| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Session | Specimen |
| Marks | 7 |
| Topic | Momentum and Collisions |
| Type | Collision with coefficient of restitution |
| Difficulty | Moderate -0.3 This is a standard mechanics question on impulse and collisions requiring straightforward application of impulse-momentum principles and Newton's experimental law. Part (i) is trivial recall (impulse = Ft), parts (ii-iii) involve routine conservation of momentum and restitution calculations with no conceptual challenges, making it slightly easier than average overall. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Impulse = \(6 \times 1.5 = 9\) N s (units required) | B1 | 1 mark |
| (ii) Let the post-collision velocities of \(A\) and \(B\) be \(u\) and \(v\) respectively | M1 | Use of equations relating impulse and change of momentum |
| (iii) Use of 'speed of separation = \(e \times\) speed of approach' | M1 | Obtain \(e = 0.5\) |
(i) Impulse = $6 \times 1.5 = 9$ N s (units required) | B1 | 1 mark
(ii) Let the post-collision velocities of $A$ and $B$ be $u$ and $v$ respectively | M1 | Use of equations relating impulse and change of momentum | M1 | $0.1 \times 3 - 0.2 = 0.1 \times u$ | A1 | $0.2 \times 1 + 0.2 = 0.2 \times v$ | A1 | Obtain $u = 1, v = 2$ | 4 marks
(iii) Use of 'speed of separation = $e \times$ speed of approach' | M1 | Obtain $e = 0.5$ | A1 | 2 marks\begin{enumerate}[label=(\roman*)]
\item Determine the impulse of a force of magnitude $6$ N that acts on a particle of mass $3$ kg for $1.5$ seconds. [1]
\end{enumerate}
Particles $A$ and $B$, of masses $0.1$ kg and $0.2$ kg respectively, can move on a smooth horizontal table. Initially $A$ is moving with speed $3$ m s$^{-1}$ towards $B$, which is moving with speed $1$ m s$^{-1}$ in the same direction as the motion of $A$. During a collision $B$ experiences an impulse from $A$ of magnitude $0.2$ kg m s$^{-1}$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the speeds of the particles immediately after the collision. [4]
\item Determine the coefficient of restitution between the particles. [2]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 Q10 [7]}}