Copy of Cratering - Notebook Template (1)

Cratering (Part 1) Autumn 2023 Name: Max Zuckernik Name: James Blaisdell Ndaayezwi Name: Samy Kouidri Date: 10/23/23 Course: PHYS 13100 Lab Section / TA Name: Nathaniel Rowe Initial observations As your group begins, what do you notice? What things will be important to keep in mind as you design and conduct the experiment? What (if anything) do you learn from the group discussion that informs how you will take data? ● The larger the mass, the larger the crater ● Maintain consistency in drop height, measuring crater diameter, uniformity in sand before the drop, etc ● We have eliminated more uncertainties by using our apparatus with the magnet Department of Physics, University of Chicago

Collecting data and plotting Record your data here, and make sure to plot as you go. Use this space also to record observations and thoughts, including details about your procedure (including pictures, if it would help) and how you are minimizing (and quantifying) your uncertainties. Our setup has eliminated a good amount of human uncertainty. We propped our ball up on an apparatus that holds the ball in place with a magnet. When we are ready to drop the ball, we lift the magnet, which gets us a consistent drop every time. This has allowed us to get extremely precise measurements in our set up. When the ball drops, we use the lamp to cast a shadow on the sand to see the crater easier, and then we measure the diameter of the crater using a ruler. After that, we charted all of our observations on a data sheet, including our statistical uncertainties. To get the height of the drop, we estimated the total depth of the sand at a uniform level to be about 5.5 cm. We added the uncertainty values together when calculating the height of the drop, and simply subtracted 5.5 to get the difference between the drop and the top of the uniform sand. Overall, we have greatly minimized any possible sources of error in our measurements. 𝑈 = 𝑚?ℎ Ball 1: Height: 36.0 cm = 0.36 m Weight: 0.1 g = 0.0001 kg 𝑈 = 0. 0001 * 9. 8 * 0. 36 = 0. 0003528 ? Ball 2: Height: 43.0 cm = 0.43 m Weight: 0.4 g = 0.0004 kg 𝑈 = 0. 0004 * 9. 8 * 0. 43 = 0. 00169 ? Ball 3: Height: 50.0 cm = 0.50 m Weight: 1.0 g = 0.001 kg 𝑈 = 0. 001 * 9. 8 * 0. 5 = 0. 0049 ? Ball 4: Height: 100.0 cm = 1.0 m Weight: 3.5 g = 0.0035 kg 𝑈 = 0. 0035 * 9. 8 * 1 = 0. 0343 ? Ball 5: Height: 140 cm = 1.4 m Department of Physics, University of Chicago

Conclusion: Given our data, it seems that the graph for better matches our data than the graph for ? * ? 1/4 . For the graphs, we A = 14.9 and B = 11.9. We used these scalar values because they ? * ? 1/3 seemed to best match our data for each respective graph. Therefore, given our data, the crater diameter is proportional to the fourth root of the Kinetic energy. Photo of Setup Department of Physics, University of Chicago

Department of Physics, University of Chicago

Department of Physics, University of Chicago

Department of Physics, University of Chicago

value is closer to 1 and therefore the data and model agree more than the general χ 2 prediction model. The general power prediction being slightly lower than 1 means that we probably needed more data to test the model. The ⅓ power prediction is much greater than 1 which indicates that the model probably does not agree with the data. Applying your scaling law Extending your model to larger crater sizes ■ How did your predictions (from the model) match the measured values? Our prediction for the lower height was consistent with the measured value as the average measured value, 15.5 cm, fell within our prediction of 15.45 0.28 cm. ± However, our prediction for the higher height was not consistent as the average of the measured values was 16.6 cm while our predicted value was 18.17 0.33 cm. The ± discrepancy between the predicted value of the higher height and the measured values might be because of differences in the height it was dropped as well as a few of the drops making an elliptical shape instead of a perfectly circular shape. ■ Was there much scatter in the predicted values from your classmates or were all groups roughly in agreement? All groups had roughly the same predictions and they all ended up being fairly consistent with the actual drops. This is probably because all groups did basically the same experiment and got similar results. Applying your model to known craters on Earth Sedan Crater: 390 m → 39,000 m Prediction: ? = ( 𝐷 ? ) 4 ? = ( 39000 11.83 ) 4 ? = 1. 18 × 10 14 ? Department of Physics, University of Chicago

Uncertainty: δ? ? = 4 0.21 11.83 = 0. 071 0. 071 × 1. 18 × 10 14 = 8. 378 × 10 12 ? Final answer: ? = 1. 18 × 10 14 ± 8. 38 × 10 12 ? Conclusion: Our value is about 2 orders of magnitudes larger than the actual kinetic energy. The projected model predicted more joules of energy than reality. The reason for this could be because of the materials of the surface and\or the type of collision (bombs aren’t necessarily one-to-one with meteorites). Chicxulub: 100 km → cm 10 7 Prediction: ? = ( 𝐷 ? ) 4 ? = ( 10 7 11.83 ) 4 ? = 5. 11 × 10 23 ? Uncertainty: δ? ? = 4 0.21 11.83 = 0. 071 0. 071 × 5. 11 × 10 23 = 3. 63 × 10 22 ? Department of Physics, University of Chicago