| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Particle on table with string above |
| Difficulty | Standard +0.3 This is a straightforward circular motion problem requiring resolution of forces and application of F=ma=mv²/r. The geometry is given (string length 3a, vertical distance a), speed is provided, and students need to find tension and normal reaction using standard methods. It's slightly above average difficulty due to the algebraic parameters rather than numbers, but follows a standard template for M3 conical pendulum problems. |
| Spec | 3.03i Normal reaction force6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(OP = a\sqrt{8}\) | B1 | |
| \(R(\leftarrow)\): \(T\sin\theta = \frac{mv^2}{a\sqrt{8}}\) | M1 A1 | |
| \(T\frac{\sqrt{8}a}{3a} = \frac{m \times 4ga}{a\sqrt{8}}\) | B1 f.t. | \((\sin\theta)\) |
| \(\Rightarrow T = \frac{3mg}{2}\) | M1 A1 | (6) |
| \(R(\uparrow)\): \(T\cos\theta + N = mg\) | M1 A1 | |
| \(\Rightarrow N = mg - \frac{3}{2}mg \times \frac{1}{3} = \frac{1}{2}mg\) | M1 A1 | (4) |
## Question 3:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $OP = a\sqrt{8}$ | B1 | |
| $R(\leftarrow)$: $T\sin\theta = \frac{mv^2}{a\sqrt{8}}$ | M1 A1 | |
| $T\frac{\sqrt{8}a}{3a} = \frac{m \times 4ga}{a\sqrt{8}}$ | B1 f.t. | $(\sin\theta)$ |
| $\Rightarrow T = \frac{3mg}{2}$ | M1 A1 | (6) |
| $R(\uparrow)$: $T\cos\theta + N = mg$ | M1 A1 | |
| $\Rightarrow N = mg - \frac{3}{2}mg \times \frac{1}{3} = \frac{1}{2}mg$ | M1 A1 | (4) |
**(10 marks)**
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{45c51316-7d58-4c16-9b5f-1d7421060a88-3_485_855_1073_584}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
A particle $P$ of mass $m$ is attached to one end of a light inextensible string of length $3 a$. The other end of the string is attached to a fixed point $A$ which is a vertical distance $a$ above a smooth horizontal table. The particle moves on the table in a circle whose centre $O$ is vertically below $A$, as shown in Fig. 1. The string is taut and the speed of $P$ is $2 \sqrt { } ( a g )$.
Find
\begin{enumerate}[label=(\alph*)]
\item the tension in the string,
\item the normal reaction of the table on $P$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 Q3 [10]}}