| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2005 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Horizontal circular track – friction only (no banking) |
| Difficulty | Moderate -0.5 This is a straightforward application of circular motion formulas with constant angular velocity. Part (i) requires using s=rθ with θ=π/2 radians, and part (ii) uses the standard centripetal acceleration formula a=v²/r. Both are direct substitutions with no problem-solving insight needed, making it slightly easier than average. |
| Spec | 6.05b Circular motion: v=r*omega and a=v^2/r |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\frac{1}{2}\pi = \omega \times 50\) or \(L = 220 \times 50\) | M1 | For using \(\theta = \omega t\) or \(L = vt\) |
| \(220 = (\pi/100)r\) or \(11000 = r(\frac{1}{2}\pi)\) | M1 | For using \(v = \omega r\) or \(L = r\theta\) |
| Radius is approx. 7000 m | A1 | [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Acceleration is \(6.91\,\text{ms}^{-2}\) | M1, A1 | For using \(a = v^2/r\) or \(a = \omega^2 r\) [2] |
## Question 2:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{1}{2}\pi = \omega \times 50$ or $L = 220 \times 50$ | M1 | For using $\theta = \omega t$ or $L = vt$ |
| $220 = (\pi/100)r$ or $11000 = r(\frac{1}{2}\pi)$ | M1 | For using $v = \omega r$ or $L = r\theta$ |
| Radius is approx. 7000 m | A1 | **[3]** |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Acceleration is $6.91\,\text{ms}^{-2}$ | M1, A1 | For using $a = v^2/r$ or $a = \omega^2 r$ **[2]** |
---2\\
\includegraphics[max width=\textwidth, alt={}, center]{a20a6641-d771-4c89-b40f-168a0c61f99d-2_456_871_1228_635}
An aircraft flies horizontally at a constant speed of $220 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Initially it is flying due east. On reaching a point $A$ it flies in a circular arc from $A$ to $B$, taking 50 s . At $B$ the aircraft is flying due south (see diagram).\\
(i) Show that the radius of the arc is approximately 7000 m .\\
(ii) Find the magnitude of the acceleration of the aircraft while it is flying between $A$ and $B$.
\hfill \mbox{\textit{CAIE M2 2005 Q2 [5]}}