| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2009 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Particle on smooth curved surface |
| Difficulty | Moderate -0.3 This is a straightforward application of conservation of energy with clearly defined heights and speeds. Part (i) requires a single energy equation between A and E, while part (ii) requires recognizing that maximum speed occurs at the lowest point C. Both parts use standard SUVAT/energy principles with no geometric complications or novel problem-solving required. |
| Spec | 6.02d Mechanical energy: KE and PE concepts6.02e Calculate KE and PE: using formulae6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \([\text{mgh} = \frac{1}{2}m\dot{v}^2]\) | M1 | For using PE loss = KE gain |
| Height is \(1.8\text{m}\) | A1 | 2 |
| (ii) \(\frac{1}{2}m\dot{v}^2 = \text{mg}(1.8 + 0.65)\) or \(\frac{1}{2}v^2 = \frac{1}{2}m\dot{v}^2 = \text{mg} \times 0.65\) | B1ft | |
| Maximum speed is \(7\text{ms}^{-1}\) | B1 | 2 |
(i) $[\text{mgh} = \frac{1}{2}m\dot{v}^2]$ | M1 | For using PE loss = KE gain
Height is $1.8\text{m}$ | A1 | 2 |
(ii) $\frac{1}{2}m\dot{v}^2 = \text{mg}(1.8 + 0.65)$ or $\frac{1}{2}v^2 = \frac{1}{2}m\dot{v}^2 = \text{mg} \times 0.65$ | B1ft |
Maximum speed is $7\text{ms}^{-1}$ | B1 | 2 |2\\
\includegraphics[max width=\textwidth, alt={}, center]{a9f3480e-7a8a-497d-a26a-b2aba9b05512-2_609_967_536_589}
A smooth narrow tube $A E$ has two straight parts, $A B$ and $D E$, and a curved part $B C D$. The part $A B$ is vertical with $A$ above $B$, and $D E$ is horizontal. $C$ is the lowest point of the tube and is 0.65 m below the level of $D E$. A particle is released from rest at $A$ and travels through the tube, leaving it at $E$ with speed $6 \mathrm {~ms} ^ { - 1 }$ (see diagram). Find\\
(i) the height of $A$ above the level of $D E$,\\
(ii) the maximum speed of the particle.
\hfill \mbox{\textit{CAIE M1 2009 Q2 [4]}}