Physics 112 Lab: Volume of Table Top

Many of you will go off into careers where you will often be required to measure something and report back the result to your boss and/or other co-workers. This lab will introduce you to doing something very similar. Granted, the volume of a table top has very little to do with Physics 112, but at least the goal is easy enough so that you can concentrate mostly taking accurate and precise data, convincing your “boss” (me) that you did your measurements correctly, calculating uncertainty, and presenting your results in an organized fashion.

So pretend I’m your boss. I want to know the volume of your table top (the black part). Here is what you will do:

  1. You will work with your tablemates (groups of no more than 4). Determine the most precise and accurate way of measuring the dimensions of the table top.
  2. Every dimension must be measured three times by each person in your group (each person should then have made a total of 9 measurements, 3 for each dimension).
  3. Each one of you will write a report explaining your result and how you got it. I would prefer that this report were handwritten, and I encourage you to write it up as you do the experiment to save time. It will be due no earlier than the start of the next class period. The format of these reports will be as follows:

Name/Partners/Date/Title (0.4 points) – At the top, write your name, the name(s) of your partner(s), the date you did the experiment, and give the report a title that has something to do with the experiment.

Introduction(0.2 points)– This section states the goal of the experiment. Most of the time, this need only be one sentence long. The goal here, of course, is to measure the volume of the tabletop.

Theory(0.5 points)– Here, you derive an equation that relates the quantity that you are ultimately trying to determine with quantities you wish to measure. For example, if you wish to measure the acceleration of gravity, you would derive the equation g = ½ a t2 (or something like that). For this lab, there is no need to derive the equation volume = l w h, but you must state this formula and define what each term represents (w = width or second longest dimension, etc.). (If you come up with a better way to measure the volume using a different formula, you may need to derive that one.)

Experiment(2.0 points) – In this section you describe how your data was taken. This must ALWAYS include a diagram. Indicate clearlywhich table you are measuring. Every person in your group must measure the length, width, and height 3 times. This means that if there are 4 people in your group, your group will have 12 measurements of the length, 12 of the width, and 12 of the height. Include ALL of these measurements in a table in your report. Pretend this handout does not exist. You must write enough about how you measured things here in order to convince me (your “boss”) that you did everything correctly. This usually requires writing down little details about how you dealt with the rounded edges, the holes, the sometimes confusing-to-use measuring devices, etc. Inaccurate or imprecise data will cost you points.

  1. Analysis (1.0 points) – Here is where you crunch your numbers. For each length-width-height trio of data, calculate the volume. You should wind up with several values for the volume (one for each trio). The volume you report to your boss as thevolume of the table is the average of these several values. The uncertainty in the volume you report is given by the standard deviation in these values for the area. Some of you have fancy calculators that will do this for you. You may also use Excel on one of our laptops available to you. Otherwise, the formula for standard deviation is

where N = the number of measurements, = the average value of the measurement, and xi = the value of the ith measurement.

Discussion (0.5 points) – In this section, talk about your result. Is it reasonable? Does it agree with other measurements? Why or why not? In this lab, we have no manual for these tables that specifies the volume of the tabletops, but you may compare your result with other groups in the class.

  1. Conclusion (0.4 points) – Clearly state your end result (with uncertainty). If it agrees with other measurements or theory, say so. If it does not agree with other measurements or theory, state what was wrong with the other measurements or theory. IF YOU MADE A MISTAKE WITH YOUR MEASUREMENTS, GO BACK AND REPEAT THEM. Do not turn in a lab report where you knowingly made a mistake in your measurements! Also, nothing new should be said in the conclusion. It should just sum up your main result and the conclusion of your discussion section. The conclusion should be at the very end of your report, and be no longer than a couple of sentences. If your boss has no time to read through the report when she/he gets it but just wants to know the result, they should easily find it at the end. If he/she has to do a lengthy search through the report to find it, she/he will get cranky.

The lab report should be organized, but if there are things crossed out or erased, that is OK. Do NOT erase anything! Spelling and grammar do not matter unless I cannot tell what you are trying to communicate.

Richard A. Thomas – UST Physics