The Physics Factbook™
Edited by Glenn Elert  Written by his students
An educational, Fair Use website
topic index  author index  special index
The feature film SpiderMan is about a young man who obtains extraordinary powers by being bitten by a genetically altered spider. He begins to experiment and develop his powers and realizes that he can shoot web out of his forearms. Soon after that, he realizes that he can shoot his web onto objects, such as tall buildings. He furthers this power by using his web as a rope, and swinging from place to place.
In Chapter 8, entitled "Scaling the heights", SpiderMan is first learning how to use his web to swing from place to place. He attempts to swing from one roof on to another by shooting his web onto a crane over a far building, and swinging himself onto a lower building's rooftop. Since he's new at this, his plan doesn't work out well. He's able to swing to the far building, but he is unable to stop himself. He reaches his lowest point, and then swings back up a bit, crashing into a billboard.
The height of the building SpiderMan starts off on is 6 stories, or 18 meters high (assuming one story is 3 meters). The height of the building he wants to swing to is 1 story, or 3 meters high. The crane which he shoots his web onto is 7 stories, or 21 meters high. In order to calculate SpiderMan's initial potential energy, we must use the formula
U = mgh
where U represents potential energy, m represents mass, g represents the acceleration due to gravity (9.8 m/s^{2}), and h represents height. In this specific case, m is 68 kg, and h is 15 meters (not 18 meters, because he's swinging to the roof of a building that's 3 meters off the ground).
U = mgh = (68 kg)(9.8 m/s^{2})(15 m) = 9996 joules
Since SpiderMan starts off not moving, he has only potential energy. At the bottom of his swing, he has only kinetic energy, given by
K = ½mv^{2}
where v is velocity, and once again, m is mass. We don't know SpiderMan's velocity at the bottom of his swing. In order to calculate it, we apply the law of conservation of energy, where the sum of energy initially equals the sum of the energy finally. Therefore, kinetic energy at the bottom of the swing is equal to SpiderMan's initial potential energy, or
½mv^{2} = mgh
Using the magic of algebra, we can solve for v, and find that
v = sqrt(2gh) = sqrt(2(9.8 m/s^{2})(15 m)) = 17.15 m/s
The velocity at the bottom of his swing is found to be 17.15 m/s (38.36 mph, or 61.74 km/h).
In order to calculate the tension in SpiderMan's web, we must use centripetal force, the net force acting on SpiderMan. The centripetal force is the force directed toward the center of the circle, that keeps an object moving in a circle, and is given by the formula
F_{c} = mv^{2}/r
Where m is the mass of the object, v is the velocity of SpiderMan's swing, and r is the radius of the circle formed while SpiderMan swings. In this situation, centripetal force is equal to the tension in the rope subtracted from the weight of SpiderMan. Tension is a force found in objects such as wires, strings, ropes, or webs, in this case. Weight is the force found by multiplying an object's mass by the acceleration due to gravity (mg). Therefore
mv^{2}/r = T–mg
and using the magic of algebra once again, we solve for T, and find that
T = mv^{2}/r + mg = (68 kg)(17.15 m/s)^{2}/(18 m) + (68 kg)(9.8 m/s^{2}) = 1777 newtons
In more conventional units, 1777 newtons is equal to 399 poundsforce, or 181 kilogramsforce.
In Chapter 43 of SpiderMan 2, entitled "A Train to Catch", Dr. Octopus seizes the controls of a train full of passengers, and puts the train at maximum speed. He then breaks the controls, leaving the train on course to drive straight off the elevated track. Spiderman is the only person that can save the train and its passengers from the deadly crash. He initially attempts to stop the train with his own strength, but fails miserably and doesn't slow the train down. He then attempts to fire his webs onto the surrounding buildings, creating a makeshift sling of himself and his webs. He is unsuccessful once again, but realizes that he's onto something. Finally, he fires numerous webs onto the surrounding buildings, and again makes a sling of himself. Finally, the train begins to slow down, and Spiderman stops the train right before it would have crashed.
When Dr. Octopus breaks the controls of the train, it's moving at an initial speed of 35.76 m/s (80 mph). Each car of the train is a 2200 series, as according to http://www.chicagol.org/multimedia/Spiderman2/. The mass of one car of the train is 21,500 kg (47,399 lbs), as according to http://www.chicagol.org/trains/roster/2200.html, and since the train has 6 cars total, its total mass is 129,000 kg (284,396 lbs). Assuming there are 20 passengers in each car of the train, and assuming they all have a mass of 67.5 kg (149 lbs), the total mass of the train is 137,100 kg (302,254 lbs). Finally, the time the train was stopped was found to be 46 seconds. Since we know that the train ends up completely stopped, we can calculate the acceleration of the train over the time that it is stopped, using the formula a = (v–v_{o})/t: a represents the acceleration, v is the final velocity, v_{o} is the initial velocity, and t is the time over which the object is accelerated.
a = (v–v_{o})/t = (0–35.76 m/s)/46 s = 0.78 m/s^{2}
In this case, the acceleration is negative, since the train is being slowed down rather than sped up.
Using the acceleration and the total mass of the train and its passengers, we can calculate the force Spiderman exerts to stop the train (tension in his web). We can calculate this by applying Newton's Second Law of Motion, where ΣF = ma. ΣF is the net force (in this case, tension), m is the mass, and a is the acceleration.
ΣF = ma = (137100kg)(0.78 m/s2) = 106,938 newtons
In more conventional units, 106,938 newtons is equal to 24,041 poundsforce, or 10,905 kilogramsforce.
As a bonus, we decided to calculate the total distance the train traveled from the time Dr. Octopus destroyed the controls to the time SpiderMan stopped it. We can do this using the formula
s = v_{o}t + ½at^{2}:
s is distance, a represents the acceleration, v_{o} is the initial velocity, and t is the time over which the distance is traveled.
s = v_{o}t + ½at^{2} = (35.76 m/s)(46 s) + ½(0.78 m/s^{2})(46 s)^{2} = 819.72 meters
In the movie SpiderMan 2, a young student (Peter Parker) is struggling with his discovered abilities and trying to keep it a secret. He also has to juggle a separate life outside his spiderlike abilities and keep people from finding out who he really is. He encounters numerous challenges throughout the movie both as being a real man and SpiderMan.
In chapter 13, titled "Web Failure" we see SpiderMan swinging above many buildings. He unexpectedly loses his power to shoot his web and falls. SpiderMan experiences freefall for 4 seconds before he hits the roof of a building. During the freefall, SpiderMan experiences an acceleration due to gravity of 9.8 m/s^{2}. By having the time and the acceleration due to gravity, we can use a simple kinematic equation to find the distance SpiderMan falls before hitting the roof of the building.
y = ½at^{2}
y = ½(9.8 m/s^{2})(4 s)
y = 78.4 m
If we ignore the force of drag acting upward on SpiderMan as he falls, we can also determine SpiderMan's vertical speed at the instant before he hits the roof of the building. We use the formula:
v^{2} = v_{o}^{2} + 2as
v^{2} = (2)(9.8 m/s^{2})(78.4 m)
v = 39.2 m/s
Daniel Saronson, Michael Robbins, Gafei Szeto, David Rozenberg  2005
Follow up studies:
Physics on Film pages in The Physics Factbook™ for 2005
Another quality webpage by Glenn Elert 
home  contact bent  chaos  eworld  facts  physics 
