Laboratory exercises are not just about
getting the right result, but about recognizing that fundamental physics
principles shape our everyday experiences and underlie many of the devices that
we use in our personal and professional lives. Please do not treat the
laboratories as cookbook exercises. Permit yourself to think! Thoughtful answers to the questions
in blue will give you most of the laboratory credit.
You can discuss the lab with your fellow students and the lab instructors in
the Canvas discussion forum.
Open a Microsoft Word document to keep a log of your
experimental procedures and your results. This log will form the basis of
your lab report. Address the points highlighted in blue.
Grading scheme for all labs:
25% for completion
In order to receive full
credit, you have to complete the entire lab and answered all parts.
Use full sentences explaining your results, show work, insert and properly label tables
and plots, proofread, and use correct units. Make comments if you were
stuck or if your results seem to have errors. Mention what could have
caused these errors in your results and how they could be improved.
The reports are to help you, so use them as kind of like a journal to help
you think through the material.
25% for accuracy
You do have to put effort into
these labs. This is a 4 credit-hour course with lab, so just like for
in-person labs, you have to set aside time to work on the labs.
50% for a reflection at the end of your report in a
short essay format
You should reflect on the
material and mention how well you understood it. Ask questions if you have
any. Just stating that you understood the lab and have no questions without
any comments will not be sufficient for full credit.
Examples: Did you understand what you were doing during an exercise or activity, or did
you just follow instructions? Do your results make sense to you, or do you expect them to be wrong? Why? Do you have suggestions on how to improve the exercise or activities so students
can learn more from them? ...
Task:
Install the app PhyPhox on your smartphone (iPhone or Andoid).
It gives you access to most of the sensors in your phone and has setups for many
experiments. Explore some of the measurement that you can make with this
app. It will be helpful in some of the later labs.
Introduction to the tools
Exercise 1
Your main tool for analyzing data will be the Microsoft Excel
spreadsheet program. Let us go ahead and start
using it.
Assume you have performed an experiment, measuring the position of an object
moving along a straight-line path as a function of time. Your data are
shown in the table below. You suspect that the object moved with constant speed, covering equal
distance in equal time intervals. You want to verify this by producing a
plot of position versus time and confirming that it is well-fitted by a straight
line. If yes, then the slope of the straight line is equal the speed of the
object in units of m/s.
Time (s)
Position (m)
0
0.00
1.5
2.64
3
5.22
4.5
7.61
6
10.22
7.5
12.84
9
15.43
10.5
17.98
12
20.52
13.5
23.03
15
25.37
Basic instructions for producing the plot are given below. Experiment with the various options
Excel presents to you.
(a) Open Excel and enter your data.
Highlight the table in the browser, right click Copy, and paste the table into an Excel spreadsheet by putting your
cursor into cell A1 and clicking the Paste button.
(b) Produce a graph of position versus time.
Highlight your data in Excel.
On the Excel menu bar click Insert, Chart, XY (Scatter), and pick one of the
subtypes. Excel will plot the second column versus the first column.
Highlight your graph, click the + sign next to it, and give the chart a title and label the axes. The label for the
x-axis should be "Time (s)", and the label for the y-axis should be "Position
(m)".
(c) Study your graph. The plot of position versus time should resemble a
straight line. The slope of the best fitting straight line should yield the
average speed of the object. You can find this slope by adding a trendline to
your graph.
Right-click your data and choose "Add Trendline". Choose "Linear", "Display equation on chart". (You can also set the intercept at zero
for this data set.) An equation y = ax + b will appear on your graph,
where the number a is the slope and the number b is the y-intercept.
(d) The fit is not perfect. The data you have collected contain
experimental uncertainties. To find the resulting uncertainty in the slope
you must use the regression function.
Position the cursor in an empty cell. On
the menu bar click Data, Data Analysis, Regression. For the input y-range
choose the entries in column B. For the input x-range choose the entries in
column A. (Again, put your cursor in the appropriate textbox and highlight the
chosen cells.) Under output options check new worksheet, and under residuals
choose residual plots and line fit plots. Click OK.
[If you do not find data analysis on the menu, then you have to add the
Analysis ToolPak Add-In. Click File, then click Excel Options and then
click the Add-Ins. Click the Go button while Excel Add-Ins is selected and
check Analysis ToolPak.]
The regression function finds the best fitting
straight line for your data. Under SUMMARY OUTPUT, X Variable, you will find
the slope of this line. It should be the same value you got from the trendline. The cell to the right of the slope contains the standard error in this
slope from the fit. The slope of the position versus time graph is the
velocity. The residual plot and line fit plot give you visual feedback on how
well a straight line can be fitted to your position versus time data.
Note: The trendline is the best fitting straight line to the data.
It is the same line you get from the regression function line fit plot.
The slope of this trendline is your best estimate of the average speed.
The statistical uncertainty in the average speed is the standard error in the
slope you get from the regression function. This uncertainty only includes
the error due to the scatter in the data points, not any systematic error, such
as a calibration error.
Paste your labeled plot of position versus time
(including the trendline) into your Word document and answer the questions
below.
What is the slope of the best fitting straight line? What is the uncertainty
(standard error) in this slope? Do you think that a straight line produces a
good fit to the data?
What is the average speed and the uncertainty in the average speed of the
object?
Is the object moving with approximately constant speed, or is its
speed increasing or decreasing? Justify your answer. (How do you know?)
To practice entering and copying formulas, let us calculate the speed of the object for
each small time interval from the raw data.
Type Speed (m/s) into cell C1.
We want cell C2 to hold the speed of the object between t = 0 and t = 1 s.
Speed is distance covered divided by the time interval. The distance
covered is the difference between the entries in cells B3 and B2 and the time
interval is the difference between the entries in cells A3 and A2.
Type =(B3-B2)/(A3-A2) into cell C2. This yields the average speed of the
object in the small time interval between the first and the second measurement.
(Formulas always start with an equal sign. A formula can be a simple
numeric expression such as =2*4, or it can include longer expressions
involving other cells and statistical and mathematical functions.)
Copy the formula into cells C3-C11. To copy a formula, position your
cursor in the cell that contains the formula, choose copy from the menu bar,
highlight the cells that will receive the formula, and choose paste from the
menu bar. (Quickly
copy/paste in Excel, Youtube video)
Construct a plot of speed versus time. Let us use the a method that
does not depend on the data occupying adjacent columns.
Put your cursor in an empty cell.
On the Excel menu bar, click Insert, Chart, XY (Scatter), and pick one of the
subtypes.
Right-click the chart and choose Select Data, Add.
Position your cursor in the X-Values text box and highlight entries 2 through 11
in the time column.
Now position your cursor in the Y-Values text box, erase any entries in this
box, and highlight entries 2 through 11 in the speed column.
Type "speed versus time" into the Name text box.
Give the chart a title, and label the axes. The label for the
x-axis should be "Time (s)", and the label for the y-axis should be "Speed
(m/s)".
Paste your labeled plot of speed versus time into your Word document.
There is a huge scatter in the values, because of experimental uncertainties
in the measurements of small distances and time intervals. But if we make
many measurements we expect the average of these uncertainties to decrease with
the number of measurements. (The fitting routine producing the trendline averages over all data
points and therefore produces a speed value with a much smaller uncertainty.)
Let us find the average value of all entries in column C.
Into Cell D1, type Average Speed (m/s).
Into cell D2 type the formula =average(C2:C11).
What is the value of the average speed? How does it compare to the
slope of the straight-line fit?
Understanding Motion - Distance and Time
Exercise 2
Sometimes the best way to measure the position of a moving object as a
function of time is to make a video recording and then analyze the video clip. In this
exercise you will analyze a clip showing a cart moving on an air track. You will determine the position of
the cart as a function of time by stepping through the video clip frame-by-frame
and by reading the time and the position coordinates of the cart off each
frame. You will construct a spreadsheet with columns for time and position, and
a plot of position of the cart versus time.
To play the video clip or to step
through it frame-by-frame click the "Begin" button. The "Video Analysis" web
page will open. You can toggle between the current page and the "Video
Analysis" page.
"Play" the video clip. When finished, "Step up" to frame 0. In some
browsers you have to click "Pause" first.
In the setup window, choose to track the x-coordinate of
an object.
From now on make sure that the zoom level of your browser stays constant (100%
is best) and while you are calibrating or taking data the video frame stays
fixed in the browser window.
Click "Calibrate". Then click "Calibrate X".
The video clip shows a track with a scale in centimeter.
Position the cursor over some marked position in the left part of the frame,
for example, the 50 cm mark, and click the left mouse
button. Then position the cursor over some marked position in the
right part of the frame, for example, the 70 cm mark, and click the left mouse button again. This will record the
x-coordinates of the chosen positions. Enter the distance between
those positions into the text box in units of meter. For the example
positions, you would enter 0.2 into the text box. Click "Done".
Click the button "Click when done calibrating". A spreadsheet will open up.
Pick the point on the cart whose position you will track, for example the tip of
the white arrow on the cart.
Click "Start taking data".
Position the cursor over your chosen point.
When you click the left mouse button, the time and the x-coordinate of your chosen point
will be entered into the spreadsheet.
You will automatically step to the next frame of the video clip.
Repeat for each frame in the video clip until the cart has traveled
approximately 20 cm. Then click "Stop Taking Data".
Highlight and copy your table. Open Microsoft Excel, and paste the table into an Excel
spreadsheet. Depending on your browser, you may have to use "Paste" (Edge)
or "Paste Special, Unicode Text" (Chrome).
Your spreadsheet will have two columns, time (s), and x (m).
Check if the cart moved with constant speed, covering equal
distances in equal time intervals. Produce a plot of position versus time
as in exercise 1. Add a trendline.
Paste your labeled plot of x(m) versus time
(s) (including the trendline) into your Word document and answer the questions
below.
What is the slope of the best fitting straight line? What is the uncertainty
(standard error) in this slope? Do you think that a straight line produces a
good fit to the data?
What is the average speed and the uncertainty in the average speed of the
cart?
Is the cart moving with approximately constant speed, or is its
speed increasing or decreasing? Justify your answer.
Vectors
Exercise 3
Use an on-line simulation from the University of Colorado PhET
group to explore vector addition.
Click
HERE to open the simulation.
Click the "Lab" image. Explore the interface
You can move the origin of the coordinate system.
If you click a vector, you can display its values in the boxes on top.
Checking "Sum" draws the vector sum of all vectors of a given color.
This simulation only allows integer values for the x- and
y-components of a selected vector. Consequently, you cannot always exactly set the values of magnitude and
direction. Choose the closest values.
The vectors can be easily translated, which is an important
learning goal for this simulation.
Use the simulation to solve the following problems:
(a) You walk 15.5 m in a direction 14.9^{o} North of East.
Use the simulation to represent your displacement vector.
How far did you move in the North direction?
How far did you move in the East direction?
How would you calculate the North and East
components of your displacement vector if you could not use the simulation?
Check that you get the same results.
(b) To get to a restaurant, you leave home and drive 9
miles South and then 17 miles West.
Use the simulation to represent your displacement vector.
If a bird flew from your house to the
restaurant in a straight line, what distance would it cover?
In what direction would it fly?
How would you calculate the magnitude and
direction of the bird's displacement vector if you could not use the
simulation? Check that you get the same results.
(c) Suppose you and a friend are test-driving a new car. You drive out of the car dealership and go 12 miles
East, and then 5 miles
South. Then, your friend drives 15 miles West, and 10 miles North.
Use the simulation to find the magnitude and
direction of the car's displacement vector.
Describe how you use the simulation to add
vectors.
(d) An airplane is flying North with a velocity of 200 m/s with respect
to the air. A strong wind is
blowing East at 30 m/s with respect to the ground.
What is the airplane's resultant velocity (magnitude and
direction) with respect to the ground? (In the simulation, scale your vectors appropriately.)
In one or two sentences, state the goal of this lab.
Make sure you completed the entire lab and answered all parts. Make
sure you show your work and inserted and properly labeled relevant tables
and plots.
Add a reflection at the end of your report in a short essay format.
Save your Word document (your name_lab1.docx), go to Canvas, Assignments, Lab
1, and submit your document.