| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on smooth incline, particle hanging |
| Difficulty | Standard +0.3 This is a standard M1 pulley problem with straightforward kinematics in part (a) and routine application of F=ma to both particles in part (b). The algebra involves resolving forces and solving simultaneous equations, which is typical for this topic. Part (c) tests understanding of modeling assumptions. While multi-part, each step follows standard procedures without requiring novel insight. |
| Spec | 3.02h Motion under gravity: vector form3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\text{Acc} = g\sin 60° = 8.49 \text{ ms}^{-2}\); \(v^2 = 2as: 16.97\); \(v = 4.12 \text{ ms}^{-1}\) | M1 A1 M1 A1 | |
| (b) \(T - g\sin 60° = a\), \(Mg - T = Ma\); \(a = \frac{g}{5}\) | M1 A1 A1 | |
| Add: \(Mg - g\sin 60° = M\frac{g}{5} + \frac{g}{5}\); \(M(\frac{4g}{5}) = \frac{g}{5} + g\frac{\sqrt{3}}{2}\) | M1 A1 | |
| \(\times 10, +g: 8M = 2 + 5\sqrt{3}\); \(M = \frac{(5\sqrt{3} + 2)}{8}\) | M1 A1 | |
| (c) Assumed pulley is smooth. If not, tensions in two sections of string are not equal | B1 B1 | 13 marks |
(a) $\text{Acc} = g\sin 60° = 8.49 \text{ ms}^{-2}$; $v^2 = 2as: 16.97$; $v = 4.12 \text{ ms}^{-1}$ | M1 A1 M1 A1 |
(b) $T - g\sin 60° = a$, $Mg - T = Ma$; $a = \frac{g}{5}$ | M1 A1 A1 |
Add: $Mg - g\sin 60° = M\frac{g}{5} + \frac{g}{5}$; $M(\frac{4g}{5}) = \frac{g}{5} + g\frac{\sqrt{3}}{2}$ | M1 A1 |
$\times 10, +g: 8M = 2 + 5\sqrt{3}$; $M = \frac{(5\sqrt{3} + 2)}{8}$ | M1 A1 |
(c) Assumed pulley is smooth. If not, tensions in two sections of string are not equal | B1 B1 | 13 marks4. $X$ and $Y$ are two points 1 m apart on a line of greatest slope of a smooth plane inclined at $60 ^ { \circ }$ to the horizontal. A particle $P$ of mass 1 kg is released from rest at $X$.
\begin{enumerate}[label=(\alph*)]
\item Find the speed with which $P$ reaches $Y$.\\
$P$ is now connected to another particle $Q$, of mass $M \mathrm {~kg}$, by a light inextensible string. The system is placed with $P$ at $Y$ on the plane and $Q$ hanging vertically at the other end of the string, which passes over a fixed pulley at the top of the plane.\\
The system is released from rest and $P$ moves up the plane with acceleration $\frac { g } { 5 }$.\\
\includegraphics[max width=\textwidth, alt={}, center]{cc75a4a5-1c3a-4e36-acfd-21f6246f2a38-1_358_321_2024_1597}
\item Show that $M = \frac { 5 \sqrt { } 3 + 2 } { 8 }$.
\item State a modelling assumption that you have made about the pulley. Briefly state what would be implied if this assumption were not made.
\section*{MECHANICS 1 (A) TEST PAPER 8 Page 2}
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [13]}}