I don’t know who invented this crazy challenge, but the idea is to put someone in a sculpted bowl of ice cream and see if they can get out. Check it out! The bowl is shaped like the inside of a sphere, so the higher you go up the sides, the steeper it becomes. If you think an icy sidewalk is slippery, try getting on an icy sidewalk.
What to do when faced with a problem like this? You are of course building a physical model. We’ll start by modeling how people walk on flat terrain, then apply it to a slippery slope. There are actually three possible escape plans, and I used this template to generate animations so you can see how they work. So, first of all:
How do people walk?
When you walk from your front door to the mailbox, you probably don’t think about the mechanics involved. You solved this problem when you were little, didn’t you? But that’s what scientists do: we ask questions that no one has ever asked.
Speaking of which, have you ever wondered why is ice slippery? Believe it or not, we don’t know. The direct reason is that it has a thin watery layer on the surface. But Why? This liquid film exists even below freezing point. Physicists and chemists have been discussing this for centuries.
Regardless, to start walking, there must be a force in the direction of movement. This is because changing motion is a type of acceleration and Newton’s second law says that the net force exerted on an object is equal to the product of its mass and its acceleration (F = enabled). If there is acceleration, there must be a net force.
So what is this force that pushes 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 says that every action has an equal and opposite reaction. This means that the Earth exerts a Before-point a force at you, which we call a friction force.
The magnitude of this frictional force depends on two things: (1) The specific materials in contact, which are captured in a coefficient (m): a number generally between 0 and 1, with lower values being more slippery and less grippy. And (2) the force with which these surfaces are pushed together, what we call the normal force (N).
Normal force is a rather strange concept for physics beginners, so let me explain. Normal means perpendicular to the contact surface. This is an upward pushing force that prevents you from plunging through the ground under gravity. If you stand on flat ground, these two forces will be equal and opposite, thus canceling each other out, so there will be no vertical acceleration.
One final note: there are two types of friction coefficients. The first is where you have two stationary objects, like a beer mug on a bar, and you want to know how hard you can push before you make it move. This limit is determined by the static coefficient of friction (ms).
Then, when the bartender slides your cup across the bar, the resistance to friction, which determines how far it goes, is determined by the kinetic coefficient of friction (mk). This number is usually lower, because it’s easier to keep something moving than to get it started.
So now we can quantize the statics (Ffs) and kinetics (Ffk) friction forces:
