| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2020 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Conical pendulum – horizontal circle in free space (no surface) |
| Difficulty | Moderate -0.3 This is a standard conical pendulum problem requiring resolution of forces and application of circular motion equations (T cos θ = mg, T sin θ = mrω²). It's a routine M3 question with straightforward setup and calculation, slightly easier than average due to its textbook nature, but not trivial as it requires understanding of both vertical equilibrium and horizontal centripetal force. |
| VILV SIHI NI JIIIM IONOO | VIIN SIHI NI JIIIM IONOO | VARV SIHI NI JIIIM ION OC |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \(\omega = \frac{2\pi}{0.5} (= 4\pi)\) | B1 | Use of period to find \(\omega\) |
| \(R = m\omega^2 \times 0.35 \left(= \frac{28m\pi^2}{5}\right)\) | M1 | Equation of motion horizontally, must be considering \(R\), acceleration in either circular motion form |
| \(F_r = mg\) | B1 | Resolve vertically; if only seen within friction inequality, must be correct way round |
| \(F_r \leq \mu R\) | M1 | Use of \(F_r \leq \mu R\); condone strict inequality |
| \(mg \leq \mu \frac{28m\pi^2}{5}\) | DM1 | Substitute in \(F_r\) and \(R\); could be an equation; dependent on first M mark |
| \(\mu \geq 0.18 \quad (\mu \geq 0.177)\) | A1 | cao |
## Question 1:
| Working/Answer | Mark | Guidance |
|---|---|---|
| $\omega = \frac{2\pi}{0.5} (= 4\pi)$ | B1 | Use of period to find $\omega$ |
| $R = m\omega^2 \times 0.35 \left(= \frac{28m\pi^2}{5}\right)$ | M1 | Equation of motion horizontally, must be considering $R$, acceleration in either circular motion form |
| $F_r = mg$ | B1 | Resolve vertically; if only seen within friction inequality, must be correct way round |
| $F_r \leq \mu R$ | M1 | Use of $F_r \leq \mu R$; condone strict inequality |
| $mg \leq \mu \frac{28m\pi^2}{5}$ | DM1 | Substitute in $F_r$ and $R$; could be an equation; dependent on first M mark |
| $\mu \geq 0.18 \quad (\mu \geq 0.177)$ | A1 | cao |
**Note:** If equation used throughout and correct inequality added for final answer, full marks available if no incorrect working seen. **[6]**
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VILV SIHI NI JIIIM IONOO & VIIN SIHI NI JIIIM IONOO & VARV SIHI NI JIIIM ION OC \\
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\includegraphics[max width=\textwidth, alt={}, center]{ace84823-db30-463e-b24b-f0cd7df73746-03_62_37_2659_1914}\\
\hfill \mbox{\textit{Edexcel M3 2020 Q1 [6]}}