dropbox DROPBOX! Prepare to safely archive your data and prepare to share files with lab partners. See Archive Data link.


Please CATCH the cart with your hand, cushion or something. Do NOT let the cart de-rail as this can damage the cart and be dangerous.

Okay, procedure change up:
We shall not use the AirTracks, instead we will use the Dynamics Tracks.
Here are the procedure changes to apply to your lab manual:
Procedure Step
(2) Use 2x4 instead of 1 cm block
(3) Place Sticky Note in the center of the track at 210 cm.
(4) SKIP
(5) Start your first "fall" 10 cm from Sticky Note

When finished with the experiment, please clean everything and arrange as seen in the picture below.
(The cart should be up-side-down to keep from rolling.
You can see the Sticky Note placed at 210cm in the center of the track.)

Please CATCH the cart with your hand, cushion or something. Do NOT let the cart de-rail as this can damage the cart and be dangerous.

Cool Stuff!
There is a Vernier Caliper Helper and Sample (in Color pdf) at the Printit WebSite.

Search for Vernier Caliper once there.

New datasheet for Spring 2013:

New Data Table 2013
We will have a hard copy for you in lab class week of Feb. 4th.

In a week or two you will do an exercise to learn computer spreadsheets.
You will be asked to use the data you take in this lab and put your data into the spreadsheet as you perform the tutorial. Keep this mind as you draw your graphs and find a fit line for this lab. Soon, you will do this on the computer and compare the computer's results to yours!


Please note: If the movie is too small,
please watch via youtube using the YOUTUBE button on bottom right of each video.
And, some videos have much higher quality. Find the HD version using the gear icon.
We hope to post new videos soon about week two and the postlab.

Data and Graphs - Empirical Part 1

Data and Graphs with Incline: Part 1: Procedure and Equipment

Data and Graphs with Incline: Part 2: Procedure and Uncertainties

Week 2: Data and Graphs - Empirical Part 2 - Building the Empirical Formula
PDF notes used to make this movie.
Week 2: Data and Graphs - Empirical Part 3 - Uncertainties and Error Propagation Is my g consistent with the accepted g within the confines of my measurement uncertainties? PDF notes used to make this movie.
The Vernier Caliper: A 16 minute tutorial The Vernier Caliper: A quick 2 minute reminder for those who previously learned about vernier calipers: Here is a video to help with analysis for error propagation that affects the uncertainty in your value for gravity (g)

There is a "Q&A" forum near the bottom of this and other web pages. You might want to look there for answers to your questions about the "Write-Up."

--> g = 2 Slope / (sin theta)
= 2 (0.0475??) / 0.01 = 9.5 m/s^2
(The ?? because I don't know the slope you got...)
So, g calculated = 9.5 m/s^2

(9.8 - 9.5) / 9.8 * 100%
= 3.1 % Discrepancy
Mon. 05, Feb 2001, 07:43

SUBJECT: #17 and #20

I do not understand #17 and #20. In #17, Delta t is t(max)-t(min)/2, then what is t(avg)?

In #20, what is Resolution and what is 'H'?

thank you
Tue. 06, Feb 2001, 16:58
#17) Delta t = [tmax - tmin] / 2
The idea is kind of like this:
How "far away" are the extreme measurements from the mean measurement. We will call this "uncertainty in our time measurement".
The relative uncertainty says, okay, then what percent is this time uncertainty as compared to the actual measurement. If my uncertainty in time was (+-)0.02 s and the actual times being measured were on the order of 340 seconds then the relative uncertainty is very small. If the times being measured were on the order of 0.1 seconds, then the relative uncertainty is much, much bigger.
So relative uncertainty takes the uncertainty and divides by the average.
Where average time in our experiment is (t1 + t2 + t3)/3.

#20) I am afraid Resolution and "H" should have been found by you in the lab... :( But things happen. I know. :)

Resolution of the Vernier Caliper was 0.005 cm. (Way overkill for this experiment, but that is what question #20 is trying to show you.)

"H" was the height of the block as measured by the vernier caliper. It should be somewhere around 1.00 cm.

Great questions.
Wed. 07, Feb 2001, 07:51

Where do I find the values for the predicted slope, predicted displacement, etc.
Wed. 18, Sep 2002, 15:58
The Lab Manual and Write-Up take you through a systematic thought process. Continue through the process and you should see Equation (5) deals with mpredicted and Equation (7) deals with Displacementpredicted.Douglas
Wed. 18, Sep 2002, 16:21

How do we get the greek symbols to show up in the postlab? It won't let me copy my equations or other symbols into the boxes from word. Any suggestions?
Hinterreiter, Matthew
Wed. 04, Jun 2003, 16:17
View this on the lab web site (The Schedule Page); it is formatted better than in your email.
I'm afraid you won't be able to transfer from MSWord if you use "Symbol" font or Equation Editor.
There is a button at the top of the quiz page. It's called "Answer Formats."
There you will find "Essay" instructions. Read them very carefully.
In summary, there is a table of symbols. The red text is what you need to copy/paste into your answer text box. The symbols you see should not be copied; the actual symbols are present to show you what the red text will look like when you push the "Preview" button. Here are two examples:
The code α becomes α
The code x<sup>-3</sup> becomes x-3.
It seems bad at first, but copy/paste is not so bad and once you get used to it, most symbols will come naturally to your brain, as long as you remember (for most) to start with & and end with a semicolon.Douglas
Thu. 05, Jun 2003, 07:21

On problem #2 on the postlab, what do you mean by "list each measurement name..."? How many you do want, and do we find these in the lab?Rachel
Mon. 02, Jun 2003, 17:38
It's a GOOD question! :)
Good Example of Answer:
Position Initial, 20.0-160.0 cm ± 0.002 [m] due to slight variation in where we held glider.
Position Final, 10.0 [cm] ± 0.005 [m] due to eye catching position for speedy glider.
time, 2.0 [s] - 34.0 [s] ± 0.3 [s] due to uncertainty in worst set of three measurements t1,t2,t3.
Block Height 0.995 [cm] ± 0.05 [mm] due to resolution of vernier.
Distance b/w Supports 1.00 [m] ± 0.005 [m] due to uncertainty from multiple measurements.

It is important to only list measurements. Notice I didn't list "displacement" as a measurement, because displacement is a calculation. Yes it has uncertainties, but it is a special combination of measured uncertainties; and in general we won't be discussing how these uncertainties interact with one another within calculations. If this topic interests you, I recommend "An Introduction to Error Analysis" by John Taylor.

It is also very important to represent your measurement name with a representative value. That value (or those values) must match the precision of your uncertainty. i.e. 3 [m] ± 0.002 [m] is not correct. 3.000 ± 0.002 [m] is more correct. Some people prefer to express uncertainty as a percentage. 0.002/3.000 = 0.1 %; so you might write 3.000 [m] ± 0.1%.

If you aren't sure which value to use for your measurement uncertainty; consider at least two things: readability, repeatability. Take the time example above. Here, repeatability had more uncertainty than the readability. Let me explain.
The stopwatch actually read to the hundreths place 0.01 [s], but my 3 count repetition of time measurement showed the worst uncertainty (tmax - tmin)/2 to be much greater than the readability.
Thus 0.3 [s] was chosen because it is much greater than 0.01 [s].

It is a good idea to use a leading zero to alert the reader that a decimal point is coming. ie. .3 is not as easy to read as 0.3

Finally a word about significant figures.
3.102 has four sig figs.
0.3102 has four sig figs.
0.03102 has four sig figs.
0.031020 has five sig figs.
310200 has four sig figs.
310200.0 has seven sig figs.

Oh, and for computers
32.5 x10-3 should be written as 3.25E-02
Mon. 02, Jun 2003, 18:09

On question #3 on the postlab... What do you mean the state the equation of your data for displacement vs time^2? Is that the same as Predicted slope...?
1/2*(g)*(sintheta)..Do we use this equation??
Tue. 03, Jun 2003, 16:05
Dear A.K.
(View on the web page rather than your email for proper formatting.)
Let's say I do an experiment to find out how much juice can be found from a lemon. I plot the data as Amount of Juice vs. Number of Lemons. I see a linear trend and I find the mathematical equation to be
But this equation means nothing to anybody but me; and the fact is, if I write this equation in my notebook, I will likely forget what it models. So I need to rewrite the equation such that it matches the physical world in which it was derived.
y=Amount of Juice[ml]. x=Number of Lemons. These are my variables and they must appear in my new equation replacing the x and y. Next, I know the 1.2 (vertical intercept) must have units of [ml], because the equation must be dimensionally correct. For the same reason, the 25.4 must have units of (Hmmm, it's the slope; which is rise over run.) [ml/lemon]. So here is my revised equation:
Amount of Lemon Juice = 25.4 [ml/lemon] * Number of Lemons - 1.2 [ml]

That is the equation of my data. It seems to me that this newly formatted equation is far more descriptive than the y=_x+_ format. Turns out that I had not cleaned out my measuring cup prior to the experiment. It had something caked onto the bottom of the cup so as to effectively make each measurement look as if it where 1.2[ml] more than it should have been without this systematic offset.
Wed. 04, Jun 2003, 06:25

I submitted my prelab questions just one time, but the screen said that
Your submittal number 3 has a score of 90/100.
I thought I have 2 more left.
Tue. 02, Sep 2003, 13:06
Please use the Quiz Help form. I can't track down the problem with the little information you gave to me...
There find the Quiz Help Form. Or you can find it near any pre/post lab link.
Tue. 02, Sep 2003, 14:54

I'm a bit unclear re: what gets handed in and when for the Data/Graphs lab, based on Derrick saying in lab on 8/29 that we'd spend an hour on this together on 9/5. Does this mean we'll spend the 1st hour on 9/5 to finish our group write-ups or are they due at 10a.m. on 9/5?
2nd question: Is the on-line post lab for Data/Graphs due before lab on 9/5 or 9/12? (are post labs due 1 week after we do the in-lab work, or 2 weeks later?). If the lab parnters are not available to meet prior to 9/5 (and if this applies to future labs), is it ok to hand our own write-ups individually?
3rd question: Derrick mentioned we'd all hand in our own "page" for each write up. Please clarify what this is.
Thanks and sorry for my initial confusion! (the answers aren't clear to me in syllabus). Hope you check your email early!:)
Fri. 05, Sep 2003, 01:01
Ms. J.,
1) You have one week to finish the Write-Up's. All Write-Up's will be due the following week after they are last scheduled. Data and Graphs is scheduled for two weeks. It is due the week following the second lab session for D&Graphs.

2) PostLab is due before class the same day the Write-Up is due. (In this case 9/12/2003.) But, you can always check that by looking at the "Deadline" seen on the LogIn page for the PostLab.

2.5) That is up to your instructor whether or not you turn in individual Write-Ups when a partner does not contribute. It makes sense to me that the person who didn't show should not get credit for the group's work.

3) You each hand in a "Cover Sheet" with your name on it. If there were three in your group, you would hand in three cover sheets attached to one set of data table and plot(s).

I hope this is early enough.
Fri. 05, Sep 2003, 05:28

Hi Douglas,
For question #14 on the write-up, we did not notice the resolution for the stopwatch. Can you help?
For question #25 (if we answered yes to #24) can we leave this one blank?
We are asked to write the line equation on the graph next to the predicted displacement line in question #11.c., should we also write the line equation for our line?
Then for question #28 would we use the line equation for our line and not the predicted displacement line?
Thanks for your time.
Fri. 05, Sep 2003, 16:48
#14: It is 0.01 seconds. But don't forget that there is a discussion in the analysis that shows the time uncertainty is greater than the resolution.
#25: yes

Yes. Always include the equation for your data. I am shocked that I can't find that specific instruction in the Data and Graphs Analysis. Maybe I just missed it. Humphhh.

#28: Yes, as the question states, you the equation for your data, not the predicted.

No problem.
Fri. 05, Sep 2003, 17:58

Hi Douglas,
Could you let me know what the greek symbol in question #2 of the post-lab means? I think it is average but I am not sure.
Sun. 07, Sep 2003, 20:42
I think you are referring to the σ.
It means, in this context, uncertainty or standard deviation.
Mon. 08, Sep 2003, 05:29

Hi Douglas,
For question #2 on the postlab are we to type out all 16 trials? Are we to include all column headings for the data table as the time squared is not "measured" nor is the predicted displacement?
Thanks again.
Sun. 07, Sep 2003, 21:05
Please read the Q&A at the Data and Graphs web page (link at the bottom of this email.) This question is asked; and the answer is spelled out with great detail.Douglas
Mon. 08, Sep 2003, 05:31

On question #3 on the postlab we need to put the units in brackets for our equations. Do we need to put in the units for sin(theta) since theta is in degrees?
Thank you!
Mobeck, Wendy
Wed. 10, Sep 2003, 17:18
1) θ is in °'s. Sin θ is unitless.
2) The questiion asks for your equations; both your data's experimental and your data's theoretical equations. Neither one should have Sin θ; instead, both have a numerical value for the slope. One slope value is from the plot. The other "slope" value is from your calculation 1/2gsinθ where θ=HL-1.
Thu. 11, Sep 2003, 05:17

Mr. Douglas,
On the page that has the data table, below that is a column that has column titles, explanation/formula, Calculation:trial one, Value: Trial one. I'm a little confused on what to write down for the "calculation" part and "Value" part. I also don't understand what the predicted displacement is. Thanks for ur time
Oladiran, Oluwadamilola`
Fri. 20, Feb 2004, 11:02
Average Time?
Average of t1,t2, and t3 for the glider to fall the same displacement.
Calculation: (3.34+3.29+3.31)/3
Value: 3.31[s]

Predicted displacement is found by working through the Write-Up. You are eventually going to "build" or derive the equation. Keep working through the Write-Up.
Fri. 20, Feb 2004, 12:05

Mr Douglas,
The answers i'm getting don't make any sense to me, for #6, the predicted value was 30%of my measured value,i.e, my measured value is way higher than the predicted value, but it says right underneath prlm 6 that "Hopefully, u found that the predicted slope is much higher than the measured slope" Is it ok that my answer is directly opposite to this. Thanks 4 ur time.
Oladiran, Oluwadamilola
Sat. 21, Feb 2004, 08:56
That is a problem.
Read questions 1-6 more carefully. We are expecting you to assume that a=g.
Your slope should be around 0.049 m/s/s.
Your predicted slope should be around 4.9 m/s/s.
But of course, this isn't correct based upon the poor assumption that a=g.
Please clarify your question with actual calculations and values, if this doesn't help you.
Sat. 21, Feb 2004, 09:45

On question #1 of the postlab, it asks for the theoretical equations for diplacement and slope. Which equations would be the theoretical ones? Diplacement= Final position-Start position? Displacement= (1/2gsin(theta))t^2 ? Slope=(1/2gsin(theta))?
Mon. 23, Feb 2004, 12:36
Displacement = 1/2 g sinθ t2 is our theory. Now, I'll let you figure out the slope...Douglas
Mon. 23, Feb 2004, 12:47

Hi Douglas,
Question #9 I am looking something like m/s^2 or m/times^2, but couldn't find it. Is g = a? and H=Height and L=Lenght?
Ghorbani, Reza
Mon. 30, Aug 2004, 04:42
g ≠ a.
H = Height
L = Length.

Displacement = ½ a t2
And for an inlcine we have
     a = g sin θ
∴ Displacement = ½ g sin θ t2
And also for an inlcine we have
     sin θ = HL-1
Which leave us with
    Displacement = ½ g HL-1 t2
Now, consider what is being plotted from this last equation.
Mon. 30, Aug 2004, 05:52

Hey Douglas, the angle we are getting from the calculations from equation 3 or 4 is .58 dgree's. this seems way to small. What are we doing wrong?
.05m/s^2 = 1/2g*sin(theta)
.05 is our slope. We also plotted it in excel and it came out to the same. I'm having a hard time with how everything relates, too
Phillips, Kent
Wed. 01, Sep 2004, 18:12
I don't know for which questions you asked this; but keep in mind that our theory doesn't call for us to know θ; but sin θ.
But, to answer your question, it makes sense to me, if the angle turns out to be small.
Consider the fact that you have a 1 meter span between supports. Then you only raise the incline by 0.01[m]. This is not very high.
To the right are two plots. The big plot is θ vs. block height for blocks that are small (0-10cm). The smaller plot is θ vs. block height from 0-1m(→90°)
Just like your calculation, at 0.01[m], there is an agle of about 0.5°.

I hope this helps,
Thu. 02, Sep 2004, 04:54

On the Write up Eq(6). Just what is the measured slope?Anonymous
Sat. 04, Sep 2004, 11:36
You plotted D vs. t2.
What is the slope you calcuated from that plot?
Sun. 05, Sep 2004, 15:44

hey Douglas,
For writing equations on the pre/post labs is it exceptable to write a unit of measurement like this [m/s2] or do we have to write it like this [ms-2] or are they both correct?
Wed. 15, Sep 2004, 08:12
Either is fine, but inline [m s-2] is easier to read and reduces a typical math reader error where students some times think
s/(m kg) = s/m kg.
But this is not true. In fact
s/m kg ≠ s/(m kg).
s m-1 kg-1 makes it less prone to reader error.
Wed. 15, Sep 2004, 09:24

Hey Douglas,
I am really confused on #9 of the prelab. Is there supposed to be a graph or extra information included? I am not sure what H, L, and g equal. I would guess that the slope of distance versus time^2 would be rise/run, hight/length, or have units of [m/s^2).
Thanks for your help
Fri. 02, Jun 2006, 14:18
All information is complete. Nothing else is needed.
Q: The slope of Distance versus Time2 is...?
Well, we know the following:
Displacement = 1/2 g sin(θ) Time2

Of course, the slope is the part in red:
1/2 g sin(θ)

But what is sin(θ) for the fixed incline?

L / |
/ | Height
/ |
/θ |

Where L is the length (Or distance between airtrack supports.)

So, in this context, what is sin(θ)?

This is a pretty leading hint. Let me know, if you need some further help.
Sat. 03, Jun 2006, 06:17

If the answer is .3497 and I want an answer with three significant digits what do I round to. 0.350?
Tue. 06, Jun 2006, 17:19
Yes, 0.3497 to three sig. figs. is 0.350
Thu. 08, Jun 2006, 11:43

On question 5 on the Pre-lab, to find the slope of the trend of the data given,
I would use rise/run but how would I estimate the value for the "best fit line"?
Tue. 05, Sep 2006, 19:49
First ask this question: Is D vs. T really linear? Does the data appear to be linear? (or quadratic?) If quadratic, then what is the slope?Douglas
Wed. 06, Sep 2006, 08:26

Question #5 of the Pre-Lab asks: What is the slope for the trend of this data. The plot looks linear (y= 0.3497x-0.5136) with the slop 0.350. I'm getting the wrong answer.
I don't understand what am I doing wrong. Thanks for your help.
Sat. 03, Feb 2007, 01:14
Linear? That is the question. Is d vs. t supposed to be linear? Does the data look linear?Douglas
Tue. 06, Feb 2007, 08:41

is there the prelab for the data and graphs the same for both weeks since its due on the same day?Anonymous
Tue. 13, Feb 2007, 11:37
There is only one prelab for each experiment, no matter if the experiment is two weeks or one week.Douglas
Fri. 16, Feb 2007, 10:57

In one of the responses above, in reference to question 2 on the post lab, you say that you didn't list displacement as a measurement because it is a calculation. On the actual question, it says "Consider Displacement a measurement instead of startP and finalP." I'm confused, what exactly are you asking for?Anonymous
Sun. 18, Feb 2007, 18:15
You can use either
1) Start P and Final P as two measurements, list their representative values, their uncertainties (different for each one!) and the rationale for the uncertainty.


2) Displacement, its representative range, its uncertainty and the rationale for the uncertainty (The uncertainty in the sum of two measured quantities is the sum of the uncertainties.)
Mon. 19, Feb 2007, 09:42

Hi Douglas. I am confused about question #4 on the post lab. It asks what the value for the height of the riser block used given the displacement equation. I didnt think that we used the block in the equation so I am confused on how to work backwards to figure it out. Could you give me some direction to head in? ThanksAnonymous
Wed. 12, Sep 2007, 21:33
D = 1/2 g sinθ t2 + Do

But what is sinθ?
sinθ = H/L; where H is the height of the riser block; L is the distance between supports. It was H and L that created the incline.

D = 1/2 g (H/L) t2 + Do

I hope that helps a little or a lot. :)oug
Thu. 13, Sep 2007, 09:22

On question #2 on the post lab, above you said to list the initial position and final position separately because the displacement isn't a measurement. On the actual post lab, however, it says to consider displacement a measurment instead of using start and final positions. Which would you prefer?Anonymous
Mon. 15, Sep 2008, 19:24
Either one is fine.Douglas
Tue. 16, Sep 2008, 07:38

hi Douglas
Should a linear trend be added to data that is not linear ?
Fri. 19, Jun 2009, 15:04
No, a linear trend should not be added to data that is not linear.Douglas
Fri. 19, Jun 2009, 15:54

After question one, there is a word count limit expressed as "paragraph symbol" < 100 words. Does this mean that our whole answer must be less than 100 words, or that the answer should be broken into appropriate paragraphs, each of which should be less than 100 words?
If it is the former, than I think I am having trouble understanding how to write a summary of the entire experiment in only 100 words.
Fri. 18, Jun 2010, 18:13
That is a good question. Entire summary should be one paragraph of 100 words or less. You can actually do this one in less than 75 words.
Some guidelines:
Purpose and Procedure should each be one sentence long.
Focus on being concise and precise with your written word.
Try removing article "the." Remember, this is a summary not a set of reproducible instructions.
If you need more help, please let me know.
Sat. 19, Jun 2010, 03:41

Hey Douglas! I have a question about the data and graphs. Would you like us to do line of best fit with graph D vs T or with D vs T^2? And the question we are trying to answer is whether Distance is proportional to time correct? Anonymous
Tue. 14, Sep 2010, 12:45
D vs T^2 should have a line of Best Fit. D vs T should have an annotation describing whether or not D vs T is proportional.Douglas
Tue. 14, Sep 2010, 15:20

For the first question on the Data & Graphs post-lab, I have finished the summary of the lab but I am a little unclear about which equation it is asking for. We did an equation on the distance vs. time squared graph for the measured displacement and slope as well as the predicted displacement and slope, is it asking for the predicted displacement and slope? If so I am not sure how to format the equation on here. Thank you for your help!
Fri. 11, Feb 2011, 10:46
Your data plot should contain two equation in form of y=mx+b. Where y and x are replaced by Displacement and Time^2. The m and b are replaced with the decimal values for slope[m/s^2] and intercept[m]. The reason I address this first is to show that those equation are the final analysis.
Question one is asking for the overall theory. When we summarize the experiment we are speaking about the theory equation. Later in the quiz, you are asked to report the equations for the data plot. But for question one, simply use the theoretical formula (derived in your lab manual and writeup) called "predictive displacement." In this theoretical formula instead of the decimal numbers for slope and intercept, use the physical variable names.
Fri. 11, Feb 2011, 19:48

For Question #6 on the postlab, the question reads "Should a linear trend be added to data that is not linear?" None of the answers that are there to choose from are correct...(the correct answer is no, a linear trend should not be added to data that is not linear." Or maybe I am confused..Aguirre-Wong, Francesca
Sun. 18, Sep 2011, 01:22
The answer you provided above is acceptable, but as you said, that answer was not given. If data is not linear and you don't add a linear trend, then what other choices do you have:
a) walk away
b) find another trend that might work
I vote for (b) since science requires (b) to continue its discovery.
Tue. 20, Sep 2011, 03:24

For question #2 on the post lab, is the Theoretical Equation for "your experiment" the equation for the other line on our graphs? The "predicted displacement"?
Sat. 17, Sep 2011, 09:42
Yes. :)Douglas
Tue. 20, Sep 2011, 03:27

Hi Dr. Howie,
I was wondering if you could please help me with #4 on the post lab. I know I can use 1/2*g*H/L*t^2= D but I am confused on how to find height when time is not given. I know that 1/2*g*sin theta is m in the equation y=mx+b but am not sure how to find time without displacement and vice versa. Please help! Thank you very much.
Mon. 18, Jun 2012, 19:21
sin theta is really H/L

So the slope of D vs t^2 is equal to 1/2 g H/L.
If you know the slope, L, and assume g to be 9.8 m/s/s, then solving for H is possible without knowing D nor t.
I hope this helps.
Mon. 18, Jun 2012, 21:08

On #2 on the postlab it asks for the measurements and you state previously not to use displacement rather to use start and final position, but on the lab it asks for displacement. So if we are to use displacement should I use the average measurement for displacement or take our last trial (final -initial). ThanksAnonymous
Tue. 19, Jun 2012, 10:49
Sorry about that confusion.
Use either average or the range.
Wed. 20, Jun 2012, 05:37

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