| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Collision with friction after impact |
| Difficulty | Standard +0.3 This is a standard two-part mechanics question combining conservation of momentum (routine application) with friction/kinematics (straightforward use of equations of motion). Part (a) is a direct momentum calculation with given final velocity for A. Part (b) requires working backwards from stopping distance using v² = u² + 2as and F = μR, but follows a well-practiced procedure. The 'show that' format and multi-step nature elevate it slightly above the most basic M1 questions, but it remains a textbook-style problem requiring no novel insight. |
| Spec | 3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model6.03b Conservation of momentum: 1D two particles |
| Answer | Marks | Guidance |
|---|---|---|
| \(2m = 3mv\) so \(v = \frac{2}{3}\) ms\(^{-1}\) | M1 | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\mu = \frac{10}{9g} = 0.113\) (3dp) | M1 | M1 A1 |
**(a)** cons. of mom. $4m \times 2 - 3m \times 2 = 0 + 3mv$
$2m = 3mv$ so $v = \frac{2}{3}$ ms$^{-1}$ | M1 | M1 A1 |
**(b)** $R = mg$, $F = ma$
but $F = \mu R$, so $a = \frac{-\mu R}{m} = \frac{-\mu mg}{m} = -\mu g$
use with $u = \frac{2}{3}, v = 0, s = 0.2$
$v^2 = u^2 + 2as$ ∴ $0 = \frac{4}{9} - 0.4\mu g$
$\mu = \frac{10}{9g} = 0.113$ (3dp) | M1 | M1 A1 | M1 | M1 | M1 A1 | (10) |
---In a physics experiment, two balls $A$ and $B$, of mass $4m$ and $3m$ respectively, are travelling towards one another on a straight horizontal track. Both balls are travelling with speed 2 m s$^{-1}$ immediately before they collide.
As a result of the impact, $A$ is brought to rest and the direction of motion of $B$ is reversed.
Modelling the track as smooth and the balls as particles,
\begin{enumerate}[label=(\alph*)]
\item find the speed of $B$ immediately after the collision. [3 marks]
\end{enumerate}
A student notices that after the collision, $B$ comes to rest 0.2 m from $A$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Show that the coefficient of friction between $B$ and the track is 0.113, correct to 3 decimal places. [7 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [10]}}