Mission Unphysical

In a famous scene from the first of Tom Cruise's Mission Impossible movies, disavowed CIA agent Franz Krieger uses a harness, a carabiner, and four pulleys (one of them is arguably better called a "pushey") and rope to lower agent Ethan Hunt (Tom Cruise) through the ceiling of a room at CIA headquarters in order to steal something.

It's a fun and suspenseful scene to watch, but here I want to talk about how silly this pulley system is.

Franz is lying down in a narrow air duct above the vent through which he is lowering Ethan. The vent is near his feet, and he's slowly releasing line through a pulley (kept out of sight) that is mounted above him, and closer to the hole. From that pulley, the line comes back toward him, through a pulley that is attached with a carabiner to a harness on his chest. The line then goes back toward the hole, but up again to a different (visible) high-mounted pulley, then it descends toward the hole and over a "pushey" mounted on the end of a low-mounted shaft protruding up and over the hole. From here, the line goes straight down and is attached to Ethan Hunt.

One is led to believe that because of the complexity of this pulley setup, it must serve some practical purpose. Before we guess about that purpose, let's first consider the simplest possible pulley setup that might have been used.

Without any pulleys, the line would just go down the hole, getting scraped over the edge of the hole. That wouldn't be silent enough given the needs of the mission, and the friction caused would make it very hard to lift Ethan when his mission is done (though it would ease lowering him). Mission parameters require pulleys. Plus pulleys are interesting, as we shall see.

The simplest pulley setup would involve a single pulley, placed directly above the vent. If such were possible, then Franz could just release the line through that pulley and the line would go down through the vent. He'd have to anchor his feet somehow, though, or he'd slide toward the hole. Assuming he and Ethan are about the same weight, without anchored feet, Franz would find himself dangling just above the hole (under the pulley), balancing Ethan. But let's just assume he has good footing. If he does, this would work if he's strong enough to support Ethan's weight with his hands.

But why did Franz use the unstable, precarious "pushey" (other than to create the tension-building risk of the line slipping off of it)? The only reasonable answer is that there was no secure place directly above the vent to mount a pulley. The two high-mounted pulleys in the movie are both farther away from the hole than the "pushey" is. So there simply must be some "bad ceiling" close to and above the hole. Let's go with that assumption, then.

Given how precarious the "pushey" is, it probably wouldn't make sense for it to be the only pulley. That is, things are safer if we run the line first through a high-mounted pulley, serving to stabilize the line so that it isn't wiggling around (from hand motion) while going over the "pushey." Still, with or without the high pulley, having some duct feature to step on to stop one's sliding would be crucial. Friction alone simply would not be enough to stop Franz from sliding along the smooth metal duct and either smashing into the "pushey" or dangling from the high-mounted pulley.

So, at this point we've rationalized the pushey, and a single high-mounted pulley, assuming the footing is good, to prevent sliding.

But what the heck are the two other pulleys for (one on Franz's chest, and another high-mounted one)? One is led to believe that these extra pulleys are to somehow make Franz's job easier, but how?

Franz's number one job is to support Ethan's weight. There's a standard way of making such a job easier using pulleys. It's called a block-and-tackle system. Franz's system is evocative of a block-and-tackle, but something is deeply wrong with it. In fact, it makes Franz's job a lot harder than it would be if he had only a single pulley above the hole!

A block-and-tackle, properly set up, is a means of reducing the force required to lift a weight by increasing the apparent distance that you must pull it. Remember, from physics, that energy is force times distance. Lifting a fixed weight through a fixed distance takes a fixed amount of energy. A block-and-tackle system doesn't change the total energy needed, but it reduces the force you must pull and increases the amount of line (the distance) that you must pull in order to lift the weight the desired distance.

I won't go into detail regarding how block-and-tackle systems work. But the point is, that they make lifting something easier by reducing the force needed. With that in mind, let's look at what Franz's system is doing for him.

The first principle to understand is that since a pulley spins freely, it balances the tension on each side of it. So, if a line is going through a pulley, that means that there's equal tension both before and after the pulley. A pulley is not a brake.

With that in mind, consider Franz's system. The line goes through four pulleys, and at one end is Ethan Hunt, dangling. That means that Franz's hands are holding all of Ethan's weight. That alone would be a problem that could only be mitigated if Franz had a good place to step while lying down because air ducts are made of slippery metal! So, this four-pulley system is actually no better than a one-pulley system.

But it is actually much worse, because of Franz's chest harness and pulley. Because of this, Franz has an additional two times Ethan's weight pulling on his chest harness. The two line segments pulling from his chest to the high pulleys each have the tension of Ethan's entire weight.

Adding to that force the force being maintained by Franz's hands, he now has three times Ethan's weight pulling him toward the high-mounted pulleys. Even with his feet well anchored, he's probably going to get lifted up and smash into the ceiling. If his feet falter, he certainly will do so.

And with his feet well anchored, he's supporting, horizontally, the weight of three Ethans with his legs, for no useful reason whatever.

In fact, this pulley system is a block-and-tackle tailor-made to make it easy for Ethan (or someone half his weight) to pull Franz up into the high pulleys!

It's a fun movie scene, but if you understand the simple physics of how lines and pulleys work, it makes no sense!

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