January 17, 2019
I’m not sure what it is, but something keeps drawing me into physical competition shows. It used to be [Ninja Warrior](https://www.wired.com/2016/06/physics-favorite-ninja-warrior-stunts/), but now there is a new one—Titan Games. It’s essentially a competition with different crazy events. It’s not the competition that I like, it’s those weird situations that they put these people in. I just like it.
Of course I can’t just watch the show. I have to do some type of physics thing—because that’s who I am and what I do.
Now for the event. It’s called the Lunar Impact. The only thing in the event that is related to the moon is the curved walkway the contestants are on. After climbing up to this 30-foot-high platform, the two people push on a moveable wall. The goal is to push the wall so far that the other human falls off the “moon walk.”
I’m not going to tell you how to win this battle, I am just going to point out one of the most important factors in a win—friction. Oh sure, you still need to push. You still need to be strong and to wear down the other person. But if you have all this and you don’t have friction, you lose.
Friction is pretty complicated. Just think about it. If you have two surfaces in contact, there is an interaction between some of the surface atoms in one material and the atoms in the other material. Even for small surfaces, this is a ginormous number of interactions. It’s too many atoms to deal with. Instead of dealing with billions and billions of things, we make a simpler model. That’s really what physics is all about—models.
Let’s go over the static friction model by starting with some simple experiments. Take a block and put it on a table. Now push it horizontally (but don’t let it move). Maybe it looks like this.
Since the block is at rest, the total force on it must be zero. There are actually four forces to look at here.
- The downward gravitational force (depends on the gravitational field and the mass of the block).
- The upward force from the table (we call this the normal force—N).
- The sideways pushing force from the finger.
- There MUST be a backwards pushing force to cancel the finger force. This is the static friction force.
OK, time for the next experiment. What happens if you push DOWN on the block while also pushing sideways? Here is what that would look like.
You might notice something different in this case. You should be able to push horizontally with a greater force and the block still won’t move. So, what changed? Since there is now an extra force pushing down (from the top finger), the table (normal force) has to push up with an even greater force to keep the total vertical force at zero. Now we can see the connection. The greater this normal force (from the table), the greater the maximum frictional force.
But wait! There is one other important thing to consider with this frictional model. What if I push horizontally with my finger with a force of 1 Newton (pretend there is a readout on my finger) and the block doesn’t move? That must mean that the frictional force is also 1 Newton. Now suppose I push with 2 Newtons and the block doesn’t move? The frictional force would then have to be 2 Newtons to keep up with the finger. But what if the frictional force STAYED at 2 Newtons and I only pushed with 1 Newton? In this case, the net force would be against the finger and it the block would accelerate in a direction opposite the push. That would be crazy.
This means that for static friction, there is a maximum frictional force but no minimum. The frictional force has a magnitude of whatever it needs to keep the two surfaces stationary—up to some maximum amount. With that, I can now write a mathematical model for the magnitude of a frictional force.
Let’s go over each part of this equation—just to be clear. On the left is the magnitude of the friction force. Notice that forces are vectors, but this is just the magnitude. This is because the frictional force and the normal force (N) are in different directions. That means you can’t make a simple relationship between the two values. Next is the “less than or equal to” sign. This just means that the static frictional force cannot be more than the right side of the expression—but it can be less. Finally, the two other values are μs (the coefficient of static friction) and N (the normal force). The coefficient of static friction is just a value for the two types of surfaces interacting (like rubber and steel).
OK, but what does all of this have to do with the Lunar Impact? Yes, let’s get to that. If I assume a completely frictionless wall, this would be a force diagram for two people trying to win the battle.
This diagram is a little busy, so let me just point out a few things. The red box is the bigger human (if they were the same size it would be boring). Although the red human pushes to the LEFT on the wall, the wall pushes back to the RIGHT. Whichever human has a larger wall force would “win” assuming all other things are equal. The way to get the biggest wall force is to have the biggest frictional force. And here is the important point. The red human has a bigger mass and bigger gravitational force leading to a larger normal force. If both humans have similar strength, the red human wins. It’s just physics.
OK, I am assuming the two humans have similar shoes. If one of them decides to wear leather-bottomed shoes, they are just not worthy of being a Titan. (I am assuming that leather-bottomed shoes would have a much lower coefficient of friction than normal rubber-bottomed shoes.)
But wait! There is another way to win against a more massive person. The key is to get a greater frictional force. The only way (other than changing shoes) to get this greater force is to increase the normal force. You can’t change your mass, but there is something you can do. Check out this modified wall-push diagram.
What’s different in this case? The blue human isn’t pushing horizontally on the wall. Instead, Blue Human is pushing up and to the right. This means the wall pushes back on the human down and to the left (as indicated by the force arrow). Since there is a downward component to the wall force, that means the normal force has to be even greater than just the weight. A greater normal force means the maximum static frictional force is also greater. Now the blue human can have a fighting chance. Oh, sure that also means pushing a lot harder on the wall. But at least the competition won’t be only in the hands of physics.
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