Friday, September 25, 2015
Here comes the Spider-Man.
The book I chose to do research on is The Physics of Superheroes and the chapter being "Can He Swing From a Thread? - Centripetal Acceleration" In this chapter, author James Kakalios challenges the comic book minds on if Spider-Man can actually swing from a thread at the speed that he does, would it be able to accommodate for his weight and possibly the weight of others that he may be carrying? To solve this he looked at the following factors. Newton's second law of motion shows us that force is needed to change an object's motion. A change in motion or acceleration is made evident by a change in magnitude or change in direction. The force that would be acting on Spider-Man while he is swinging in a parabolic arc or semi-circles would be the force of gravity and the force from the tension in the webbing. Due to these forces he is constantly changing acceleration during the swing. Since the webbing is providing some of the force acting on Spider-Man it must be incredibly strong in order to hold his weight and the weight of others while providing an outside force. If the webbing were to snap mid swing, Spider-Man would go falling in the direction at which he was pointing when the web line snapped. The acceleration acting on Spider-Man provided by the web is identical to that of the acceleration of the moon by Earth's gravity. If there was no gravity acting on the moon then it would simply fly off with the same velocity that it had initially, just like Spider-Man falling off of his thread. The author provided us with an equation to show the acceleration of an object being constantly directed onto a circular orbit with a velocity ((v * v)/R = v^2/R) with "R" being the radius of the circle. The webbing must provide a force (mv^2/R) in order to change the direction of the swing and to support his weight. The faster he swings, the greater the centripetal acceleration will be (v^2/R). For example, when Spider-Man swings from a web 200 feet long at a speed of 50 mph the acceleration would be 27 feet/sec^2 as well as the acceleration of gravity (32 feet/sec^2). With Spider-Man weighing approximately 160 pounds and the force needed to change his motion being 135 pounds, the webbing would have to hold nearly 300 pounds and then other possible passengers on top of that. Kakalios then states that real spider silk is actually five times stronger per pound than steel cables and even more elastic than nylon. The webbing is made of thousands of rigid filaments that are a few billionths of a meter wide with fluid-filled channels that distribute out the tensile force along the webbing instead of just on one strand. The high tensile strength of real spider silk can support a weight of more than 20,000 pounds per square centimeter. Even a thinner webbing could hold 6,000 pounds, so 3,000 pounds, or even a runaway train, would be no problem for Spider-Man's webbing.