank

worksheet should appear. Enter the sample data and column headings shown below into cells in your Excel file. Save the file.

Creating and Editing a Graph

Use your mouse to select all the cells that contain the data that you want to graph. To graph this data,

select Chart from the Insert menu $($or click on the Chart Wizard icon that should be visible on the toolbar$).$ You

will see a series of dialog boxes.

Step $1$: Choose $"$XY $($Scatter$)"$ with no lines, and click "Next."

Step $2$: This screen allows you to choose which data to plot. Since you did this before starting the

Chart Wizard, just click "Next."

Step $3$: This screen has multiple menus. Experiment with the settings to see what they do$.$ Make sure

your final graph has a descriptive title, axes that are labeled $($with units$),$ and no legend. When you

are done, click "Next."

Step $4$: This screen selects where you will store the graph. Choose $"$As an object in$"$ to store the graph

in the same worksheet as the data and click "Finish".

You can move your graph by clicking near its center and dragging it$.$ The size can be adjusted by dragging

one corner. Most graph features can be modified by double$-$clicking on the feature you want to change.

You can also right$-$click on a feature to get a menu. Try changing the color of the plot area, the numbers on

the axes, and the appearance of the data points. It is recommended that you change the background area to

white by double$-$clicking on a blank portion of the graph Plot Area and then selecting $$None$$ under Area.

$[$In case you use Mac or the above guidelines didn't help, please follow the following guide to label x and y$-$axis$]$: Under Chart Tools $--->$ Chart Design $--->$ Add Chart Element $--->$ Axis Titles, Select both $$Primary Horizontal$$ and $$Primary Vertical$$ to label each axis$$

$[$Optional$]$: Right$-$click on a data point and choose "Format Data Series..." Click on the $"$Y Error Bars" tab. Choose

"Both" under "Display" and "Fixed Value" under "Error Amount". Then enter the uncertainty for the y$-$values

in the box marked "Fixed Value." You can add $$X Error Bars$$ similarly. Note: Error

bars may not be visible if they are smaller than the size of the data marker.

Adding a Trendline:

The primary reason for graphing data is to examine the relationship between the two variables plotted on the

X and Y axes. To add a trendline and display its corresponding equation, right$-$click on a data point and

choose "Add Trendline." Choose the graph shape that best fits your data and is consistent with your

theoretical prediction $($usually Linear$).$ Click on the "Options" tab and check the boxes for "Display equation

on chart" and $$Display R$-$squared value on chart.$$ A good fit is indicated by an R$2$ value close to $1\mathrm{.}0.$