Note: This is a series of posts with my favorite physics labs. These labs are intended for the algebra-based college level course (but clearly could be adapted for other courses). Feel free to use this in a way that makes you happy.

Objective

This is the first lab of the course, so the goal is two part:

• Practice with measurements and uncertainty.
• Practice making graphs (linear graphs)

The graph thing might seem silly, but students need work on this and it’s used in pretty much every lab for the semester.

Measurements and Uncertainty

Here is my version of this whole thing. VERY SHORT.

• We like to measure stuff in physics – however, we can never measure stuff perfectly. One way to account for error in measurements is to include an uncertainty. Suppose I measure a length, it could be reported as L = 0.13 +/- 0.01 meters. This says the length is most likely between 0.12 and 0.14 meters.
• There are three ways to get this uncertainty.
  • Approximation. If you can only record a value once (or repeating won’t give you anything new) then the best option is to just be a human and assign a reasonable value. The uncertainty can’t be smaller than half the smallest division on your measuring device.
  • Standard deviation. If you can repeat the measurements, you can calculate the average and the standard deviation. The standard deviation would be the uncertainty. Note: make sure you get at least 5 values or you will just be kidding yourself.
  • Calculation. If you want to get the area of a table, you measure the length and width and then calculate the area. This means you will have to calculate the uncertainty also. You can do this with the “crank three times” method. Use your uncertainties to find the smallest and largest possible values. The uncertainty is then halfway between these values.

Here is a short lecture on measurements.

Now for some practice.

• Take an aluminum block (or really any block). Find the volume and density with uncertainty.
• Reaction time. Take a ruler and hold in vertically near another human’s fingers. Drop it and measure how far it falls before it is caught. Repeat 10 times, get the average and standard deviation.

Graphing

In physics, we like to build models. If the model is expressed as an equation, what better way to show the model is legit than to make a linear graph. OK, let’s just get to it. Here is a quick tutorial on graphing.

Now for some practice. Find a bunch of circular objects of different size (at least 4 different sizes). Measure both the circumference and diameter. Now create a plot of circumference (vertical axis) vs. diameter (horizontal axis) and find the slope. Recall that we have the following relationship:

$C = \pi D$

So, if we plot C vs. D the slope should be pi.