A molecule of mass m travelling at speed v hits a wall in a direction perpendicular to the wall. The collision is elastic.

Question 2

A molecule of mass m travelling at speed v hits a wall in a direction perpendicular to the wall. The collision is elastic.

What are the changes in the kinetic energy and in the momentum of the molecule caused by the collision?

change in momentum             change in kinetic energy

A                      0                                              0

B                      0                                              mv²

C                     2mv                                         0

D                     mv²                                         0

Reference: Past Exam Paper – November 2012 Paper 13 Q12

Solution:

Answer: C.

For an elastic collision, energy is conserved. [B is incorrect]

For any collision, momentum is always conserved.
Momentum of molecule before collision = mv


Thus, after hitting the wall, the molecule should still have the same amount of momentum. However, the molecule would move in the opposite direction after hitting the wall. Since momentum is a vector quantity, we need to account for this change in sign. Thus,

Momentum of molecules after collision = – mv


Change in momentum = final momentum – initial molecule
Change in momentum = (– mv) – mv = (–) 2mv 

For the change in momentum, the sign may be neglected.