ConceptConceptDocsDocuments

Edexcel IAL Mathematics M2.4 collisions

Practise M2 collisions by combining momentum, impulse, restitution, kinetic energy loss and wall rebounds in one- or two-particle models.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • Pair conservation of momentum with restitution to find post-collision speeds or ranges for e.
  • Use impulse as change in momentum, including vector components and wall rebounds.
  • Check second-collision conditions by comparing rebound speeds after applying f or e.

Covered syllabus points

M2.4.1 - Momentum as a vectorM2.4.2 - Direct impact of elastic particlesM2.4.3 - Successive impacts of up to three

M2.4 - Collisions question 1

[Maximum number: 14]

Particle P has mass 4 m and particle Q has mass 2 m.

The particles are moving in opposite directions along the same straight line on a smooth horizontal surface.

Particle P collides directly with particle Q.
Immediately before the collision, the speed of P is 2 u and the speed of Q is 3 u.
Immediately after the collision, the speed of P is x and the speed of Q is y.
The direction of motion of each particle is reversed as a result of the collision.
The total kinetic energy of P and Q after the collision is half of the total kinetic energy of P and Q before the collision.

Question (a)

(a)

Show that y=83uy=\frac{8}{3} u

The coefficient of restitution between P and Q is e.

[ 6 ]

Question (b)

(b)

Find the value of e.

After the collision, Q hits a smooth fixed vertical wall that is perpendicular to the direction of motion of Q.

Particle Q rebounds.
The coefficient of restitution between Q and the wall is f.
Given that there is no second collision between P and Q,

[ 3 ]

Question (c)

(c)

find the range of possible values of f.

Given that f=14f=\frac{1}{4}

[ 3 ]

Question (d)

(d)

find, in terms of m and u, the magnitude of the impulse received by Q as a result of its impact with the wall.

[ 2 ]
All question bank results loaded