Superhero Hour

We’re going to select our cable to be more than adequate to handle that amount of force
Grant Imahara

This 2007 episode saw the Mythbusters scale tall buildings, change in phone booths, and bust themselves in the nose.  It also involved an attempt to turn a car (based on a Batmobile) around a tight turn using a cable launched at a pivot point.

Grant used some (emphasis on some) physics to help figure out what sort of cable they’d need.  To figure out the tension in the cable, Grant turned to centripetal force/acceleration.

Centripetal acceleration is \frac{V^{2}}{R}, so of course, the centripetal force would come out to \frac{m V^{2}}{R}.  Just as Grant said, it’s a function of the car’s mass, speed, and the turn radius.  Let’s try to figure out how/why Grant predicted they would need 7000 lbs of force.  I’m going to guess that they were making the turn with a 15 foot (~ 5 meter) radius.  We know the speed was 30 mph (13 m/s), and I’ll guess that the car’s mass was 2000 lbs (900 kg).  A little algebra later:

 \frac{m V^{2}}{R} = \frac{(900\: kg)(13\: m/s)^{2}}{5\: m} = 30,000 \: N = 6700 \: lbs

Hey, that’s pretty close to 7000 lbs!  Not bad.  I promise, those were my first guesses.  Okay, so why did it break then?  Well, there are a couple of things I can think of.

The cables they used may be able to support 7000 lbs when applied gradually along an unmolested run of rope.  The reality of the situation is much harsher.  For one, the cable wrapped around the steel structure is kinked where it presses against the edge, compromising strength and intensifying the stress.  Furthermore, generally when something is loaded very quickly, it appears to behave weaker than it otherwise would.  This is because when an object experiences impact loading, it doesn’t have the ability to dissipate energy as efficiently as it would in a more gradual loading situation.  Of course, that can hardly be avoided in this case.

Maybe Batman used a spider web cable.  Or nanotubes.  Nanotubes can do anything.

Space elevator?

No problem.

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