Question

We look at a collision between two identical atoms that form a molecule in the process. We assume that each atom has mass ? and can be considered as a point particle.
We assume that all external forces are small relative to the forces between the atoms. We therefore do not need to take
consideration of some external forces.

We begin with a simplified model where the connection is instant (without spring). Atom A moves in ?direction in distance ? = ? from axis at speed ?₀. Atom B is at rest
at origin. There is no force between the atoms until atom A arrives at position ?⃗ = ??̂. At this moment the atoms are joined together, and the atoms remain at a fixed distance ? to each other. We assume the link between the atoms in the molecule is rigid (without springs).

a) Find the velocity of the mass center of the molecule and the angular velocity around the mass center
after pairing. Explain the procedure and justify your answer.

We try to make the model more realistic by connecting the atoms through a massless
spring with spring constant ? and equilibrium length ?. Atom A moves in the x-drection in the distance ? = ?
from the axis at speed ?₀, while atom B is at rest at origin. The pairing occurs when atom A arrives
to position ?⃗ = ??̂. The atoms remain connected through the spring afterwards.

(b) Write down the expressions for the forces ?⃗ _AB and ?⃗_BA from A to B and vice versa
using distance vector Δ?⃗ = ?⃗_B- ?⃗_A, distance | Δ?⃗ |, equilibrium length ? and spring constant ?.
Check that the force vectors ?⃗_AB and ?⃗_BA has the right direction.

Answer 1