Question

A particle with total energy E is moving in a potential energy region U(x). Motion of the particle is restricted to the region when?

1. U(x) > E
2. U(x) < E
3. U(x) = 0
4. U(x) ≤ E

Answer 1

1

Explanation:

We can imagine a "potential well" which is basically a big net that an object - like a cat - sits in.

When it has minimum energy, the cat is pretty much just sitting at the bottom of the well, no motion. But then, if it gets excited, it starts to run around, climbing up the wall. It obviously can't go too high up unless it has a ton of energy, so because its energy is less than the energy of the potential well's energy, the cat is stuck.

So a particle is stuck in a potential well if it doesn't have enough energy to escape, i.e. when U(x) > E.

As a sidenote, this is not true if we talk about actual subatomic particles, as they have a thing called quantum teleportation that can get them out of potential wells since they can basically teleport out. It's really cool but not really important here.