I love Iron Fist, so of course I watched the new Netflix series Iron Fist. I'll withhold comment on whether it's any good because I'm a physicist, not a TV critic. But I will say the show provides some fun opportunities to look at physics with questions like how much energy he packs into his superpowered punch. One in particular involves .... oh. Wait. This isn't a big spoiler, but I'll warn you just in case. Spoiler ahead. There. You've been warned.
So in one early episode, Iron Fist falls some distance before catching himself on a pole. It got me thinking about how far he could fall and still safely stop himself. Then I wondered what kind of acceleration he'd experience on impact, and what magnitude of arm strength force he would need to stop. Let me draw the scene in question:
In this diagram, Iron Fist falls some distance h and stops over some distance s (I will estimate values for h and s later). Seeing this, the first thing you need to know is that time doesn't matter. Well, maybe it matters, but not here. This scenario deals only with forces and displacement, so the best approach is the Work-Energy Principle:
I hear you saying, "Well that doesn't look like much." Maybe so. Nevertheless, this is a very powerful equation. It states that the work done on a system is equal to the change in energy for that system. What is work? Here is a basic definition:
In this expression, θ represents the angle between the force and the displacement of the force (Δr). To use this, I must first choose a system. In this case, I will make Iron Fist the system. That means two forces can perform work on the system: the gravitational force and the pole. With Iron Fist as the lone system, the only change in energy will be in kinetic energy. Yes, you also could have gravitational potential energy, but only if you didn't also have the work done by gravity (you can't have it both ways). Putting this together, I get:
Here I am calculating the work and the change in energy for the motion from point A to point C---but you could do this for any two points. If Iron Fist falls from rest at point A, his velocity (and thus kinetic energy) will be zero at that point. When he stops at the end of the fall, his velocity is zero there, too (at point C). This means that the work done by gravity must be the opposite of the work done by the pole. Notice that the gravitational force does positive work since the angle between gravity and the displacement is zero (cosine of zero is 1). For the pole, it pushes up while Iron Fist moves down, so it does negative work. Using the definition of work, I get:
Now that I have an expression for the magnitude of the force the pole exerts on Iron First, I can find some real answers. All I need are estimates for these values:
- Mass of Iron Fist = 75 kg.
- Falling distance of three stories, (h + s) = 10 meters.
- Stopping distance = 1 meter (this is the distance from when he first touches the pole to when he stops).
Using these values, I get a pole force of 8,085 Newtons. This is the force the pole exerts on Iron First, but because forces are an interaction between two objects, this is also the force that Iron Fist must push on the pole to stop. A force this large might be too high for normal humans using only their arms. But what if he also hits the pole, using more than his arms to stop? Is it possible to survive something like that? It might be better to examine the acceleration instead of the force.
Knowing the pole force, I can calculate the net force (gravity plus pole)---but remember these are in opposite directions for a total of 6,615 Newtons. Using the force-acceleration relationship, I can find the acceleration (in one dimension):
This gives a stopping acceleration of 107.8 m/s2 or 11 G's. According to NASA data on the human tolerance of acceleration, this should be survivable. Of course, this calculation is just for the average stopping force and the average stopping acceleration. The real acceleration wouldn't be quite so constant and probably would peak at some higher value. Still, Iron Fist is a superhero and can do things you can't, so I'm going to say surviving this fall is plausible if you're Iron Fist. Anyone who isn't Iron Fist probably shouldn't try it.
In case you need something to do, I thought up some homework questions.
- What if, instead of using his arms to break his fall, Iron Fist hits the pole with his chest and stops over a distance of, say, 10 cm. What is his acceleration? Is it survivable?
- Let's say he stops with a combination of arm force and hitting the pole. If he can exert an arm force of 3,000 Newtons (I totally made that up) and hits the pole over 10 cm distance, what is his maximum acceleration?
- If he stops over a distance of 1 meter (as in my calculation), what is greatest height he could fall and still stop with an acceleration of 30 g's (something that could be survivable)?
