Friday, September 28, 2012

Physics in Film: The Physics of Spiderman

Written by Rachel Weinstein

In Spiderman 2, Peter Parker manages to stop an out of control freight train, thereby saving all of its passengers from imminent death, using his supernatural strength and his incredible web.  There are interesting physics behind this scene, which exemplify how extraordinary Peter Parker is compared to an average spider.

In this scene, the train is depicted as flying out of control at around 80 mph (35.76 m/s).  Peter manages to stop the train in 50 s. 

Vinitial: 35.76 m/s
Vfinal: 0 m/s
T: 50s
A: -35.76/50 = -.715264 m/s^2 

The overall force that is needed to stop the train is equal to the mass of the train times the acceleration.  The average freight train weighs 120 tons.

120 tons x 2000 lb/ton x 1 kg/ 2.2 lb = 109,090 kg

F = ma
F = (109,090)(.715264) = 78,028.149 N in the opposite direction the train is moving in.

Peter generates this force by shooting 12 strands of web towards the buildings on either side of the train.  Assuming that these strands are shot out on an even plane at even and very small time intervals, the assumption can be made that the strands are of similar length and consequently, the force of tension on each strand can be considered to be about the same.  In reality, this is not exactly what occurred and the force of tension on each strand would be slightly different depending on the angle and length of the string.  The force of tension in reality would also be constantly changing because the strand is stretchy, but to simplify the problem, I assumed that it is maximally stretched and the force of tension is not changing.

Thus, the force of tension on each strand equals: 78,028 N/12 = 6502N

Because the clip shows some of the strands starting to snap, we can say that this force is the maximum force of tension that the thread can withstand.  If we assume that the strength of the thread is related to the radius, we can compare actual spider webbing to Spiderman’s webbing.  A regular spider’s web can roughly withstand 2.0 x 10^-3 N of force.  A single thread has a radius of roughly 3.9 x 10 ^ -6 m.  Spiderman’s strand of web can withstand 6502 N and is estimated by me to be a cm thick. So…

(2.0 x 10^-3)/(3.9 x 10^ -6) : 6502/.01
512.82 N/m : 650234.58 N/m

If a spider’s thread was as thick as Spiderman’s:

512.82 N/m x .01 m = 5.128 N

Spiderman’s webbing is stronger:
6502/5.128 =   1,267.9 times stronger than your average spider.

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