Lab Introduction
Purpose: The purpose of today's activity is to practice lab techniques including measurement, reproducibility, significant figures, graphing, analyzing data, and lab report writing.
Product: After completing the following activities, write your first lab report following the lab report format. Include both activities in the same report, being careful to format your report so that it is easy to follow what you did.
Activity 1: You will be given a piece of string. This is your new unit of measure. You may name it anything you wish.
1. After naming your unit, measure your height and your lab partner's height in your new unit. You may use any technique you see appropriate, but remember what you did, and write down your procedures explaining why you decided to do it that way.
2. To qualify your result, reproduce the measurement several different times. Use Excel to make a data table detailing your results. You will most likely get slightly different result with each measurement, which is ok. Make sure you record each result exactly as you measured it. Then, average your measurements.
3. Report your height with the correct number of significant figures, and explain how you arrived at the accuracy of your answer.
4. Use a standard unit of measure (perhaps a meter stick) to measure the length of your unit. Once you've done this, you will have established a conversion factor. Convert your height to a standard unit, being careful to keep the correct significant figures.
5. Measure your height with the standard unit. Depending on the accuracy of your measurements and the significant figures you kept, your measured height should be the same as your conversion from the previous step. Measure a couple more times, recording your results in a table, and finding the average.
6. Draw appropriate conclusions from your findings.
Activity 2: Determine the coefficient of restitution of a bouncing ball. For our purposes, the coefficient of restitution is simply the amount of mechanical energy lost with each bounce (i.e. the % of bounce height vs. the previous height)
An online simulation for this experiment is here: http://ed.oc.edu/mt/gps/1/ballbounce3.htm
1. Select a ball and a length measuring device.
2. Select a specific, reproducible drop height. Make sure you drop the ball from exactly the same height each time.
3. Use your measuring device to determine the height of each successive bounce. The first bounce should be a little lower than the drop height, the second a little lower than the first, and so on. Be as accurate in your data collection as is reasonable.
**Note that you will have to drop the ball from the same place each time, counting the bounces and measuring only one each time. You’ll need a very flat surface, and one that is consistent! For instance, if you hear a “dead” bounce (like the floor is hollow at some point), you need to re-drop.
4. Record in Excel. Don’t forget to report the units you used.
5. Use your data to make a scatter plot (not connected) in Excel with Bounce height on the vertical axis and Bounce number on the horizontal axis.
6. After you have finished your graph, right click on one of the points and add a trendline.
**When you add the trendline make sure to select the Options tab and check the boxes to display equation on chart and display R2 value.
7. Determine which trendline is the most appropriate. i.e., which goes nearest the most points as well as makes good sense. An R2 value nearest 1 is one indicator. Another is the nature of the equation of best fit. By this we mean how does the equation “behave” as we continue to vary one variable.
Questions:
What type of mathematical function did you find? (e.g. linear, exponential, logarithmic, power, etc.)
Compared with the other choices, explain why this type of function is best for describing what is happening. (Try searching if you aren’t sure. A website or two might be helpful!)
Analyze: Use the equation you found to predict the initial drop height mathematically. Think about what values of x or y would represent the initial drop height. Show what numbers you plugged in and where. Compare this value to your actual initial drop height. Explain any discrepancy. (Note: if you chose the wrong equation, this question might reveal that!)
Predict: If, instead, you used another ball that was either more bouncy or less bouncy, which coefficient(s) (numbers) in your equation would change, and how (increase or decrease)? If you are unsure, feel free to conduct an experiment! Explain.
Finally, use your equation to determine the coefficient of restitution of the bouncing ball.