I don’t know who came up with this crazy challenge, but the idea is to put someone in a carved bowl of ice and see if they can get out. Check it out! The bowl is shaped like the inside of a ball, so the higher up the sides you are, the steeper it gets. If you think an icy sidewalk is slippery, try driving uphill on the icy sidewalk.
What do you do when you face such a problem? Of course you build a physical model. We’ll start by modeling how people walk on flat ground and then apply that to a slippery slope. There are actually three possible escape plans, and I used this model to generate an animation so you can see how they work. So first:
How do people walk?
When you move from your front door to your mailbox, you probably don’t think about the mechanics involved. You solved this problem when you were a little kid, right? But that’s what scientists do: we ask questions that no one has thought about.
Speaking of which, have you ever wondered why ice is slippery? Believe it or not, we don’t know. The immediate reason is that it forms a gaunt, watery layer on the surface. But Why? This liquid film exists even below the freezing point. Physicists and chemists have been arguing about this for centuries.
Either way, 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 states that the net force on an object is equal to the product of its mass and 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 exert a backward force on the Earth. Newton’s third law states that every action produces an equal and opposite reaction. This means that the Earth has an influence forward-directing the force back at you, which is called the force of friction.
The magnitude of this friction force depends on two things: (1) The specific materials in contact, which is captured by the coefficient (M) – A number usually ranging from 0 to 1, with lower values indicating more slipperiness and less traction. And (2) how difficult these surfaces are pressed together, which is called the normal force (N).
The normal force is a pretty strange concept for those novel to physics, so let me explain. Normal means perpendicular to the contact surface. This is the upward pushing force that prevents you from falling through the floor due to gravity. If you are standing on flat ground, these two forces will be equal and opposite, canceling each other, so there will be no vertical acceleration.
One final note: there are two types of friction coefficients. The first is when you have two stationary objects, say a pint on a bar, and you want to know how difficult you can push before causing it to move. This limit is specified in Art stagnant friction coefficient (MS).
Then, as the bartender slides your cup down the bar, the frictional resistance – which determines how far it goes – is determined by kinetic friction coefficient (Mk). This is usually lower because it is easier to keep something moving than to get it moving.
Now we can quantify the stagnant (Ffs) and kinetic (Ffk) friction forces: