I don’t know who invented this crazy challenge, but the idea was to put someone in a carved bowl of ice and see if they could get out. Check it out! The bowl is shaped like the inside of a sphere, so the higher the sides you go, the steeper it will be. If you think an icy sidewalk is slippery, try climbing an icy sidewalk.

What do you do when faced with a problem like this? You create a physics model, of course. Let’s start by modeling how people walk on flat ground, and then apply it to a slippery slope. There are actually three possible escape plans, and I’ve used this model to create animations so you can see how it works. So, first things:

How Do People Walk?

When you shuffle from your front door to the mailbox, you probably don’t think about the mechanics involved. You solved that problem when you were young, right? But this is what scientists do: We ask questions that no one stops to wonder.

Speaking of which, are you surprised? why is the ice slippery?? Believe it or not, we don’t know. The direct reason is that it has a thin, watery layer on top. but Why? That liquid film exists even below the freezing point. Physicists and chemists have argued about this for centuries.

However, to start walking, there must be a force in the direction of movement. This is because change in motion is a form of acceleration, and Newton’s second law states that the net force on an object is equal to the product of its mass and its acceleration (F = in). If there is acceleration, there must be a net force.

So what is the force that drives you forward? Well, when you take a step and push off with your back foot, your muscles apply a backward force to the Earth. And Newton’s third law states that every action has an equal and opposite reaction. That means the Earth is moving a ahead-pointing the force back at you, which we call frictional force.

The magnitude of this frictional force depends on two factors: (1) The specific materials in contact, which is obtained by a coefficient (m)—a number usually between 0 and 1, with lower values ​​being more slippery, less grippy. And (2) how hard these surfaces are pushed, which we call the normal force (N).

The normal force is a rather strange concept for physics newbies, so let me explain. normally means perpendicular to the contact surface. It is an upward pushing force that prevents you from sinking to the floor under the force of gravity. If you were standing on level ground, these two forces would be equal and opposite, canceling each other out, so there would be no vertical acceleration.

One last note: There are two different types of frictional coefficients. One is where you have two stationary objects, like a mug of beer on a bar, and you want to know how hard you can push before you can move them. That limit is determined by static friction coefficient (m_s).

Then, when the bartender slides your mug down the bar, the frictional resistance—which determines how far it goes—is determined by kinetic friction coefficient (m_k). It’s usually lower, because it’s easier to keep something moving than it is to start moving.

So now we can calculate the static (F_fs) and kinetic (F_fk) frictional force: