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.
F=MA
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.

Sunday, September 20, 2015

Kinetic Impact

While it's really easy to just look at a giant space rock and say "let's just blow it up", there are far more interesting and complex options, including just hitting it with something
People smarter than me call it kinetic-impact, and it could be a fairly effective way of knocking an asteroid off its course without the use of nuclear explosives. The idea is that we would ram something into the asteroid as hard as we could to push it into a different orbit or off its course, thus missing Earth. This basically becomes a huge example of a collision problem. Which means, of course, that NASA would need to know the mass and velocity of the asteroid so they could send something big enough and with enough force that it would actually work. Plus, they would need to know years, maybe decades, in advanced to actually pull this off. However, even if they gathered all of the relevant information, there could still be one issue. It would probably be safer to lodge our projectile into the asteroid (what if our projectile were to come back towards us?), so the surface of the asteroid would alter the outcome immensely. If it were too hard, our projectile might not be able to lodge into it. If it were too fragile, the asteroid might shatter, and then we have a whole other problem on our hands.

While no research seemed to show that this has been properly tested before, it seems we got fairly close with the Deep Impact mission of 2005. They launched a probe straight into a comet to see what it was made of, as stated by aeronautical engineer Rusty Schweickart “In a way, the kinetic impact was demonstrated by the Deep Impact mission back in 2005, but that was a very big target and a small impactor that had relatively no effect on the comet. So, we haven’t really demonstrated the capability to have the guidance necessary to deflect a moderately sized asteroid.”

Essentially, the main idea behind this plan is that we could knock it away without the risks that come with blowing it up. It certainly is not as effective as the use nuclear explosives (which, honestly, we would probably use if the time comes), but it is a different take on the idea.

I don't have a witty tagline to write at the end like I usually do.  ¯\_(ツ)_/¯

Sunday, September 13, 2015

Physics: Erased


Everybody knows of the classic railgun, and anybody who knows what they're talking about knows that Eraser is indisputably the best move ever created in the history of mankind. Here is an example why:

During one climatic scene of the movie, Arnold Schwarzenegger must use two railguns at once to fend off the baddies. This scene totally makes physical sense and here is why.
First, we begin with a picture to help visualize the scene:



Now that you can perfectly visualize the scene at hand, we can try to put some numbers behind it. Here is what we already know:

M,a (Mass of Arnold) = 100 kg (estimated with Google).
M,b (Mass of Bullet) = 0.01kg (estimated by rounding the weight of a heavy bullet.)
Vi,a (the initial velocity of Arnold) = 0 m/s (as he is not moving before he shoots.)
Vi,b (the initial velocity of the bullet) = 0 m/s (as it does not move before it is shot.)


M,v (Mass of Arnold's victim) = 80 kg (the approximate weight of the average man.)
M,b (still) = 0.01 kg
Vi,b = 3x10^7 m/s (as the movie says the bullet moves close to the speed of light)
Vi,v = 0 m/s (as he is not moving before he is shot.)

Now, to prove that this masterpiece of a movie is realistic, we must use that information to see if the law of conservation of momentum is kept. (Pf = Pi)
I'll start by finding the final velocity of the victim with the bullet lodged in him.

Vf = (M,b)(Vi,b) / (M,v + M,b)

Vf = (0.01kg + 3x10^7m/s) / (80kg + 0.01kg)

Vf = 37,000m/s
(This also tells us what Vf,b on Arnold's side is)
Already we've come across perfect physics, as the victim in the movie abso- wait. No he doesn't. This is right at all. That's ridiculous. This means that the baddie should have flown back at impossible speeds after the bullet lodged in him.

Now we'll do the same for Arnold. If the momentum is conserved, then the recoil should be pretty hefty.

Vf = -(M,b)(Vf,b) / (Ma)

Vf = -(0.01kg)(3x10^7m/s) / (100kg)

Vf= -3x10^4 m/s
Arnold doesn't seem to move at ALL when he fires not just one of these guns, and he fires two! If he doesn't fly back, his arms should at least be ripped from their sockets as if they were made of wet paper. Could it be that the greatest movie ever does not contain accurate move physics??

I rate Eraser -3x10^4 out of 10 on physics accuracy.

Saturday, September 5, 2015

Physics Impossible 3

Agent Ethan Hunt has simply one task standing in his way before he can save his wife and show off how cool he is: steal the MacGuffin and bring it to the bad man. The challenge before him is to infiltrate the high security building where the rabbit's foot is located, but Tom Cruise isn't about to simply walk in. He decides to swing from the taller building next to desired one, intending to land on the roof. Assuming he has a rope that can withstand the tension of this stunt, how long does the rope need to be for him to accomplish the feat? Fortunately for physics-loving viewers, Zhen Lei lays out most of the information we need:

The building Hunt needs to be on is 162m tall.
The adjacent building he will be swinging from is 226m tall.
The distance between the two is 47.55m long.

This tells us one thing: the rope has to be longer than 47.55m (plus a little extra to ensure that he lands ON the roof and not on the ground 162 meters below).

Hunt starts his impossible mission by running away from his target and jumping off the starting building. This allows him to swing towards the correct building. He would probably need to jump relatively far to make the swing. The farthest distance a human being has jumped is 8.9m, so we can assume it is less than, but somewhere around near it (considering the amazing physical ability Hunt has shown off in this movie).

So, Hunt would need a rope that can cover the 47.55m gap, give him about 10 feet (3.048m) of leeway to ensure a "safe" landing, and include the distance of the jump he makes at the beginning. 
A better question would be where he got a rope that long on such short notice. 

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In another scene, Hunt displays the aforementioned amazing physical ability. This time the only thing preventing him from getting to his wife is about a mile and a half of Shanghai. He appears to be very quick in the scene. TOO quick. Could he have run that distance in that amount of time? 

Over the phone, Benji is directing Hunt to the location of his wife. At one point he tells Ethan to run 3/4 of a mile, and then another 1000 yards after that. That, in addition to the small amount of running before and after those sprints, is about 2.5km, or about a mile and a half. After a quick google we find that the world record for the fastest mile ran was done in 3:43. Well, the movie shows the great Tom Cruise running 2.5km in about 1 minute and 10 seconds. 
And I would have gotten winded by just running up the stairs in the beginning of the scene. 

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Finally, in the bridge scene where Hunt is under attack by bullets, missiles, and whatnot, we are met with one more glaring case of bad movie physics. At one point during the dramatic action sequence, Hunt must run and jump over an incredibly large gap to catch the baddies (which he fails to do anyway). Is it possible for him to jump over a gap that size? 
The gap is about the length equal to that of a couple cars bumper to bumper. The average car length is somewhere between 4.5m and 4.8m, so this sets its size at good ten-ish meters at the very least. As I mentioned before, the record for the longest jump is 8.9m, so even though Hunt only barely made the jump, he probably just destroyed a world record. 

I suppose it's called Mission Impossible for a reason (and I'm sure that joke has never been said in this class before).

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