Lab.

Objectives

The learning objective of this lab is for you to practice linearizing a set of data and extracting useful information from it. This type of analysis is very common throughout all of science and engineering. It will also serve you well in future Physics lab reports.

While that summarizes the learning objecting, the experimental goal of this lab is for you to measure the constant ? from data that I provide to you. You'll also get accustomed to some of the required components of formal physics lab reports. Briefly, the typical sections in a formal lab report that I require are:

• Introduction: Explains what the goal of the lab is and what you expect
• Theory: Explains what physics predicts in terms of relationships, including slopes of graph.
• Procedure: Explains how data was gathered and how uncertainty of the raw data was determined.
• Data: Provides the reader all raw data and uncertainty.
• Analysis: Uses the data and as described previously in theory to calculates the final answer. This is often done using the slope of some new graph.
• Conclusion: Reminds the reader what the goal was and states clearly the outcome and gives any other useful discussion.

You won't be doing all of the sections above, only Theory, Data, Analysis, & Conclusion since those are typically the areas that students need the most practice on.

You are welcome to work together on this lab, but every person must turn in their own assignment, and what you turn in must represent your own understanding. Don't hesitate to ask me or others questions if you need help.

Data Imagine that a group of students have circles of different sizes. They measure the diameter and area of each circle along with the uncertainty of each of their measurements. Their data is provided below. There are also some mistakes in the data: we'll deal with the mistakes soon. Circle Diameter (ch -s B W What to do and turn in Submit to this assignment a single PDF le (it can be multiple pages) that addresses all of the prompts below. {Most people use Word to type of their lab, then Export or Save as a PDF.) 1. There are three mistakes in the data table that has to do with roundingisig gsfplace values. Identify those mistakes and rewrite the affected data points using the conventions discussed in lecture. 2. Often in labs you will need to report your collected data in some easy-to-read way; tables are an essential part of that. but visual graphs are easier to understand. Use the (corrected) data values to make a graph of area vs diameter. (Whenever you see variablei vs variableZ. that means variablel is on the vertical axis and variable2 is on the horizontal axis.) Your graph of the six data points should have: (1) good axes labels with units: [2) a descriptive title at the top; and (3) horizontal & vertical uncertainty bars l[error bars) for every data point. Make sure your graph is easily readable in your document; the numbers on the axes and any t info should be easily readable. (FYI. a graph like this would typically go in the Data portion of a formal lab report.) 3. Your graph probably wasn't linear. That's because the relation between the area A of a circle and its 2- diameter D is A = % linear D2, which means we expect a graph of area on the vertical axis 8: diameter squared on the . Notice that A is neither proportional nor linear in D. However, we see thatA is horizontal axis to be linear with some slope and some vertical intercept. Using your knowledge of linearization, explain in words what a theoretical graph of A vs D2 should look like; I've already told you it should be linear, so what you need to do is just explain what the slope should be and what the vertical intercept should be. There's no actual graphing you need to do here. NJ Just explain in words what the graph should look like. This is an important question since it inuences the rest of the assignment. Ask if you are unsure. (FYI, a description of what a graph ought to look like typically goes in to the Theory portion of a formal lab report.) . Eventually you will plot A vs D2, but before that you will need to compute the D2 values and the associated uncertainties 6(D2). Thus, create a new table of the A and D2 values that you will plot, along with their uncertainties. Don't forget units, and round all values using the conventions discussed in lecture; this means there shouldn't be any mistakes in your table as there were in the original given data above. (FYI, tables like this where you are manipulating the original data usually belong in the Analysis section.) . Now make a graph ofA vs D2. Your graph should have (1) good axes, (2) a title, (3) uncertainty bars for every data point, and (4) straight "best fit\" lines that will make it easy for you to get the best slope and the slope's uncertainty. Make sure your graph is easily readable in your document; the numbers on the axes and any t info should be easily readable. (FYI, graphs like this typically belong in the Analysis section of formal lab reports.) . State clearly what your best-t slope is and what its uncertainty is. Be sure to simplify any units. . State clearly what your vertical intercept is and what its uncertainty is. Be sure to simplify any units. . Now that you know the slope and its uncertainty. use them to calculate the value of II and its uncertainty. (FYI, this and the previous two items are typically done in the Analysis portion of formal lab reports. Notice how we are getting a single value of n\" from all the data points all at once, rather than six individual values of H.) . Determine whether your value of n agrees or disagrees with the accepted value of 3.1416 i 0.0001. Explain in one sentence how you know it agrees or disagrees