You should have a permanent notebook dedicated to the lab portion of this course.  You should keep a record of the lab work you do, including free-hand sketches of apparatus and reasonably accurate but not meticulous hand-sketched graphs (you will likely use the computer to make meticulous graphs, but in the hand-sketching process you think about important aspects of the graph that don't necessarily become apparent if you use a machine to do the sketching).

Some of your data will be taken by a computer or with the aid of a computer, and you will not be expected to write down the hundreds or thousands of data points involved in that process, but you should keep a small sample indicative of the results you obtain, and preliminary observations on trends and other aspects of your data which might be relevant to what you are observing.

You should also keep a record of where your data files are located, and you should maintain a secure backup of all your data files.  If you lose your data, you might end up having to repeat your experiment.

You might at any point in the course be asked to reproduce information from your lab work.  You lab notebook will be the key to being able to do so.

Indicate below, in your own words, the importance of maintaining a good lab notebook.

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It will be very important in your course that you report data in a way that can be both easily understood and electronically processed by your instructor and by your fellow students.

Report 4 two-digit numbers (e.g., 78 is a two-digit number; you can make up any four such numbers you like), one to each line, with a short note starting at the 5th line indicating how you chose your numbers (the note and the explanation should be brief and uncomplicated; it's not intended to be difficult.  Anything you put down will be fine.) 

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Next report four 2-digit numbers in one line, separated by commas, and a short note starting at the 2d line briefly explaining how this format is different than the one in the preceding box.

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Suppose we have a meter stick oriented to that readings run in cm from left to right.  Suppose we also have some object sitting at the 15 cm position.  Another object at the 25 cm position will be 10 cm to the right of the first object, so the position of the second object relative to the first is +10 cm (remember that increasing numbers go to the right, so + indicates an object to the right of the reference position). 

A third object sitting at the 5 cm mark will have a position relative to the first of -10 cm (as we move to the left readings on the meter stick decrease, so the - sign indicates a position to the left of the reference object).

An object with a position relative to the first object of -5 cm will be 5 cm to the left of the reference object, which will place it at the 10 cm mark of the ruler. 

Call the position of the first object the reference position.  Then an object at +25 cm relative to the reference position will be 25 cm to the right of the 15 cm mar, putting it at the 40 cm mark.

Jot down your answers to the following in your lab notebook.  It is suggested that you accompany your answers with a sketch.  If you don't yet have a dedicated lab notebook

• What would the position relative to the reference object of an object at the 20 cm mark? 

• Where on the ruler would be an object at position -7 cm relative to the reference object?

• If an object is at the 2 cm mark on the ruler, what is its position relative to the reference position?

• What is the position on the ruler of an object located at +35 cm with respect to the reference position?

Place your answers in the first line of the box below, with commas between your answers.  Place only numbers and commas in this line. 

On the second line specify the meaning of the numbers on the first line, and the units represented by those numbers (the units here are centimeters).

Then give a brief explanation of your understanding of the concept of relative position.

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Suppose the y positions 5, 12, 21, 37, in cm, occur at respective clock times 2,4,6,8  seconds.  A comma-delimited table of y vs. t would then consist of 4 lines with the t value first and the y value second. 

Important convention:  When we list one quantity vs. the second quantity, it's the second quantity, the one after the 'vs.', that goes in the first column.  Remember this.

So the table corresponding to the above information would be

2, 5

4, 12

6, 21

8, 37

Suppose now that temperatures of 80, 60, 50 and 45 deg occur at clock times 3, 10, 24 and 41 minutes. 

Report this temperature vs. clock time data in the box below, in comma-delimited format as explained above.  Use numbers only--no units.  The units will be explained in your additional lines.

Then add a sentence or two starting in the fifth line, which specifies what these number mean: which number is first, which is second, and why; what quantity is belng listed vs. what; and in what units each quantity is being reported.

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Suppose that in a flow experiment depths of 30, 20, 14 and 9 cm occur at depths of 2, 12, 24 and 36 seconds.  List the clock times only in the first line, separated by commas.  List the depths only in the the second line, also in comma-delimited format.  Starting in the third line, briefly explain what you did.

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Now go into Notepad or another text editor, list the ordered pairs indicating the data just given above, but in tab-delimited format. 

You have to go into another program to enter tabs because if you try to enter a tab on the form, it will 'jump' you to the next box.

Enter your data so that on the first line you have your first clock time, then a single tab (hit the 'tab' key on your keyboard), followed by the first depth.

Then add a line for each subsequent data point, so that you have reported your information on four lines delimited by tabs. 

On the fifth line, specify the units of the data you have given.  Starting in the next line give a very brief explanation of what you just did. 

Then highlight, copy and paste this data into the form.

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Suppose that the third column of the Timer program shows the numbers 3.7, 4.3, 5.2, 3.9, 4.3.  Recall that the third line consists of the time intervals between clicks.

The clock time of the first click would be in the middle column.  If necessary, briefly review the TIMER program, or the data you have obtained from that program.

We will define the 'first click' as the one that occurred at the beginning of the 3.7-second interval.

What would be the clock time relative to the first click of each of the four given numbers from the third line?

List these clock times in the first line in comma-delimited format.  In the second line indicate the units of the numbers you have placed in the first line, and explain how you obtained the clock times.

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Suppose that in a room at temperature 23 C, an experiment reports 50 C, 40 C, 35 C and 31 C.  Report these temperatures in Celsius degrees in the first line, using comma-delimited format.  In the second line report in the same format the temperatures relative to room temperature.  In the third line specify what the units are, that the second-line temperatures are relative to room temperature, and also report the room temperature.

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Finally, suppose that the temperatures given above occur at clock times 10, 20, 30 and 40 minutes.  Report temperature vs. clock time in comma-delimited format, one temperature and one clock time to a line. 

Then in a fifth line, report in comma-delimited format the average rate of temperature change with respect to clock time, in degrees Celsius per minute, on each of the three intervals. 

Starting at the sixth line state what is reported in your lines, and how you obtained your average rates.

Since the question here concerns temperature T vs. clock time t, the quantity A would in this case be the temperature T and the quantity B would be the clock time t. So an average rate of change of temperature with respect to clock time would be

• ave rate = (change in T) / (change in t).

This would be identified with the slope between two points of the T vs. t graph.

For example if the temperature T changes from 50 degrees to 20 degrees while clock time t changes from 40 minutes to 50 minutes, the change in T is -30 degrees, the change in t is 10 minutes, and the average rate of change of T with respect to t is

• ave rate of change of T with respect to t = (change in T) / (change in t) = -30 deg / (10 minutes) = -3 deg / minute.
   

This is interpreted as an average rate of -3 degrees per minute, meaning that on the average we expect a decrease of 3 degrees every minute.

This would be associated with two points on the graph of T vs. t, the two points being (40 min, 50 deg) and (50 min, 20 deg). The 'rise' from the first point to the second would be 20 deg - 50 deg = -30 deg, and the 'run' would be 50 min - 40 min = 10 min, so the slope of the line segment between these points would be

• slope = rise / run = -30 deg / 10 min = -3 deg / min.

We see that the slope represents an average rate of change of temperature with respect to clock time. We would get other average rates between other pairs of points.
 

The current question asked you for three average rates (one for each time interval). If you obtained correct values for your average rates, then just store this explanation away for further reference, and no response is required. However if you did not give the three correct average rates, you should submit a response as requested below, including an explanation of the process you use.

Common errors include the following:

• Failing to include units at every step of the calculation.

• Incorrect signs (average rates should be negative), which results from lack of attention to detail in application of the definition of average rate.

• Dividing temperatures by clock times; average rates are based on changes in the two quantities, not on the quantities themselves.  If you got something like 5, 2, 1.16, .78 then you divided temperatures by clock times. 

Temperature divided by clock time is a meaningless calculation. 

• For example the temperature in this room is 20 Celsius and it has been 135 minutes since I sat down at the computer. 

20 Celsius / (135 minutes) = 1.47 degrees Celsius / minute,

but that caculation is meaningless and isn't an average rate of change of any quantity with respect to any other quantity. 

Had the temperature changed from, say, 17 Celsius to 20 Celsius in that time, then there would be a temperature change if +3 Celsius in 135 minutes so the average rate of change of temperature with respect to clock time would have been 3 Celsius / (135 minutes) = .03 deg Celsius / minute, which does have meaning.

Suggested title: Rates from Formatting Experiment