Standard +0.8 This is a moderately challenging mechanics problem requiring systematic application of impulse-momentum principles, careful sign convention handling, and algebraic manipulation through multiple steps. While the techniques are standard for Further Maths, the need to work with impulse magnitude (requiring consideration of two cases), find both final velocities, calculate initial and final KE, and simplify to the given answer makes this more demanding than a routine collision question.
Two particles, of masses \(3m\) and \(m\), are moving in the same straight line towards each other with speeds \(2u\) and \(u\) respectively. When they collide, the impulse acting on each particle has magnitude \(4mu\). Show that the total loss in kinetic energy is \(\frac{4}{5}mu^2\). [6]
Two particles, of masses $3m$ and $m$, are moving in the same straight line towards each other with speeds $2u$ and $u$ respectively. When they collide, the impulse acting on each particle has magnitude $4mu$. Show that the total loss in kinetic energy is $\frac{4}{5}mu^2$. [6]
\hfill \mbox{\textit{CAIE FP2 2012 Q2 [6]}}