| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2014 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Two strings, two fixed points |
| Difficulty | Standard +0.3 This is a standard M3 circular motion problem with two strings. It requires resolving forces vertically and horizontally, applying F=mrω², and solving simultaneous equations. The geometry is straightforward with given angles and lengths. While it involves multiple steps, it follows a well-practiced method with no novel insight required, making it slightly easier than average. |
| Spec | 6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks |
**Part (a)**
M1 for resolving vertically. Two tensions (resolved) and a weight must be seen.
$T_a \cos 30° + T_b \cos 60° = 3g$
A1 for two correct terms
A1 for all terms (inc signs) correct
**Part (b)**
M1 for NL2 horizontally. Two tensions (resolved) and mass $\times$ acceleration needed. The acceleration can be in either form.
$T_a \sin 30° + T_b \sin 60° = 3r \times 2$
A1 for the two tensions, correctly resolved and added
A1 for $30.4 \cos 30°$
**Solving:**
M1 dep for solving the equations to obtain either tension. Dependent on both previous M marks.
$T_b = 35.4$ (N)
A1 for either tension correct
$T_a = 13.5$ (N) must be 2 or 3 sf
A1 for the second tension correct. Both tensions must be given to 2 or 3 sf to gain the marks. (Penalise once for more than 3 sf)
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e5b08946-7311-4cf7-9c5f-5f309a1feed7-05_951_750_121_635}
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\caption{Figure 2}
\end{center}
\end{figure}
A particle $P$ of mass 3 kg is attached by two light inextensible strings to two fixed points $A$ and $B$ on a fixed vertical pole. Both strings are taut and $P$ is moving in a horizontal circle with constant angular speed $6 \mathrm { rad } \mathrm { s } ^ { - 1 }$. String $A P$ is inclined at $30 ^ { \circ }$ to the vertical. String $B P$ has length 0.4 m and $A$ is 0.4 m vertically above $B$, as shown in Figure 2 .
Find the tension in\\
(i) $A P$,\\
(ii) $B P$.\\
\hfill \mbox{\textit{Edexcel M3 2014 Q3 [9]}}