My three-year-old has an obsession with Spider-Man. She has been putting bad guys in jail for the past week with the help of her Spider-Man action figure. So, being who I am, I could only resist conducting a mechanical assessment of the fictitious hero's web for so long.
I have deconstructed the physics of superheroes before. My approach is to ignore the mutation aspect - to accept the background story that gave the hero his or her powers. My concern is instead, given such powers, is the rest reasonable? For Spider-Man, I'd like to focus on the web that he shoots from his wrist to the buildings of New York City as a principal means of transportation. Can a thin web realistically sustain the tension that manifests within it when Spider-Man swings through the city?
Consider the awesome illustration below (mad 'Paint' skills) that shows the famous web-slinger swinging from the top of a building using web length '
R'.
If Spider-Man is initially at rest (at 1), then a simple energy conversion analysis (gravitational potential energy converts to kinetic energy) shows that at the bottom of his swing (at 2), his speed
v is given by (2
gR)^0.5, where
g is the surface gravity. Here, aerodynamic effects were ignored as were any elastic or visco-elastic effects associated with the web. A free body diagram for Spider-Man is drawn in the figure at the instant the web is vertical (at 2). The tension in the web points up while the gravitational force points downward. Applying Newton's Second Law in the normal (
n) direction gives the following (note that there is an upward acceleration associated with this circular path):
Ft - Fg = ma
where m is Spider-Man's mass. This becomes:
Ft = m(g + v^2/R) = m(g + 2g) = 3mg
