| Exam Board | OCR MEI |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2021 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Train with coupled trucks/carriages |
| Difficulty | Moderate -0.8 This is a straightforward connected particles question with clear setup: apply F=ma to the whole system for acceleration, then isolate the head to find tension. The calculations are simple (converting grams to kg, basic arithmetic with given forces), and the method is standard textbook procedure requiring no problem-solving insight—easier than average A-level mechanics. |
| Spec | 3.03a Force: vector nature and diagrams3.03b Newton's first law: equilibrium3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Total mass 390 g (0.390 kg); \(12 - 4 \times 2.5 = 0.390a\) | M1 | Newton's second law; condone missing or incorrect resistance or incorrect total mass. Allow for \(T - R = ma\) if correct substitution of values seen in part 9aii |
| Fully correct equation need not be simplified | A1 [2] | 3.3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(5.13 \text{ m s}^{-2}\) | B1 [1] | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct vertical forces | B1 | Allow 'weight' or \(120g\) N oe for \(0.12g\) N |
| 12 N and 2.5 N correctly drawn and labelled with no extra forces | B1 | Allow 'resistance' for 2.5 N and 'tension' for 12 N providing it is clear that the tension in the string is distinct from the tension in the ribbon |
| Tension in the ribbon correctly drawn and labelled | B1 [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| N2L for the head only: \(12 - 2.5 - T = 0.12a\) OR N2L for the three body sections together: \(T - 3 \times 2.5 = 0.270a\) | M1 | N2L with correct mass and their acceleration. Allow missing or incorrect resistance. Allow for mass in grams if same error seen in part (a) |
| \(T = 8.88\) N | A1 [2] | Allow A1 for correct answer from consistent use of grams; cao |
## Question 9:
### Part (a)(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Total mass 390 g (0.390 kg); $12 - 4 \times 2.5 = 0.390a$ | M1 | Newton's second law; condone missing or incorrect resistance or incorrect total mass. Allow for $T - R = ma$ if correct substitution of values seen in part 9aii |
| Fully correct equation need not be simplified | A1 [2] | 3.3 |
### Part (a)(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $5.13 \text{ m s}^{-2}$ | B1 [1] | cao |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct vertical forces | B1 | Allow 'weight' or $120g$ N oe for $0.12g$ N |
| 12 N and 2.5 N correctly drawn and labelled with no extra forces | B1 | Allow 'resistance' for 2.5 N and 'tension' for 12 N providing it is clear that the tension in the string is distinct from the tension in the ribbon |
| Tension in the ribbon correctly drawn and labelled | B1 [3] | |
### Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| N2L for the head only: $12 - 2.5 - T = 0.12a$ OR N2L for the three body sections together: $T - 3 \times 2.5 = 0.270a$ | M1 | N2L with correct mass and their acceleration. Allow missing or incorrect resistance. Allow for mass in grams if same error seen in part (a) |
| $T = 8.88$ N | A1 [2] | Allow A1 for correct answer from consistent use of grams; cao |
---9 The diagram shows a toy caterpillar consisting of a head and three body sections each connected by a light inextensible ribbon. The head has a mass of 120 g and the body sections each have a mass of 90 g .
The toy is pulled on level ground using a horizontal string attached to the head. The tension in the string is 12 N . There are resistances to motion of 2.5 N for the head and each section of the body.\\
\includegraphics[max width=\textwidth, alt={}, center]{4fac72cb-85cb-48d9-8817-899ef3f80a0f-08_134_794_536_244}
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item State the equation of motion for the toy caterpillar modelled as a single particle.
\item Calculate the acceleration of the toy caterpillar.
\end{enumerate}\item Draw a diagram showing all the forces acting on the head of the toy caterpillar.
\item Calculate the tension in the ribbon that joins the head to the body.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 1 2021 Q9 [8]}}