I've just been waiting to see something from the upcoming Luke Cage series that will be released soon on Netflix. Of course we already know that Luke Cage is the superhero Power Man. He has unbreakable skin and superhuman strength (but I'm not sure exactly how strong he is in the Netflix show). But here's the thing. It doesn't matter how strong you are. You can't lift up another human and hold him in front of you unless you also have a large mass.

Here is my analysis. Using this image of Luke Cage lifting a dude (most likely a bad guy), what is Luke's minimum mass?

Center of Mass and Torque

OK—technically, I have explain the physics of picking up a person. Yes, I did it for Darth Vader and also for Arnold Schwarzenegger. So, for this case I will just give a short explanation of how to find the mass of Power Man.

First, there is the idea of equilibrium. This says that if an object is at rest and not rotating then two things must be true:

The net force of the object must be zero (zero vector).

The net torque about any point must also be zero (technically also a vector).

It seems clear that a person standing on the ground would have a net force of zero (vector). Also, a person holding another person would still have a zero net force (gravitational force pulling down and the ground pushing up). But what about the torque? What is torque? I like to describe the torque as a rotational force. Just like a force can change the momentum of an object, torque can change the angular momentum of an object. The torque due to a force depends on the magnitude of that force and the distance from the point of rotation which we call the torque arm. Oh, it also depends on the angle the force makes with this torque arm.

Let's say our "object" is the combination of Luke Cage with bad dude. If this is the case then I can consider the system as having two masses (for the two people). There will be a total of three forces on this system: the two gravitational forces and the ground pushing up. Also, if I pick Luke's forward toe to be the point of rotation, the torque from the the gravitational forces have to add up to zero.

This is equivalent of saying the center of mass for the system must be directly over the contact point. So, the farther the dude (but not The Dude) is from this contact point, the greater Luke's mass must be in order to have the same torque.

Image Analysis

Now for an analysis of the image. I need two things to start with. First, I need something to scale the image. In this case, I will use the height of Mike Colter (the guy that plays Luke) with a value of 1.91 meters. Second, I need an estimate for the mass of the dude. I am just going to guess at 75 kg.

In order to get values for the locations of the center of mass of both the dude and Luke, I am going to load the image into Tracker Video Analysis—yes, you can also use this for images.

Here are my measurements.

Putting the center of mass at the ball of Luke's front foot, the dude has a torque arm of 0.294 meters and Luke's is 0.123 meters. Using my assumed mass of the dude, I can solve for the mass of Power Man.

Just for comparison, 179 kg is about 400 pounds. That's pretty massive and clearly shows that Power Man is more than just a normal human. Oh, but that is the lower limit on the mass. Luke Cage could also be much more massive so that the system center of mass would be even further back from this foot.

Bonus Experiment

Actually, this is more like a party trick. Ask a human to stand up against a wall with feet and back flush to the wall. Now see if the human can bend over and pick up something off the floor in front of the human's feet. Here is an example.

Why can't you do this? See if you can come up with a nice explanation. Hint: It is similar to the physics in this post.