| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 13 |
| 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 M1 momentum and friction problem requiring conservation of momentum, impulse calculation, and friction equations. All steps are routine applications of standard formulas with straightforward arithmetic. The multi-part structure and combination of collision + friction topics makes it slightly above average difficulty, but no novel insight is required. |
| Spec | 3.03v Motion on rough surface: including inclined planes6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Impulse \(= 0.2 \times 3 = 0.6 \text{ Ns}\) | M1 A1 B1 | |
| (b) \(200 \times 5 - 4k = 200 \times 2 + 5k\); \(9k = 600\); \(k = 66\frac{2}{3}\) | M1 A1 A1 | |
| (c) \(v = u + at: 0 = 5 + 3a\); \(a = -\frac{2}{3}\); \(\mu g = \frac{2}{3}\); \(\mu = 0.170\) | M1 A1 M1 A1 | |
| (d) \(v^2 = u^2 + 2as: 0 = 4 + 2(-\frac{2}{3})s\); \(s = 1.2 \text{ m}\) | M1 A1 A1 | 13 marks |
(a) Impulse $= 0.2 \times 3 = 0.6 \text{ Ns}$ | M1 A1 B1 |
(b) $200 \times 5 - 4k = 200 \times 2 + 5k$; $9k = 600$; $k = 66\frac{2}{3}$ | M1 A1 A1 |
(c) $v = u + at: 0 = 5 + 3a$; $a = -\frac{2}{3}$; $\mu g = \frac{2}{3}$; $\mu = 0.170$ | M1 A1 M1 A1 |
(d) $v^2 = u^2 + 2as: 0 = 4 + 2(-\frac{2}{3})s$; $s = 1.2 \text{ m}$ | M1 A1 A1 | 13 marks\begin{enumerate}
\item Two model cars $A$ and $B$ have masses 200 grams and $k$ grams respectively. They move towards each other in a straight line and collide directly when their speeds are $5 \mathrm {~ms} ^ { - 1 }$ and $4 \mathrm {~ms} ^ { - 1 }$ respectively. As a result the speed of $A$ is reduced to $2 \mathrm {~ms} ^ { - 1 }$, in the same direction as before. The direction of $B$ 's motion is reversed and its speed immediately after the impact is $5 \mathrm {~ms} ^ { - 1 }$.\\
(a) Find the magnitude of the impulse exerted by $A$ on $B$ in the impact. State the units of your answer.\\
(b) Find the value of $k$.
\end{enumerate}
The surface on which the cars move is rough, and $B$ comes to rest 3 seconds after the impact. The coefficient of friction between both cars and the surface is $\mu$.\\
(c) Find the value of $\mu$.\\
(d) Find the distance travelled by $A$ after the impact before it comes to rest.\\
\hfill \mbox{\textit{Edexcel M1 Q5 [13]}}