| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2014 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Oblique collision of spheres |
| Difficulty | Challenging +1.8 This is an oblique collision problem requiring decomposition into components parallel and perpendicular to the line of centres, application of conservation of momentum, Newton's experimental law with restitution coefficient, and energy calculations. While M4 content is advanced, this follows a standard oblique collision framework with straightforward arithmetic given the specific trigonometric values, making it challenging but methodical rather than requiring novel insight. |
| Spec | 6.02d Mechanical energy: KE and PE concepts6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
\includegraphics{figure_1}
Two smooth uniform spheres $A$ and $B$ have equal radii. The mass of $A$ is $m$ and the mass of $B$ is $3m$. The spheres are moving on a smooth horizontal plane when they collide obliquely. Immediately before the collision, $A$ is moving with speed $3u$ at angle $\alpha$ to the line of centres and $B$ is moving with speed $u$ at angle $\beta$ to the line of centres, as shown in Figure 1. The coefficient of restitution between the two spheres is $\frac{1}{5}$. It is given that $\cos \alpha = \frac{1}{3}$ and $\cos \beta = \frac{2}{3}$ and that $\alpha$ and $\beta$ are both acute angles.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of the impulse on $A$ due to the collision in terms of $m$ and $u$. [8]
\item Express the kinetic energy lost by $A$ in the collision as a fraction of its initial kinetic energy. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2014 Q5 [12]}}