A particle of mass m, travelling with speed u, collides with a stationary particle of mass M.

Question 18

A particle of mass m, travelling with speed u, collides with a stationary particle of mass M. The velocities of the two particles before and after the collision are shown.

Which vector diagram correctly shows the momenta before and after the collision?

Reference: Past Exam Paper – March 2016 Paper 12 Q10

Solution:

Answer: B.

This question is on collisions in 2D.

 

(Momentum = mass × velocity)

From the conservation of momentum,

Sum of momentum before collision = Sum of momentum after collision

Sum of momentum before collision = mu + 0 = mu

Momentum is a vector quantity and so, we need to account for the direction.

Before the collision, the momentum is mu horizontally to the right.

From the conservation of momentum, adding the momenta of the 2 particles after collision should give a resultant = mu horizontally to the right

After collision,

Momentum of particle m = mu / 2 at an angle β below the horizontal

Momentum of particle M = Mu / 3 at an angle α above the horizontal

mu = Sum of momentum after collision

Consider the options available.

Option A: The momenta are at the wrong angles. [incorrect]

Option B: correct

Option C: wrong angles + the negative of the momentum vectors have been taken (the direction of the vectors are opposite than they should be) [incorrect]

Option D: the negative of the momentum vectors have been taken [incorrect]