Question 1: Air pressure on waves; Question 2: Weight of toner

Question 1: Air pressure on waves; Question 2: Weight of toner Acknowledgment • Intermediate Level – Provide the students with an The author would like to thank Rodney Aho for his many con- Excel file containing a thundercloud model and have tributions, meaningful discussions, and guidance in this effort. them vary the parameters (size, total charge, distance above Earth) to answer fundamental questions. As an References example, they might try to design a “safe thundercloud,” 1. J. M. Wallace and P. V. Hobbs, Atmospheric Science: An Intro- i.e., one that produces almost no surface charge density ductory Survey, 2nd ed. (Academic Press, San Diego, 2006), pp. anywhere on Earth (which would minimize lightning 252–257. strikes). This type of “cloud engineering” provides a 2. M. Becerra and V. Cooray, “A self-consistent upward-leader natural bridge to studies in atmospheric science where propagation model,” J. Phys. D Appl. Phys. 39, 3708–3715 clouds are classified by their properties. (Aug. 2006). • Advanced Level – If the students have some profi- 3. C. Saunders, “Charge separation mechanisms in clouds,” Space ciency in writing code as well as a solid grasp on the Sci. Rev. 137, 335–353 (April 2008). derivation above, they could model more complex 4. V. A. Rakov, “A review of positive and bipolar lightning dis- cloud shapes, examine edge effects near to a cloud, or charges,” Bull. Am. Meteor. 767–776 (June 2003). even simulate a small group of thunderclouds and cre- 5. B. B. Phillips, “Charge distribution in a quasi-static thunder- cloud model,” Mon. Weather Rev. 95, 847–853 (Dec. 1967). ate the corresponding electric potential/surface charge 6. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, Inc., density maps. This would definitely challenge their Hoboken, NJ, 1999), p. 37. understanding of the physics as well as the details of nu- 7. D. J. Griffiths, Introduction to Electrodynamics, 3rd ed. (Pren- merical simulation in general. tice Hall, Upper Saddle River, 1999), pp. 146, 165. 8. E. R. Williams, “Large-scale charge separation in thunder- Conclusion clouds,” J. Geophys. Res. 90, 6013–6025 (June 1985). We produced realistic electric potential and surface charge 9. R. A. Serway and J. W. Jewett, Physics for Scientists and En- density maps near a hypothetical thundercloud with minimal gineers with Modern Physics, 9th ed. (Brooks Cole, Boston, resources and with relatively simple physics. With very basic 2013), pp. 760–761. geometry and knowledge of introductory electrostatics, it 10. Readers can view the appendix at TPT Online at http://dx.doi. is possible to build models that yield good approximations org/10.1119/1.5025296 under the Supplemental tab. of the electric potential surrounding thunderclouds and the 11. M. Nakano, “The cloud discharge in winter thunderstorms of effect that the charged cloud has on Earth underneath. This the Hokuriku Coast,” J. Meteor. Soc. Japan 57, 444 –451 (Oct. modeling process could be leveraged in the classroom to cre- 1979). ate activities that highlight electrostatic physics as well as our ability to numerically simulate it. In this way, students with Matthew Neel is a physicist, researcher, and data scientist with special interests in plasma physics and quantum optics. He earned a BA in phys- varying levels of familiarity with the subject matter can be ics from Whitman College, an MS in physics from Oregon State University, engaged and encouraged in their learning. and a Professional Certificate in Data Science from the University of Washington. He currently works for the Bonneville Power Administration in Seattle, WA. Contact him by email at msn2700@gmail.com, or visit his professional profile at www.linkedin.com/in/mattneel. Larry Weinstein, Column Editor Old Dominion University, Norfolk, VA 23529; Fermi Questions weinstein@odu.edu w Question 1: Air pressure on waves w Question 2: Weight of toner When the wind is blowing, what is the difference be- How much heavier is a 100-page printed document tween the air pressure at the crest and at the trough of than 100 blank pages? (Thanks to Emily Kandel of an ocean wave due to the Bernoulli effect? Scarsdale, NY, for suggesting the question.) Find answers at TPT Online; tpt.aapt.org. Question suggestions are always welcome! For more Fermi questions and answers, see Guessti- mation 2.0: Solving Today's Problems on the Back of a Napkin, by Lawrence Weinstein (Princeton Univer- sity Press, 2012). DOI: 10.1119/1.5025297 The Physics Teacher ◆ Vol. 56, March 2018 167 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Physics Teacher American Association of Physics Teachers

Question 1: Air pressure on waves; Question 2: Weight of toner

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Acknowledgment • Intermediate Level – Provide the students with an The author would like to thank Rodney Aho for his many con- Excel file containing a thundercloud model and have tributions, meaningful discussions, and guidance in this effort. them vary the parameters (size, total charge, distance above Earth) to answer fundamental questions. As an References example, they might try to design a “safe thundercloud,” 1. J. M. Wallace and P. V. Hobbs, Atmospheric Science: An Intro- i.e., one that produces almost no surface charge density ductory Survey, 2nd ed. (Academic Press, San Diego, 2006), pp. anywhere on Earth (which would minimize lightning 252–257. strikes). This type of “cloud engineering” provides a 2. M. Becerra and V. Cooray, “A self-consistent upward-leader natural bridge to studies in atmospheric science where propagation model,” J. Phys. D Appl. Phys. 39, 3708–3715 clouds are classified by their properties. (Aug. 2006). • Advanced Level – If the students have some profi- 3. C. Saunders, “Charge separation mechanisms in clouds,” Space ciency in writing code as well as a solid grasp on the Sci. Rev. 137, 335–353 (April 2008). derivation above, they could model more complex 4. V. A. Rakov, “A review of positive and bipolar lightning dis- cloud shapes, examine edge effects near to a cloud, or charges,” Bull. Am. Meteor. 767–776 (June 2003). even simulate a small group of thunderclouds and cre- 5. B. B. Phillips, “Charge distribution in a quasi-static thunder- cloud model,” Mon. Weather Rev. 95, 847–853 (Dec. 1967). ate the corresponding electric potential/surface charge 6. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, Inc., density maps. This would definitely challenge their Hoboken, NJ, 1999), p. 37. understanding of the physics as well as the details of nu- 7. D. J. Griffiths, Introduction to Electrodynamics, 3rd ed. (Pren- merical simulation in general. tice Hall, Upper Saddle River, 1999), pp. 146, 165. 8. E. R. Williams, “Large-scale charge separation in thunder- Conclusion clouds,” J. Geophys. Res. 90, 6013–6025 (June 1985). We produced realistic electric potential and surface charge 9. R. A. Serway and J. W. Jewett, Physics for Scientists and En- density maps near a hypothetical thundercloud with minimal gineers with Modern Physics, 9th ed. (Brooks Cole, Boston, resources and with relatively simple physics. With very basic 2013), pp. 760–761. geometry and knowledge of introductory electrostatics, it 10. Readers can view the appendix at TPT Online at http://dx.doi. is possible to build models that yield good approximations org/10.1119/1.5025296 under the Supplemental tab. of the electric potential surrounding thunderclouds and the 11. M. Nakano, “The cloud discharge in winter thunderstorms of effect that the charged cloud has on Earth underneath. This the Hokuriku Coast,” J. Meteor. Soc. Japan 57, 444 –451 (Oct. modeling process could be leveraged in the classroom to cre- 1979). ate activities that highlight electrostatic physics as well as our ability to numerically simulate it. In this way, students with Matthew Neel is a physicist, researcher, and data scientist with special interests in plasma physics and quantum optics. He earned a BA in phys- varying levels of familiarity with the subject matter can be ics from Whitman College, an MS in physics from Oregon State University, engaged and encouraged in their learning. and a Professional Certificate in Data Science from the University of Washington. He currently works for the Bonneville Power Administration in Seattle, WA. Contact him by email at msn2700@gmail.com, or visit his professional profile at www.linkedin.com/in/mattneel. Larry Weinstein, Column Editor Old Dominion University, Norfolk, VA 23529; Fermi Questions weinstein@odu.edu w Question 1: Air pressure on waves w Question 2: Weight of toner When the wind is blowing, what is the difference be- How much heavier is a 100-page printed document tween the air pressure at the crest and at the trough of than 100 blank pages? (Thanks to Emily Kandel of an ocean wave due to the Bernoulli effect? Scarsdale, NY, for suggesting the question.) Find answers at TPT Online; tpt.aapt.org. Question suggestions are always welcome! For more Fermi questions and answers, see Guessti- mation 2.0: Solving Today's Problems on the Back of a Napkin, by Lawrence Weinstein (Princeton Univer- sity Press, 2012). DOI: 10.1119/1.5025297 The Physics Teacher ◆ Vol. 56, March 2018 167

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The Physics TeacherAmerican Association of Physics Teachers

Published: Mar 1, 2018

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