This video of Vietnamese police—I think they’re Vietnamese police—climbing a wall with a pole left me thinking, “What the heck?” I don’t doubt that it works, even if I don’t think I’d try it. But how does it work?
The best way to look at the problem is to create a force diagram, also called a free body diagram. In physics, a free body diagram shows an object and all of the forces acting on that object. An arrow shows the direction and magnitude of each force. If an object is in equilibrium, all these forces must add up to zero (technically the zero vector). So let’s say that the people climbing the wall move slowly enough that everything remains in equilibrium.
I’ll start with the fellow climbing the wall. Here is a force diagram when the other guys are holding the pole at some arbitrary angle. In case you can’t tell, I’ve drawn a circle to indicate the man on the wall.
There are essentially four forces on this wall climber. There is of course the gravitational force pulling down. Since this force depends on the mass of the object, I will write it as mg where m is the human mass and g is the gravitational field. The other three forces are contact forces from the wall, the pole and the wall again (as friction). Assuming the pole exerts a force only in the direction of the pole, I can break the forces into x and y components and write this as:
Here you can see that the pole pushes both horizontally and vertically with the amount of force dependent upon the angle of the pole. I can get an expression for the magnitude of this pole force, but I will first assume that the static friction pushing up is at its maximum value. This means that the magnitude of the friction force will be:
With this, I can eliminate the friction force from the two equations.
Now I can substitute for N and solve for the pole force.
If I use a human mass of 70 kg and a coefficient of static friction at 0.7 then I can plot the pole-force vs. angle.
Notice that you need the greatest force as the guy on the wall starts his climb, when the pole angle is zero degrees. That’s because you need the largest friction force because the pole pushes only in the horizontal direction. As the fellow climbs the wall, this pole force decreases because he doesn’t require as much friction as the pole helps push him up. The pole force reaches its minimum at a bit more than 50 degrees, but as the angle increases the climber has less friction helping him out. At a pole angle of 90 degrees the pole only supports his weight.
But even at the start of his climb the two guys pushing him need only about 1000 Newtons (just a little bit more than the weight of the climber). So this is clearly feasible. Still, I offer one recommendation: Have the person with the lowest mass climb the wall. That will make everything easier.
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