Graph all the things
analyzing all the things you forgot to wonder about
A bollard is a thick metal post used a piers for mooring ships. Sailors often don't tie their ship's rope directly to the bollard - instead they wrap a rope around the bollard, then tie the rope to something else.
You may be wondering if the bollard it the most
boring amazing thing you have ever heard of. It isn't, but if you wrap a rope around one just three times, a pencil could hold your ship in place.
This works for the same reason why belaying a rock climber makes any sense.
If an object is pushed into a surface with force , the force required to make it move is
If the tension (force pulling) on the right section of rope is , then the vertical component of this force is . Since is very small, the left side of the rope has a similar tension, . That means the force of friction resisting the rope's motion is about . It also means that , so the force of friction is really just
Usually people rock climb in pairs: a belayer and a climber. They are connected by a rope going through various metal draws. If the climber falls, the rope will grow taut on the uppermost draw as the belayer's weight stops the fall.
If the rope were frictionless and the climber were heavier than the belayer, this would not happen; the climber's tender brains would continue to plummet toward the rocky floor. The only thing preventing such a tragedy is the friction between the draw and the rope: when the rope grows taut, it will be wrapped around 180 of metal. Climbing ropes are relatively smooth with a kinetic coefficient of friction of . Nevertheless, that is still high enough to reduce the tension on the belayer's side of the rope to only half as much as the tension on the climber's side. In principle, someone half your weight could belay you (though your fall might be quite long before it ends), and this is all due to the exponential way that tension decreases along a rope that is wrapped. I thought that was cute.