| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2004 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Collision with friction after impact |
| Difficulty | Moderate -0.3 This is a standard two-part M1 mechanics question combining conservation of momentum with equations of motion. Part (a) requires straightforward application of momentum conservation with given relationships between velocities. Part (b) uses work-energy theorem or SUVAT equations with known values. While it requires multiple steps and careful sign conventions, it follows a predictable template with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.03b Conservation of momentum: 1D two particles |
| Answer | Marks |
|---|---|
| 3 | u |
Question 3:
3 | u
2 k g 4 k g CLM: 2u = –2v + 4w M1 A1
↓
v w Using w = 3v (⇒ 2u = –2v + 12v) and solve M1
⇒ v = 1u (*) A1 cso
5
(4)
(b) 10 = 2a ⇒ a = 5 m s–2 B1
0 = 1 u2 – 2 x 5 x 1.6 M1 A1√
25
↓
→ u = 20 m s–1 M1 A1
(5)
(a) 1st M1 for valid CLM equn
2nd M1 for correct equn for ‘v’ and ‘w’ and solving for v or w.
Final A1 is cso (dropping u and reinserting loses last A1)
(b) Allow B1 for a = ± 5
M1 for using ‘v2 = u2 + 2as’ with v = 0 and with a value for a
A1 f.t. on their a (provided this is not g), but signs must be correct
SC For using u instead of u/5 ( u = 4), allow M1 A0 M0.
Energy: ½ x 2 x (u/5)2 = 10 x 1.6 M1 A1 A1
→ u = 20 dep M1 A1A particle $P$ of mass $2$ kg is moving with speed $u$ m s$^{-1}$ in a straight line on a smooth horizontal plane. The particle $P$ collides directly with a particle $Q$ of mass $4$ kg which is at rest on the same horizontal plane. Immediately after the collision, $P$ and $Q$ are moving in opposite directions and the speed of $P$ is one-third the speed of $Q$.
\begin{enumerate}[label=(\alph*)]
\item Show that the speed of $P$ immediately after the collision is $\frac{1}{5}u$ m s$^{-1}$. [4]
\end{enumerate}
After the collision $P$ continues to move in the same straight line and is brought to rest by a constant resistive force of magnitude $10$ N. The distance between the point of collision and the point where $P$ comes to rest is $1.6$ m.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Calculate the value of $u$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2004 Q3 [9]}}