A few notes about these forces:

• F_H is the force the other person’s hand exerts on this person. I put it only in the horizontal direction. If there was also a vertical force on this leaning person (say pushing up), then this person would have to push down on the other one. The only way they can both be doing the same things is with a horizontal force.
• I have drawn the human as a one dimensional stick. In this model, the human can be under compression or tension, but no twisting allowed.
• I have assumed that the center of gravity for the human is in the middle.
• Finally, I am using ? as the angle this human is tilted above the horizontal.

The goal here is to get a relationship between how hard the two guys have to push (F_H) and the angle, ?. If the humans are in equilibrium, then the following must be true:

Where ? is the torque about one point on the human. Since the human is not rotating, the net torque about any point is zero. Putting in values for the forces, I get the following for the net-force being zero.

Using the normal model for friction (maximum friction is proportional to the product of the normal force and a coefficient of friction), I get the following:

Now, for the torque stuff. Let me find the torque about the point where the feet touch the wall. If the axis of rotation fixed, I can write torque as the scalar value:

Two things: ? (in this case) is the angle between the force applying the torque and the torque arm (r). The sign of the torque is positive if it would cause a counter-clockwise rotation. This gives the following:

A couple of points:

• Friction is not in this expression. I am assuming there is enough friction to prevent slipping.
• What happens as ? goes to zero? The force from the hand blows up. Why? Think of it this way: the torque from the hands has to counter the torque from the weight. As ? goes to zero, the hands push direction towards the rotation point. This is like trying to open a door by pushing on the hinge.

Back to the image

What about the image in questions? Using Tracker video analysis, I can just measure angles in an image. From this, my best estimate is that the guy on the left has an incline of about 1-2 degrees. The guy on the right seems to be angled down at about 8 degrees. What to do? Well, the force exerted by the hands on the left guy can be calculated. Using the above expression, I get:

Just for a comparison, this is almost 2000 pounds. Sport Science would have a field day with that number. (oh, did I say that out loud?) The other guy has a problem. For him, both the torque from the gravitational force and the torque from the hands would be in the same direction. He would not be in equilibrium. Well, I guess the left guy could push up – but that would require an even greater force.

Note – I did make some assumptions. Mainly that these people were 1-d sticks (which they are not). The muscles in the body can do some horizontal stuff – just like the oak tree with the horizontal branch that I analyzed previously. But still. This image seem highly unlikely. But maybe I am missing something. I don’t see any other signs of fakedness, but what do I know?

Oh, I tried an Error Level Analysis, but didn’t see anything that stuck out. Error level analysis basically looks at how many times different parts of the image has been saved. Here is the analysis for that particular image.

Authors: Rhett Allain

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