| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Heavier particle hits ground, lighter continues upward - vertical strings |
| Difficulty | Standard +0.8 This is a two-stage pulley problem requiring: (i) standard connected particles analysis with Newton's second law, and (ii) more sophisticated reasoning about motion after one particle stops—requiring calculation of velocity at impact, subsequent motion under gravity alone, and determining when the string becomes taut again. The second part demands careful physical reasoning about the system's behavior and multiple kinematic calculations, elevating it above routine exercises. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys |
| Answer | Marks | Guidance |
|---|---|---|
| \(T - 3g = 3a\) | M1\* | AO3.3 |
| \(5g - T = 5a\) | A1 | AO1.1 |
| \(5g - T = 5\left(\frac{T - 3g}{3}\right) \Rightarrow T = ...\) | Dep\*M1 | AO1.1 |
| \(T = 36.75\ (\text{N})\) | A1 | AO1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(a = 2.45\ \text{ms}^{-2}\) | B1 | AO3.4 |
| \(v^2 = 0 + 2(2.45)(2.5)\) | M1\* | AO3.3 |
| \(0 = 12.25 + 2h(-g)\) | Dep\*M1 | AO3.3 |
| \((2h =)\ 1.25\ (\text{m})\) | A1 | AO1.1 |
## Question 10:
### Part (i):
$T - 3g = 3a$ | **M1\*** | AO3.3 | Attempt N2L for $P$ and $Q$ – three terms, mass required, condone sign errors | M0 for $a = 0$ or $\pm g$
$5g - T = 5a$ | **A1** | AO1.1 |
$5g - T = 5\left(\frac{T - 3g}{3}\right) \Rightarrow T = ...$ | **Dep\*M1** | AO1.1 | Eliminate $a$ and attempt to solve for $T$
$T = 36.75\ (\text{N})$ | **A1** | AO1.1 | Accept $\frac{15}{4}g$, 36.8
### Part (ii):
$a = 2.45\ \text{ms}^{-2}$ | **B1** | AO3.4 | $0.25g$
$v^2 = 0 + 2(2.45)(2.5)$ | **M1\*** | AO3.3 | Use of $v^2 = u^2 + 2as$ for $P$ with $u = 0$ | M0 for $a = 0$ or $\pm g$
$0 = 12.25 + 2h(-g)$ | **Dep\*M1** | AO3.3 | Use of $v^2 = u^2 + 2as$ for $P$ with $v = 0$; $a = \pm g$
$(2h =)\ 1.25\ (\text{m})$ | **A1** | AO1.1 | oe
---10 Particles $P$ and $Q$, of masses 3 kg and 5 kg respectively, are attached to the ends of a light inextensible string. The string passes over a smooth fixed pulley. The system is held at rest with the string taut. The hanging parts of the string are vertical and $P$ and $Q$ are above a horizontal plane (see diagram).\\
\includegraphics[max width=\textwidth, alt={}, center]{efde7b10-b4f3-469f-ba91-b765a16ea835-6_428_208_932_932}\\
(i) Find the tension in the string immediately after the particles are released.
After descending $2.5 \mathrm {~m} , Q$ strikes the plane and is immediately brought to rest. It is given that $P$ does not reach the pulley in the subsequent motion.\\
(ii) Find the distance travelled by $P$ between the instant when $Q$ strikes the plane and the instant when the string becomes taut again.
\hfill \mbox{\textit{OCR PURE Q10 [8]}}