| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2015 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Oblique collision, find velocities/angles |
| Difficulty | Challenging +1.8 This is a challenging M4 oblique collision problem requiring resolution along/perpendicular to line of centres, Newton's experimental law, conservation of momentum, and solving simultaneous equations with the constraint that speed of A = 2×speed of B after collision. Requires systematic multi-step approach and algebraic manipulation beyond standard textbook exercises, but follows established M4 techniques. |
| Spec | 6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
Two smooth uniform spheres A and B with equal radii have masses $m$ and $2m$ respectively. The spheres are moving in opposite directions on a smooth horizontal surface and collide obliquely. Immediately before the collision, A has speed $3u$ with its direction of motion at an angle $\theta$ to the line of centres, and B has speed $u$ with its direction of motion at an angle $\theta$ to the line of centres. The coefficient of restitution between the spheres is $\frac{1}{8}$.
Immediately after the collision, the speed of A is twice the speed of B.
Find the size of the angle $\theta$.
(12 marks)
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{44066c44-e366-4f87-b1b2-c5a894e407fa-08_350_1123_258_408}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Two smooth uniform spheres $A$ and $B$ with equal radii have masses $m$ and $2 m$ respectively. The spheres are moving in opposite directions on a smooth horizontal surface and collide obliquely. Immediately before the collision, $A$ has speed $3 u$ with its direction of motion at an angle $\theta$ to the line of centres, and $B$ has speed $u$ with its direction of motion at an angle $\theta$ to the line of centres, as shown in Figure 1. The coefficient of restitution between the spheres is $\frac { 1 } { 8 }$
Immediately after the collision, the speed of $A$ is twice the speed of $B$.\\
Find the size of the angle $\theta$.\\
\hfill \mbox{\textit{Edexcel M4 2015 Q3 [12]}}