This article investigates an implication of being caught after falling from great height. This is seen in the film Superman (1978). A scene depicts Lois Lane falling from the top of a skyscraper, only to be caught safely by Superman. It was found that the impact of landing on Supermans arms would not have caused damage to Lois Lane.

Doggett, I

Kohli, S.S

Mansfield, T

Willis, A

English

University of Leicester Open Journals

Journal of Physics Special TopicsAn undergraduate physics journalA5 1 Did Superman really save Lois Lane?A. Willis, T. Mansfield, I. Doggett, S.S. KohliDepartment of Physics and Astronomy, University of Leicester, Leicester, LE1 7RHDecember 7, 2016AbstractThis article investigates an implication of being caught after falling from great height. This is seen in thefilm Superman (1978). The scene depicts Lois Lane falling from a helicopter at the top of a skyscraper,only to be caught safely by Superman. It was found that the impact of landing on Superman’s arms wouldhave been 9x104 Pa and would not have caused harm to Lois Lane.IntroductionIn the classic film Superman (1978), Lois Lanefalls out of a helicopter at the top of a skyscraper.Superman witnesses this and flies straight to-wards Lois and rescues her without deliveringany injuries. We investigate whether this is plau-sible or whether Lois would get injured in theprocess of her rescue. We examine the event us-ing free-fall concepts and the known lethal valuesof pressure.Theory and ResultsAfter reviewing the scene in the film it can beseen that Lois Lane is in free fall for approxi-mately 10 seconds. Using the equation of linearmotionv = u+ at, (1)where v is the final velocity, u is the initialvelocity, a is the acceleration and t is the timeof flight. Assuming that Lois is stationary be-fore she starts her free fall so that u = 0−1, wefind that the velocity Lois would be falling atwhen Superman catches her would be 98.1 ms−1.Figure 1: Diagram representing our simplistic model ofthe forces acting upon Lois Lane as she falls through theair.However, this is not taking into consideration airresistance.To find the velocity that Lois would have beenfalling while taking into account air resistancewe use the drag equation given below [1]v =√2mgρACdtanh(t√gρACd2m), (2)where m is the mass of Lois, g is the acceler-ation due to gravity, ρ is the density of air, A isthe cross-sectional area of Lois, Cd is the dragcoefficient and the terminal velocity is given byvt =√2mgρACd. (3)For this we make the assumptions that themass of Lois is 65kg [2] and that the density ofair is 1.293kgm−1[3]. We calculated the cross-sectional area of Lois when falling using the av-erage hip size of women. Assuming that Lois isa cylinder with the flat face having a circumfer-ence size of 0.914m [4]. This corresponds to anarea of 0.067m2. We take a value for the drag co-efficient of 1.2 as this is the value of a human inan upright position [5]. Substituting these valuesinto equation (2) we calculated the velocity thatLois would be falling when caught by Supermanto be 78.558ms−1.To calculate the pressure that would be trans-ferred to Lois when Superman catches her wefirst need to work out the change in momentum,dp. Assuming that Superman is stationary whenhe catches Lois thendp = mdv. (4)Therefore, dp = 5113 kgms−1. The force atwhich Superman catches Lois can now be calcu-lated using the rate of change of momentumF =dpdt, (5)where dt is the time it takes Superman to de-celerate Lois to a stationary position. After care-ful revision of the film we estimate it takes ap-proximately 1 second for this deceleration. Thismeans that the force required to stop Lois is5113N. Assuming that this force is split equallybetween Superman’s arms which we assume tohave a length of 35cm and a width of 8cm givingthe area of both his arms as 0.056m2. Using thepressure equationP =FA, (6)where P is the pressure we find that the pres-sure that Lois is subjected to would be 9x104Pa.ConclusionThe pressure was determined to not cause dam-age to her body as the pressure necessary tobreak the skin is 689476Pa [6], and to break oneof the small bones in the body is 172369Pa [7].However, Lois may incur some bruising, thoughthis is difficult to ascertain as there is no defini-tive pressure required to cause bruising. Wesuggest that the implications of Superman’s im-pact upon Lois Lane can be looked at, in thecase when Superman is not stationary when hecatches her.References[1] https://en.wikipedia.org/wiki/Drag_(physics) (28/10/2016)[2] http://www.arts.ac.uk/media/arts/research/documents/SizeUK-Results-Full.pdf (28/10/2016)[3] Paul A. Tipler and Gene Mosca Physics ForScientists and Engineers 6th Edition Pg. 424[4] http://www.telegraph.co.uk/news/health/news/8335282.html (28/10/2016)[5] https://en.wikipedia.org/wiki/Drag_coefficient#cite_note-29 (28/10/2016)[6] http://www.bcmj.org/worksafebc/updates-worksafebc (28/10/2016)[7] http://scienceline.ucsb.edu/getkey.php?key=3088 (28/10/2016)

A5_1 Did Superman really save Lois Lane?

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A5_1 Did Superman really save Lois Lane?

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