Astr 5L

I wanted to start the semester by giving students practice making measurements, plotting data, and interpreting graphs. In this lab, they learn how to record data in a table, graph data, interpret the graph to glean additional information, analyze uncertainty, report answers with uncertainty, and compare results.

In Part 1, the students place a bowl on a scale and add 10 dried beans at a time to the bowl. They record data in the table provided and graph the scale reading in grams vs. number of beans by hand. They are then asked to determine the trendline and give the physical meaning of the slope and y-intercept of their graph. The slope shows that the average mass of a bean is a fraction of a gram, which is too small to measure directly using the scale provided. The y-intercept gives the mass of the empty bowl, which they were not instructed to measure. This exercise demonstrates how the slope of a graph can reveal information that is not trivial to obtain directly, and how extrapolating a trendline can reveal information that was not measured. Students also learn how to evaluate random and systematic errors, and how to use standard deviation to describe the uncertainty of a measurement.

In Part 2, students learn the basics of error analysis and how to use standard deviation and percent difference to quantify the uncertainty and agreement between measurements.

In Part 3, they apply the lessons they learned in Part 2 to their results in Part 1. Students are asked to present the average mass of a bean they measured in Part 1, and use standard deviation and percent difference to comment on whether their measurements agree with results from other groups.

Astronomy is a unique science in that the bodies that we study are so distant that we rarely get the opportunity to perform conduct physical experiments. This lab is a great example of how astronomers use controlled lab experiments to isolate variables and test models, which can then be applied to worlds that are beyond our reach.

I open this lab by showing the slides pictured on the right. I begin by explaining how impact craters accumulate on a surface, and how we can simulate these impacts in a lab to better understand the relationship between crater properties and the projectiles that created them. Once we understand fundamental relationships such as projectile velocity vs. crater diameter, we apply this knowledge to ask more complex questions. For instance, how big was the meteor that killed the dinosaurs, and how likely is such an event to happen again?

In this lab, we investigate how the diameter of a crater depends on fast the projectile was moving. Students break into small groups of ~3 and drop marbles from various heights into a bed of sand. As one student drops the marbles, another measures the crater diameter, and another records the data. I developed a Google Sheet (pictured below) to automatically compute the mean and standard deviation of the crater diameters for each drop height and graph the data relationship between D vs v, v^2, and v^1/2.

The lab manual explains the physical motivation for each of the models listed above, but I think the significance of this portion could have been emphasized better in class. The students did very well selecting the model that best fits their data, but in the next iteration of this lab, I would like to focus more on why it is important to compare models, and what can be learned from an exercise like this.