Some Piles Of Snow Are Dangerous. Some Are Safe. What Is The difference?

The snow in the picture above is in stable equilibrium as opposed to before it fell when it was in an unstable equilibrium.

When we look around in our daily lives we see things both moving and standing still. Objects that are still and remain so are in equilibrium with their surroundings. There are three types of equilibrium and to understand the difference it is helpful to visualize a particular system. Let’s consider our system as a snowboarder on a halfpipe.

Ihalfpipe

If the snowboarder is on the curved side of the halfpipe then they cannot remain still, as they will begin to accelerate towards the center due to gravity. However, at the bottom of the halfpipe they will remain still if they start that way. Thus a still snowboarder at the bottom of the halfpipe is in equilibrium. Similarly, if the snowboarder is right on the top edge of the halfpipe they can balance there and remain still. Thus a snowboarder right at the top edge can also be in equilibrium.

These two types of equilibrium are different in one important way. If I slightly push a snowboarder at the bottom of the half-pipe they will move a tiny bit but stay pretty much where they are. Therefore the snowboarder at the bottom is in stable equilibrium: an infinitesimal displacement doesn’t change the situation. This is not true for the snowboarder balanced on the top. A small push towards the center will send the snowboarder down through the halfpipe and to the other side. Thus the snowboarder at the top edge is in unstable equilibrium: an infinitesimal displacement changes the situation drastically. This is the situation in an avalanche. The snow at the top of the mountain is very precariously balanced and even a tiny displacement, like that due to a loud sound, can trigger a massive shift in the snow.

There’s a third type of equilibrium, and that is a metastable equilibrium. Note that one way to think about the equilibria above is to think of the graph of the gravitational potential energy as a function of position. The potential energy has a minimum in the center of the halfpipe, and that is where the point of stable equilibrium occurs. Metastable equilibria occur when there is more than one minimum of the potential energy graph. In this case, small pushes on an object at one minimum won’t do anything, but a large push can make the object move to the other minimum. The halfpipe configuration that would give metastable equilibrium would be if the bottom of the halfpipe looked like the following:

Imgur

Here the snowboarder at point 1 would not move unless given a push, and is stable under small pushes. However a large enough push will move the snowboarder over the bump (point 2) and into the other equilibrium point (point 3). Hence point 1 is a metastable equilibrium, point 2 is unstable, and point 3 is stable.

Metastable equilibria become very important once you toss quantum mechanics into the mix, as a quantum mechanical system will always eventually move to the lowest possible energy state - you don’t even need a push!

Further exploration: If I could balance a pencil right on its tip, that would be an unstable equilibrium. This problem shows how even small displacements eventually change the situation dramatically.

its somewhat easy if u eliminate options ....we know that there is almost no equilliburium for moving objects...but in this pic the snow is at rest. the snow is at unstable equiluiburium at the time of avalanche...but in the pic it is shown at post-avalanche session....so it has stable equliburium....

It's an avalanche--after it's already happened. Therefore it's in a stable equilibrium because there is no threat of it crashing down and killing you.