| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Lift with passenger or load |
| Difficulty | Standard +0.3 This is a standard connected particles problem requiring application of Newton's second law to a two-body system. Part (a) involves straightforward F=ma with weight and tension; part (b) is a routine diagram; part (c) requires considering forces on one body separately but follows directly from part (a). Slightly above average due to the multi-part nature and need to work with the system then individual components, but uses only basic mechanics principles with no novel insight required. |
| Spec | 3.03a Force: vector nature and diagrams3.03c Newton's second law: F=ma one dimension |
| Answer | Marks | Guidance |
|---|---|---|
| \(9500 - 55g - 830g = 885a\) | M1 | 3.3 |
| \(a = 0.934\ \text{ms}^{-2}\) | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| Diagram with \(T\) upwards, \(R\) downwards, \(W\) downwards | B1 | 3.3 |
| Answer | Marks | Guidance |
|---|---|---|
| \(9500 - 55g - R = 55(0.9344\ldots)\) or \(R - 830g = 830(0.9344\ldots)\) | M1 | 3.3 |
| \(R = 8910\ \text{N}\) | A1ft | 3.4 |
| A1 | 1.1 |
## Question 9(a):
$9500 - 55g - 830g = 885a$ | **M1** | 3.3 | Attempt at Newton's second law – correct number of terms (condone one sign error). Weight and mass correctly used
$a = 0.934\ \text{ms}^{-2}$ | **A1** | 1.1 | Allow $827/885$. $0.9344632768\ldots$
**[2 marks]**
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## Question 9(b):
Diagram with $T$ upwards, $R$ downwards, $W$ downwards | **B1** | 3.3 | Correct diagram – three forces (tension in the cable vertically upwards, weight of the crate vertically downwards and normal contact force acting vertically downwards). Note – all three forces labelled somehow, either numerically or with letters, with no extras. Corresponding values not required but if present must be correct
**[1 mark]**
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## Question 9(c):
$9500 - 55g - R = 55(0.9344\ldots)$ or $R - 830g = 830(0.9344\ldots)$ | **M1** | 3.3 | Attempt at Newton's second law for either the crate or car – correct number of terms (accept sign errors). Allow in terms of $a$
$R = 8910\ \text{N}$ | **A1ft** | 3.4 | Correct application of N2L following through their value of $a$ from **(a)**. $8909.60452\ldots$
**A1** | 1.1 |
**[3 marks]**
---9 A crane lifts a car vertically. The car is inside a crate which is raised by the crane by means of a strong cable. The cable can withstand a maximum tension of 9500 N without breaking. The crate has a mass of 55 kg and the car has a mass of 830 kg .
\begin{enumerate}[label=(\alph*)]
\item Find the maximum acceleration with which the crate and car can be raised.
\item Show on a clearly labelled diagram the forces acting on the crate while it is in motion.
\item Determine the magnitude of the reaction force between the crate and the car when they are ascending with maximum acceleration.
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q9 [6]}}