| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2004 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Rotating disc with friction |
| Difficulty | Moderate -0.3 This is a straightforward application of circular motion principles where friction provides centripetal force. Part (i) uses F=mω²r with limiting friction μR=μmg, requiring simple algebraic manipulation. Part (ii) uses v=ωr. Both parts are standard textbook exercises with direct formula application and minimal problem-solving insight required, making it slightly easier than average. |
| Spec | 6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| (i) For using \(F = m\omega^2 r\) | M1 | (\(0.36\) N) |
| For using \(F = \mu R\) | M1 | (\(0.36 = 0.8\mu\)) |
| \(\mu = 0.45\) | A1 | 3 marks |
| (ii) (\(\mu\), \(R\) fixed \(\rightarrow\)) \(F = 0.36\) | B1 ft | |
| For using \(F = mv^2/r\) or \(F = mr(1.2r)^2\) (\(r \approx 0.5\)) | M1 | |
| \((0.36 = 0.08 \times 1.2^2/r\) or \(0.36 = 0.08 \, r(1.2r)^2)\) | ||
| [for \(F = m(v/\omega) \times \omega^2\) treat as for alternative case below.] | ||
| For using \(v = \omega r\) (\(r \approx 0.5\)) | M1 | |
| \(r = 0.32\) or unsimplified equation in \(\omega\) only | A1 ft | |
| Alternative for the above last three marks: | ||
| For using \(F = mv\omega\) | M2 | |
| \(0.08 \times 1.2\omega = 0.36\) | A1 | |
| \(\omega = 3.75\) | A1 | 5 marks |
**(i)** For using $F = m\omega^2 r$ | M1 | ($0.36$ N)
For using $F = \mu R$ | M1 | ($0.36 = 0.8\mu$)
$\mu = 0.45$ | A1 | 3 marks
**(ii)** ($\mu$, $R$ fixed $\rightarrow$) $F = 0.36$ | B1 ft |
For using $F = mv^2/r$ or $F = mr(1.2r)^2$ ($r \approx 0.5$) | M1 |
$(0.36 = 0.08 \times 1.2^2/r$ or $0.36 = 0.08 \, r(1.2r)^2)$ | |
[for $F = m(v/\omega) \times \omega^2$ treat as for alternative case below.] | |
For using $v = \omega r$ ($r \approx 0.5$) | M1 |
$r = 0.32$ or unsimplified equation in $\omega$ only | A1 ft |
**Alternative for the above last three marks:** | |
For using $F = mv\omega$ | M2 |
$0.08 \times 1.2\omega = 0.36$ | A1 |
$\omega = 3.75$ | A1 | 5 marks
---6 A horizontal turntable rotates with constant angular speed $\omega$ rad s $^ { - 1 }$ about its centre $O$. A particle $P$ of mass 0.08 kg is placed on the turntable. The particle moves with the turntable and no sliding takes place.\\
(i) It is given that $\omega = 3$ and that the particle is about to slide on the turntable when $O P = 0.5 \mathrm {~m}$. Find the coefficient of friction between the particle and the turntable.\\
(ii) Given instead that the particle is about to slide when its speed is $1.2 \mathrm {~ms} ^ { - 1 }$, find $\omega$.
\hfill \mbox{\textit{CAIE M2 2004 Q6 [8]}}