Coefficient of restitution and collisionsAQA A-Level Further Maths: Flashcards

What these 13 flashcards ask

Newton's experimental law?
Range of the coefficient of restitution?
What does e=1 mean?
What does e=0 mean?
Two equations for a direct collision?
Newton's law with velocities uA,uB,vA,vB?
Speed of a particle after hitting a fixed smooth wall?
Is momentum conserved when a ball hits a fixed wall?
Fraction of KE lost in a wall impact?
Speed after hitting n identical walls in turn?
Equal masses, A at speed u hits B at rest. Find vA and vB.
When does a second collision occur between two bodies moving in the same direction?
Does the coefficient of restitution depend on the masses?

Exam questions on Coefficient of restitution and collisions

A ball is moving at $8$ m s⁻¹ directly towards a fixed smooth vertical wall. It hits the wall and rebounds directly with speed $5$ m s⁻¹.
After rebounding, the ball hits a second fixed smooth wall, parallel to the first and made of the same material, directly. Find the speed of the ball after it rebounds from the second wall.2 marks
Two smooth spheres $A$ and $B$ , each of mass $m$ , move in the same direction along a straight line on a smooth horizontal surface. $A$ is moving at $5$ m s⁻¹ and $B$ is ahead of it, moving at $1$ m s⁻¹. The spheres collide directly. The coefficient of restitution between them is $0.5$ .
Find, in terms of $m$ , the kinetic energy lost in the collision.2 marks
A particle $P$ of mass $2m$ , moving at $4u$ , collides directly with a particle $Q$ of mass $m$ moving at $u$ in the opposite direction on a smooth horizontal surface. The coefficient of restitution between $P$ and $Q$ is $\frac15$ .
Find the speeds of $P$ and $Q$ after the collision.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).