Sunday, September 27, 2015

"The Day Gwen Stacy Died - Impulse and Momentum"

It is never the fall that kills them, but the stop.

"The Physics of Superheroes" by James Kakalios explores the unfortunate death of Spiderman's girlfriend Gwen Stacy. The dastardly Green Goblin holds Gwen over the end of the George Washington Bridge to bait Spiderman into battle. During the duel, he drops her over the edge, forcing Spiderman to leap into action and rescue her! He heroically shoots a web at her, catching her mere seconds before he hits the ground! She calms to a halting stop, and Peter Parker breathes a sigh of relief.
But it is never the fall that kills them, but the stop.
He reels up not his smiling, beautiful girlfriend, but her lifeless corpse.
As Kakalios wrote: "A death that was demanded... not by the writers and editors or by the readers, but rather by Newton's laws of motion."

Kakalios uses the equation v^2=2gh to find out Gwen's velocity as she plummets to her doom. He assumes that she is caught after she falls ~300 feet, and knowing that g is accelaration due to gravity, he finds that she is falling at almost 95 mph (a little over 42 m/s)!
He then uses Newton's second law to find how large of a force is used to stop Gwen's descent.
He rewrites it to be:
(Force)(Time) = (Mass)(Change in Speed)

While the right side of the equation is momentum, the left is impulse.
As I understand it, if you have little time to slow something down, you'll need a bigger force to stop it. Spiderman had very little time to stop Gwen from falling, which is terrible for her spine.

Kakalios finds that if Gwen's change in speed goes from 95 to 0 mph in about half of a second, and if his estimate of her weight (50kg) is correct, then 970 pounds of force is applied to her. SNAP.

Spiderman is not a stupid man, and he learns the physics error of his ways, and finds himself more successful in the future.
In one incident that involved an unlucky winder washer, Spiderman, instead of applying all of that impulse to the man, falls down to him, matches his speed, and then uses his web to swing away. This applies the ridiculous impulse to his super-spider arm, which can take it.

In hindsight, though, somebody as supposedly smart as Spiderman really should have understood that catching Gwen like that would kill her. I guess he was just under a lot of pressure.

The Physics of Super Heroes, James Kakalios, Gotham Books, 42-52.

1 comment:

  1. Good. Thanks for sticking within the parameters of the assignment. I hope you learned a few things.