| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2024 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Smooth ring on string |
| Difficulty | Moderate -0.3 This is a standard M1 equilibrium problem with a smooth ring on a string. Students must resolve forces in two directions and use the given angle information, but the setup is straightforward with no geometric complications. The smooth ring means equal tensions throughout, and the vertical position of C below B simplifies the geometry. Slightly easier than average due to the clear diagram and standard method. |
| Spec | 3.03b Newton's first law: equilibrium3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Horiz: \(2 = T\cos\theta\) | M1 A1 | Horizontal equilibrium. Correct no. of terms, dimensionally correct, condone sin/cos confusion. A1 = correct unsimplified equation |
| \(T = 2.5\) | A1 | Correct answer (ignore units) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Vert: \(T + T\sin\theta = Mg\) | M1 A1 | Vertical equilibrium. Correct no. of terms, dimensionally correct, condone sin/cos confusion and missing \(g\), equation must include \(M\). A1 = correct unsimplified equation |
| \(M = 0.41\) or \(0.408\) | A1 | Correct answer (ignore units) |
## Question 1:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Horiz: $2 = T\cos\theta$ | M1 A1 | Horizontal equilibrium. Correct no. of terms, dimensionally correct, condone sin/cos confusion. A1 = correct unsimplified equation |
| $T = 2.5$ | A1 | Correct answer (ignore units) |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Vert: $T + T\sin\theta = Mg$ | M1 A1 | Vertical equilibrium. Correct no. of terms, dimensionally correct, condone sin/cos confusion and missing $g$, equation must include $M$. A1 = correct unsimplified equation |
| $M = 0.41$ or $0.408$ | A1 | Correct answer (ignore units) |
**NB:** If different tensions used, can score all marks in (a) but nothing in (b). If $2 = T\cos\!\left(\frac{4}{5}\right)$ and never recover, allow M1A0.
---1.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e59a66b8-c2ad-41fd-9959-9d21e9455c37-02_438_1374_246_347}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a small smooth ring threaded onto a light inextensible string.\\
One end of the string is attached to a fixed point $A$ on a horizontal ceiling and the other end of the string is attached to a fixed point $B$ on the ceiling.
A horizontal force of magnitude 2 N acts on the ring so that the ring rests in equilibrium at a point $C$, vertically below $B$, with the string taut.
The line of action of the horizontal force and the string both lie in the same vertical plane.
The angle that the string makes with the ceiling at $A$ is $\theta$, where $\tan \theta = \frac { 3 } { 4 }$\\
The tension in the string is $T$ newtons. The mass of the ring is $M \mathrm {~kg}$.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $T$
\item Find the value of $M$
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2024 Q1 [6]}}