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Pearson Edexcel IAL Mathematics M2.4.2 Direct impact of elastic particles

Practise direct collisions of elastic particles using momentum, restitution, energy loss and bounds on e before and after wall rebounds.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • form CLM and Newton restitution equations to find post-collision speeds in terms of u and e
  • apply 0 < e < 1 and direction conditions to find the complete range of e
  • calculate kinetic energy lost in a particle collision after substituting the impact speeds

M2.4.2 - Direct impact of elastic particles question 1

[Maximum number: 3]

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.

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,

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