Physics Puzzler: The Physics of Pumpkin Chucking, Part 2
We looked at the physics behind launching pumpkins with a pneumatic air cannon in the last issue of The SPS Observer, but now it’s time to go old-school—dropping pumpkins from the roof! For maximum splatter, we recommend filling the pumpkins with liquid nitrogen!
Yes! Nitrogen has a boiling point of 77 K (brrr!), so its liquid form is called a cryogenic. For some points of reference, pure water freezes at around 273 K, and the lowest recorded natural temperature is around 184 K (at Vostok Station on the Antarctic Plateau).1 Many physics experiments use liquid nitrogen (LN2) as a coolant, but it’s also perfect for freezing a pumpkin into a solid block of shatterable organic matter, as seen in Fig.1.
(Obvious) Disclaimer: Do not use LN2 without proper protection, training, and the appropriate permission!
Figure 3 - Drag coefficients for various shapes7.
Hyun Joo Kim
Figure 3 - Drag coefficients for various shapes7.
A. Chucking the squash: Say we’re dropping the pumpkin pictured in Figure 1 off the roof of the physics building. If the height and equatorial circumference of the pumpkin are 30 and 65 cm, respectively, the height of the roof is 9.1 m, the hollowed pumpkin has a mass of 6.2 kg, and we fill the pumpkin halfway with liquid nitrogen, what will the acceleration of the pumpkin be right before it hits the ground? More importantly, how does this differ with an uncarved pumpkin? Does mass even matter (pun intended)?
Hints: What shape is the pumpkin? The density of liquid nitrogen is 808.4 kg/m3 at 25℃ at 1 atm.8
B. Some devilish differentials: How would we calculate the velocity without using conservation of gravitational potential energy to estimate?
Hint: Use the identity ∫0x 1/(a - bx’2 ) dx’ = (tanh-1 (√a/b x)/√ab).
Check your answers against our solutions.9
References:
1. World: Lowest Temperature, World Meteorological Organization, archived from the original June 16, 2010, retrieved December 10, 2013, from https://web.archive.org/web/20100616025722/
http://wmo.asu.edu/world-lowest-temperature .
2. Nathan, A., The Effect of Spin on the Flight of a Baseball, Am. J. Phys., vol. 76, no. 2, 2008.
3. Kagan, D. and Nathan, A., Statcast and the Baseball Trajectory Calculator, Physics Teacher, vol. 55, no. 3, pp. 134–136, 2017.
4. Spheroid diagrams by Ag2gaeh [CC BY-SA 4.0
(https://creativecommons.org/licenses/by-sa/4.0 )], from Wikimedia Commons.
5. By Marina Vladivostok [Public domain], from Wikimedia Commons.
6. By Petr Kratochvil [CC0 Public domain], from Public Domain Pictures.
7. By TheOtherJesse [Public domain], from Wikimedia Commons.
8. Nitrogen—Thermophysical Properties, Engineering ToolBox, accessed November 1, 2018, from https://www.engineeringtoolbox.com/nitrogen-d_1421.html , 2008.
9. https://www.spsnational.org/sites/default/files/files/publications/obser... .
Bookmark these activities for your chapter’s fall calendar
Ghoulish Galileo: Bring your pumpkin drop to the next level by replicating Galileo’s experiment! Will two pumpkins dropped at the same time hit the ground simultaneously? Bonus points if someone dresses up as Galileo!
Spooky Physics Conference: Once a year, William and Mary’s chapter of SPS transforms into the SSP, the Society of Spooky Physics! Undergraduates present satirical talks of physical explanations for the paranormal to a panel of esteemed spooky science experts (aka graduate students and professors in costumes). The graphs are ghoulish, the tables are terrifying, and the equations will haunt your very soul!
