Standard +0.8 This is a moderately challenging mechanics problem requiring systematic application of impulse-momentum principles and energy calculations. While the techniques are standard (conservation of momentum, impulse equations, KE formulas), students must carefully handle signs/directions, solve for post-collision velocities, and perform algebraic manipulation across multiple steps. The 6-mark allocation and need to work with two unknowns (final velocities) while using the given impulse constraint makes this above-average difficulty, though it remains a structured problem without requiring novel insight.
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 \(\frac{5}{2}mu^2\).
[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 $\frac{5}{2}mu^2$.
[6]
\hfill \mbox{\textit{CAIE FP2 2012 Q2 [6]}}