There are basically 3 parts to this lab.

## Part I: Measurement and Uncertainty

Here I wrote an introduction to uncertainty.

Measurement and Uncertainty Smackdown

If you want a super-detailed guide to measurement and uncertainty, check out this page. Really, you can think of that as a book.

Ok, so how do you calculate uncertainty? If you want to do it with vpython, here is a screen cast showing you how.

If you would prefer to use a spreadsheet to do this, here is an example of that (by Dr. Rundquist)

**What to do**

Now that you might have an understanding of uncertainty, let us use it on somethings.

- Measure the dimensions and mass of two different blocks of aluminum. Record the uncertainty in your measurements and determine the density of the aluminum (with uncertainty). For single measurements, the uncertainty can be no smaller than half of the smallest division of your instrument. You might choose to make it bigger than that.
- Find the acceleration of a falling ball. Do this from one height and drop the ball at least 10 times. Here is a lab that describes how this is done. You will need to find the uncertainty in the time by determining the standard deviation and then use the monte carlo method to determine the uncertainty in the acceleration.

## Part I-a: Finding the launch speed

Here you will use a ball launcher. Launch the ball straight up. First, record the maximum height the ball goes. Repeat this at least 6 times so that you can get an average height and an uncertainty for the average height. Use this to calculate the launch velocity of the ball with uncertainty.

Now shoot the ball up again. This time, measure the time for the ball to go up and down. Again repeat at least 6 times to get an average and an uncertainty. Find the launch velocity again with uncertainty.

Which method gives better results? Why? How do you know?

Here is a short video example of how to find the velocity of the ball from the two methods.

## Part II: Graphing and Linear Regression

What is linear regression? I am glad you asked. Check out these links:

Essentially linear regression is the process of finding a linear function that fits data. How can you practice this? First, you should understand what it is (the “by hand” way). Ok, to collect some data go back to the drop timer. Drop the ball from at least 5 different heights and record the time.

If you would like more practice with graphing and linear regression, here are two things you could measure and plot:

- Find at least 4 different circular objects with different diameters. Plot circumference vs. diameter. Find a linear function that fits this data.
- Find as many aluminum objects as you can (of different sizes). Plot the mass vs. the volume for these objects. Find a linear function that fits this data.

What could you plot so that your data should be linear? Hint: it isn’t position and time. If you don’t know how to make a graph on actual graph paper, I would do that.