Built on Facts

The Amazing Spider-Man!

Spider-Man, of mass 90kg, is perching 10 meters above the ground when he notices his (depending on the continuity) crush/girlfriend/wife Mary Jane (50 kg) being menaced by… I dunno, a menace. I’m more of a DC fan really.

He swings down toward her to spirit her our of harm’s way. Assuming he starts from rest and lets gravity do the work, how fast is he going just before he reaches her? Well, he has a gravitational potential energy mgh. And just before he reaches her, it’s all been turned into kinetic energy, half the mass times velocity squared.

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Fig. 1: A free-body diagram.

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Which works out to about 14 m/s. Now right after he reaches her, clearly they’ll be going slower. It’s a collision though, so we can’t assume all the kinetic energy stays conserved. But momentum will be. That means if we want to know how fast they’re going as a unit after he catches her, the answer will be

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v2 being the velocity after the rescue, the m with the mj is Mary Jane’s mass. So I figure that gives us a post collision velocity of 9 m/s.

And now the kinetic energy associated with that speed is going to turn back into potential energy as they swing upward in their arc. How high will it take them? Clearly not as far, they lost energy in the collision and even if they hadn’t they’re still having to split the energy between them.

So for the v we just found and their new maximum height h, we find

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Which gives the height they’ll reach on the upswing as about 4.1 meters. I’m not sure that would be adequate to get them out of harm’s way. Let’s hope it’s one of the low-rent villains. Otherwise it’s probably a job for Superman!

(Yes, this was a brief concept quiz I gave my students.)

Comments

  1. #1 Uncle Al
    March 4, 2009

    Save the girl, defeat the villain, avoid public restrooms. Perhaps he cribbed a gene cassette from Brachinini, Paussini, Ozaenini, or Metriini spp. beetles. That covers thrust and threat neutralization… but he’s gonna walk funny afterwards.

  2. #2 Chris P
    March 4, 2009

    This ties in with all those calculations you can do for space travel. How it is just about impossible to get there from here because assuming the maximum acceleration that a human can take you can never get near a velocity that would get you anywhere.

    I think I read some of it in the book about the physics of Startrek.

  3. #3 Romeo Vitelli
    March 4, 2009

    They’ve actually touched on this issue with Spider-man in the past where he accidentally broke the neck of a woman he was trying to save with his webbing.

  4. #4 rpenner
    March 4, 2009

    And then _I_ get to give a lecture on educational fair use. It’s the circle of scholarship.

  5. #5 andy.s
    March 5, 2009

    Superman would probably be just as bad. Check out this dialog in the first episode of “The Big Bang Theory”.

  6. #6 vin
    March 22, 2009

    How did the murder of Gwen Stacy get turned on Spiderman? If he had been taken to court what would his charges have been?

    1) murder in the first? the legal definition is the unlawful killing of another human being with intent or malice aforethought. Scientifically speaking he is charged with the murder of Gwen Stacy through the breaking of her neck from the force of impact from his web. Yes the action lead to her death but how can the state of NY prove intent?
    Police statements would have been that arriving officer found him grieving over the body. It is doubtful they would have been able to provide testimony to support intent. refer to the issue.

    2)Murder in the second degree – intentional killing not premeditated or planned nor committed in a heat of passion.
    Had Peter found Gwen in bed with Norman Osborn, tried to catch him with his web THEN killed her because he caused Norman to drop her or the goblin threw her in front of him so that he broke her neck with the web, THEN spiderman would be guilty of murder in the second.
    At the time of Gwen’s death he had no forknowledge of the affair. He had stopped his persuit of the Goblin to catch Gwen. Again there is no way for the state to prove intent.

    #3)death brought on by criminal acts. is there a law in new york against throwing a rope at a falling body?No. Again he would have had the support of the police testimony to support his defense of trying to save her life. where does the state prove criminal intent?

    #4) manslaughter. The PA’s last hope. he needs to prove Spiderman is guilty through trying to kill Gwen in the heat of the moment. Where is the intent in this example?
    The state of NY would have no legal basis to charge Spiderman with the murder of Gwen Stacy and the charges would have to be dropped, resulting in Jameson ripping his hair.

    Just another point since the State would have the warrant issued for Spiderman wouldn’t this kill the case right there since this would not be an accepted identity? Superheroes technically have no more legal status in our juducial system then illegal immigrants! You need to be a citizen to testify in a court of law or your deported. You have the right to face your accuser, which means the hero in question would have to reveal himself in order to help the DA make it’s case. Any first year legally blonde could get the motion quashed on the basis that the state would have no one to charge legally.

    The only one guilty of the murder of Gwen Stacy remains Norman Osborn, aka the Green Goblin.

    And since you HAD to cheat on Peter with a safe,rich daddy, screw you Gwen.Peter should have let you drop when he had the chance.

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