| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 18 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Train with coupled trucks/carriages |
| Difficulty | Standard +0.3 This is a standard connected particles question with multiple parts requiring Newton's second law applications. While it involves several steps and different scenarios (horizontal, uphill, downhill), each part follows routine mechanics procedures: resolving forces, applying F=ma, and finding tensions by considering subsystems. The calculations are straightforward with clean numbers, and the problem structure is typical of M1 textbook exercises. Slightly above average difficulty due to the multiple parts and need to consider different configurations, but no novel insight required. |
| Spec | 3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| Closed triangle with cycling arrows, all forces labelled (\(W\), \(S\), \(R\)), correct angles with 90° shown | B1, B1, B1 | Accept any consistent orientation; \(\alpha\) may be shown between \(S\) and the horizontal; SC1 for force diagram with no extra forces and all labels/directions correct |
| Answer | Marks | Guidance |
|---|---|---|
| \(R = W\cos\alpha\) | B1 | Allow FT for sin-cos interchange following wrong angle in triangle |
| \(S = W\sin\alpha\) | B1 | SC1 if both \(S\) and \(R\) are given negative signs |
| Answer | Marks | Guidance |
|---|---|---|
| Sketch graph of \(R\) against \(\alpha\) (decreasing curve from \(W\) to 0) | B1 | Condone no explicit vertical scale; do not accept straight lines |
| Correct sketch graph of \(S\) against \(\alpha\) (increasing curve) | B1 | Must be consistent with graph of \(R\) |
| \(45° < \alpha\ (\leq 90°)\) | B1 | Condone \(45° \leq \alpha\) |
## Question 2:
### Part (i)
Closed triangle with cycling arrows, all forces labelled ($W$, $S$, $R$), correct angles with 90° shown | B1, B1, B1 | Accept any consistent orientation; $\alpha$ may be shown between $S$ and the horizontal; SC1 for force diagram with no extra forces and all labels/directions correct
### Part (ii)
$R = W\cos\alpha$ | B1 | Allow FT for sin-cos interchange following wrong angle in triangle
$S = W\sin\alpha$ | B1 | SC1 if both $S$ and $R$ are given negative signs
### Part (iii)
Sketch graph of $R$ against $\alpha$ (decreasing curve from $W$ to 0) | B1 | Condone no explicit vertical scale; do not accept straight lines
Correct sketch graph of $S$ against $\alpha$ (increasing curve) | B1 | Must be consistent with graph of $R$
$45° < \alpha\ (\leq 90°)$ | B1 | Condone $45° \leq \alpha$
---2 A train consists of a locomotive pulling 17 identical trucks.\\
The mass of the locomotive is 120 tonnes and the mass of each truck is 40 tonnes. The locomotive gives a driving force of 121000 N .
The resistance to motion on each truck is $R \mathrm {~N}$ and the resistance on the locomotive is $5 R \mathrm {~N}$.\\
Initially the train is travelling on a straight horizontal track and its acceleration is $0.11 \mathrm {~ms} ^ { - 2 }$.
\begin{enumerate}[label=(\roman*)]
\item Show that $R = 1500$.
\item Find the tensions in the couplings between\\
(A) the last two trucks,\\
(B) the locomotive and the first truck.
The train now comes to a place where the track goes up a straight, uniform slope at an angle $\alpha$ with the horizontal, where $\sin \alpha = \frac { 1 } { 80 }$.
The driving force and the resistance forces remain the same as before.
\item Find the magnitude and direction of the acceleration of the train.
The train then comes to a straight uniform downward slope at an angle $\beta$ to the horizontal.\\
The driver of the train reduces the driving force to zero and the resistance forces remain the same as before.
The train then travels at a constant speed down the slope.
\item Find the value of $\beta$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI M1 Q2 [18]}}