| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Train with coupled trucks/carriages |
| Difficulty | Moderate -0.3 This is a straightforward connected particles problem requiring standard application of Newton's second law to the system and individual particles. Part (i) uses F=ma on the whole system, part (ii) repeats with changed resistance, and part (iii) isolates one truck—all routine procedures with no conceptual challenges beyond basic mechanics principles. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03o Advanced connected particles: and pulleys |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P - 500 - 300 = 20000 \times 0.2\) | M1 A1 | Apply Newton's second law to whole system |
| \(P = 4800\) N | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(4800 - 500 - 300 - 2000 = 20000a\) | M1 | |
| \(a = 0.1\) m s\(^{-2}\) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| For truck B: \(4800 - 300 - C = 10000 \times 0.1\) | M1 | Apply N2L to truck B alone |
| \(C = 3500\) N (tension) | A1 | cao |
# Question 4:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P - 500 - 300 = 20000 \times 0.2$ | M1 A1 | Apply Newton's second law to whole system |
| $P = 4800$ N | A1 | cao |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $4800 - 500 - 300 - 2000 = 20000a$ | M1 | |
| $a = 0.1$ m s$^{-2}$ | A1 | cao |
## Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| For truck B: $4800 - 300 - C = 10000 \times 0.1$ | M1 | Apply N2L to truck B alone |
| $C = 3500$ N (tension) | A1 | cao |
---4 Two trucks, A and B, each of mass 10000 kg , are pulled along a straight, horizontal track by a constant, horizontal force of $P \mathrm {~N}$. The coupling between the trucks is light and horizontal. This situation and the resistances to motion of the trucks are shown in Fig. 4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{3be85526-3872-42ac-8278-1d4a3cf75ff7-3_205_958_1516_552}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{center}
\end{figure}
The acceleration of the system is $0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ in the direction of the pulling force of magnitude $P$.\\
(i) Calculate the value of $P$.
Truck A is now subjected to an extra resistive force of 2000 N while $P$ does not change.\\
(ii) Calculate the new acceleration of the trucks.\\
(iii) Calculate the force in the coupling between the trucks.
\hfill \mbox{\textit{OCR MEI M1 2007 Q4 [7]}}