| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2022 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Forces in vector form: resultant and acceleration |
| Difficulty | Moderate -0.3 This is a straightforward vector mechanics question requiring addition of forces, resolution into components, and application of F=ma. The key steps are standard: add tension vectors, recognize that j-components cancel for eastward motion, account for resistance, and apply Newton's second law. While it involves multiple forces and vector notation, it follows a predictable template with no conceptual surprises or complex problem-solving required. |
| Spec | 1.10b Vectors in 3D: i,j,k notation3.03c Newton's second law: F=ma one dimension3.03d Newton's second law: 2D vectors |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| When the boat is modelled as a particle, the size and shape of the boat are not taken into account in the model. Any rotation of the boat is neglected. | B1 | A sensible comment |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Resistance is \(-300\mathbf{i}\) N; \((450\mathbf{i}+20\mathbf{j})+(420\mathbf{i}-20\mathbf{j})-300\mathbf{i} = 9000\mathbf{a}\) | M1 | Sum of at least two forces seen in a N2L equation. Also allow for scalar equation in \(\mathbf{i}\) direction only. Allow missing or incorrect resistance |
| \([570\mathbf{i} = 9000\mathbf{a}]\) | A1 | Accept equivalent scalar equation and statement that there is no [resultant] force or no acceleration in the \(\mathbf{j}\) direction |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\mathbf{a} = \frac{570}{9000}\mathbf{i} = 0.0633\mathbf{i} \text{ ms}^{-2}\) | B1 | Must be vector. FT their equation(s) of motion |
## Question 7:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| When the boat is modelled as a particle, the size and shape of the boat are not taken into account in the model. Any rotation of the boat is neglected. | B1 | A sensible comment |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Resistance is $-300\mathbf{i}$ N; $(450\mathbf{i}+20\mathbf{j})+(420\mathbf{i}-20\mathbf{j})-300\mathbf{i} = 9000\mathbf{a}$ | M1 | Sum of at least two forces seen in a N2L equation. Also allow for scalar equation in $\mathbf{i}$ direction only. Allow missing or incorrect resistance |
| $[570\mathbf{i} = 9000\mathbf{a}]$ | A1 | Accept equivalent scalar equation and statement that there is no [resultant] force or no acceleration in the $\mathbf{j}$ direction |
### Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\mathbf{a} = \frac{570}{9000}\mathbf{i} = 0.0633\mathbf{i} \text{ ms}^{-2}$ | B1 | Must be vector. FT their equation(s) of motion |7 In this question the unit vectors $\mathbf { i }$ and $\mathbf { j }$ are directed east and north respectively.
A canal narrowboat of mass 9 tonnes is pulled by two ropes. The tensions in the ropes are $( 450 \mathbf { i } + 20 \mathbf { j } ) \mathbf { N }$ and $( 420 \mathbf { i } - 20 \mathbf { j } ) \mathbf { N }$. The boat experiences a resistance to motion $\mathbf { R }$ of magnitude 300 N .
\begin{enumerate}[label=(\alph*)]
\item Explain what it means to model the boat as a particle.
The boat is travelling in a straight line due east.
\item Find the equation of motion of the boat.
\item Find the acceleration of the boat giving your answer as a vector.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 1 2022 Q7 [4]}}