Successive impactsEdexcel International A Level Further Maths: Flashcards

What these 12 flashcards ask

A particle hits a fixed wall at right angles with speed u. What is its rebound speed?
Which equation gives the speed after impact with a fixed wall?
What is the impulse of a wall on a particle that rebounds with speed eu?
Kinetic energy lost when a particle hits a wall with speed u?
What two equations do you use for each collision between particles?
After a particle rebounds from a wall, which direction is its velocity?
When will two particles moving in the same direction collide again?
How do you carry on in a problem with several collisions?
Why do you need a single positive direction for the whole problem?
What is the condition for no further collisions between particles in a line?
After A hits B and B rebounds from the wall, what must you check?
Does a wall collision change the total momentum of the particle?

Exam questions on Successive impacts

A particle of mass $0.4$ kg moves with speed $12$ m s $^{-1}$ along smooth horizontal ground directly towards a fixed smooth vertical wall, hitting the wall at right angles. The coefficient of restitution between the particle and the wall is $\frac23$ .
Find the magnitude of the impulse exerted by the wall on the particle.2 marks
Particles $A$ and $B$ have masses $2$ kg and $1$ kg. They lie on smooth horizontal ground in a straight line perpendicular to a fixed smooth vertical wall, with $B$ between $A$ and the wall. Particle $A$ is projected towards $B$ with speed $6$ m s $^{-1}$ . The coefficient of restitution between $A$ and $B$ is $\frac12$ , and between $B$ and the wall is $\frac13$ .
Explain why there must be a second collision between $A$ and $B$ .2 marks
Three particles $A$ , $B$ and $C$ , of masses $4$ kg, $2$ kg and $3$ kg, lie at rest in a straight line on smooth horizontal ground, with $B$ between $A$ and $C$ . Particle $A$ is projected towards $B$ with speed $6$ m s $^{-1}$ . The coefficient of restitution between any two of the particles is $\frac12$ .
Show that, immediately after the first collision, $A$ has speed $3$ m s $^{-1}$ and $B$ has speed $6$ m s $^{-1}$ .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).