Edexcel FM1 2022 June — Question 1 8 marks

Exam BoardEdexcel
ModuleFM1 (Further Mechanics 1)
Year2022
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMomentum and Collisions 1
TypeDirect collision with given impulse
DifficultyStandard +0.3 This is a standard Further Mechanics collision problem requiring impulse-momentum relationships and conservation of momentum. While it involves algebraic manipulation and solving a quadratic, the techniques are routine for FM1 students with no novel insight required. The two-part structure and need to consider direction makes it slightly above average difficulty.
Spec6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation6.03i Coefficient of restitution: e6.03k Newton's experimental law: direct impact

  1. A particle \(A\) of mass \(3 m\) and a particle \(B\) of mass \(m\) are moving along the same straight line on a smooth horizontal surface. The particles are moving in opposite directions towards each other when they collide directly.
Immediately before the collision, the speed of \(A\) is \(k u\) and the speed of \(B\) is \(u\). Immediately after the collision, the speed of \(A\) is \(v\) and the speed of \(B\) is \(2 v\). The magnitude of the impulse received by \(B\) in the collision is \(\frac { 3 } { 2 } m u\).
  1. Find \(v\) in terms of \(u\) only.
  2. Find the two possible values of \(k\).

\begin{enumerate}
  \item A particle $A$ of mass $3 m$ and a particle $B$ of mass $m$ are moving along the same straight line on a smooth horizontal surface. The particles are moving in opposite directions towards each other when they collide directly.
\end{enumerate}

Immediately before the collision, the speed of $A$ is $k u$ and the speed of $B$ is $u$. Immediately after the collision, the speed of $A$ is $v$ and the speed of $B$ is $2 v$.

The magnitude of the impulse received by $B$ in the collision is $\frac { 3 } { 2 } m u$.\\
(a) Find $v$ in terms of $u$ only.\\
(b) Find the two possible values of $k$.

\hfill \mbox{\textit{Edexcel FM1 2022 Q1 [8]}}