Physics of Rock Climbing: Part I

Welcome to the first of our Physics of Climbing installments. In this series, I will explain rock climbing through the lenses of multiple physics regimes. Today, we’ll begin with classical mechanics, which will show us the most intuitive physical phenomena in climbing.

Since we generally think of classical mechanics as Newtonian mechanics, I am going to introduce a hypothetical climber named Isaac. Let’s jump into Isaac’s experience as a rock climber.

Like the rest of us, Isaac can’t climb forever. He has some amount of energy (perhaps some is from his morning avocado toast), and he needs to use it to get up the wall. Earth exerts gravitational force on Isaac, and so furthering himself from the center of the earth gives him gravitational potential energy. You can think of it as a trade: avocado energy for gravitational potential energy (nothing is free in this world). The heavier Isaac is, the greater the force of gravity on him. However, he will accelerate just as quickly to the ground with any mass…he’s going to hit the crash pad just as fast as he would if he were heavier (neglecting air resistance, of course). We will come back to gravity later, but technically Isaac feels less gravity the higher he climbs…these effects are very small, but in terms of gravity the finish should be easier than the start.

Chalk is very near and dear to most of us, including Isaac. In order for Isaac to climb up rock, he needs friction. The amount of friction he gets is directly proportional how hard the rock pushes back on him. You see, when Isaac puts his foot on a foothold, he applies a force to the rock. Now, the rock isn’t just going to let Isaac’s foot through. It’s going to apply an equal and opposite force to his foot (thanks Newton). So, the harder Isaac pushes down on his foot, the harder the rock pushes back up at him, and the more friction he has on the rock. When Isaac really wants his foot to stay on the wall, he has to press down on it as hard as he can. But this isn’t the only way Isaac can get more friction. Different materials have different friction coefficients; for example, sand paper is very rough, but ice is very slick. If the rock is wet or well polished, Isaac won’t get great friction. There’s not much Isaac can do about how rough the rock is, but he can do something about how rough his hands are. You guessed it: chalk! Isaac has pretty sweaty hands, but when he chalks up, his hands get drier and his hands get some extra particles on them. Consequently, his friction coefficient increases, and he gets more friction. Further, when Isaac is static on a hold, his friction is at a maximum. However, if his hand is moving, he may get less friction. When it comes to friction, static is better than dynamic.

This brings us to our final stop in Newtonian mechanics: ropes. Obviously, Isaac is an avid sport climber, and he knows he has to use a dynamic (not a static) rope. His rope must be able to hold tension between gravity pulling him through a quickdraw and his belayer pulling him back. Much like friction, stretch is different depending on material. Rubber stretches quite a bit, but steel doesn’t stretch so much. When Isaac falls, he wants to be caught, but he also wants to experience this catch over a period of time. If it’s too quick, he’s going to feel a lot of force at once. If it’s longer, he experiences less force over more time. As a human, Isaac needs the latter, so he needs a stretchier rope (dynamic rope).

There’s much more to Newtonian mechanics, but this is a brief overview of how Isaac experiences rock climbing. Stay tuned to meet our other climbers from other areas of physics!