| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Two strings, two fixed points |
| Difficulty | Standard +0.8 This is a sophisticated 3D circular motion problem requiring geometric analysis to find string angles, consideration of limiting cases (one string going slack for minimum speed, strings breaking for maximum speed), and application of Newton's second law in both horizontal and vertical directions. The multi-constraint optimization and geometric setup elevate this above standard circular motion exercises. |
| Spec | 6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| 6(i) | cosθ = 0.5 and sinθ = 3/2 | B1 |
| Tsinθ = 0.2 g | M1 | Resolve vertically for P. Note tension in BP is zero |
| Tcosθ = 0.2ω2 × 0.3 | M1 | Use Newton's Second Law horizontally |
| ω = 4.39 rads−1 | A1 | |
| Total: | 4 | |
| Question | Answer | Marks |
| Answer | Marks | Guidance |
|---|---|---|
| 6(ii) | T sinθ = 0.2 g + T sinθ | |
| A B | M1 | Resolve vertically for P |
| Answer | Marks | Guidance |
|---|---|---|
| A | M1 | Use T = 5 |
| Answer | Marks | Guidance |
|---|---|---|
| A | A1 | |
| 5cosθ + 7.309cosθ = 0.2v2/0.3 | M1 | Use Newton's Second Law horizontally |
| v = 3.04 ms−1 | A1 | |
| Total: | 5 | |
| Question | Answer | Marks |
Question 6:
--- 6(i) ---
6(i) | cosθ = 0.5 and sinθ = 3/2 | B1 | θ is the angle that AP makes with the horizontal. Note tanθ = 3
Tsinθ = 0.2 g | M1 | Resolve vertically for P. Note tension in BP is zero
Tcosθ = 0.2ω2 × 0.3 | M1 | Use Newton's Second Law horizontally
ω = 4.39 rads−1 | A1
Total: | 4
Question | Answer | Marks | Guidance
--- 6(ii) ---
6(ii) | T sinθ = 0.2 g + T sinθ
A B | M1 | Resolve vertically for P
T sinθ = 0.2 g + 5sinθ
A | M1 | Use T = 5
B
T = 7.309
A | A1
5cosθ + 7.309cosθ = 0.2v2/0.3 | M1 | Use Newton's Second Law horizontally
v = 3.04 ms−1 | A1
Total: | 5
Question | Answer | Marks | Guidance\includegraphics{figure_6}
A particle $P$ of mass 0.2 kg is attached to one end of a light inextensible string of length 0.6 m. The other end of the string is attached to a fixed point $A$. The particle $P$ is also attached to one end of a second light inextensible string of length 0.6 m, the other end of which is attached to a fixed point $B$ vertically below $A$. The particle moves in a horizontal circle of radius 0.3 m, which has its centre at the mid-point of $AB$, with both strings straight (see diagram).
\begin{enumerate}[label=(\roman*)]
\item Calculate the least possible angular speed of $P$. [4]
\item Find the greatest possible speed of $P$. [5]
\end{enumerate}
The string $AP$ will break if its tension exceeds 8 N. The string $BP$ will break if its tension exceeds 5 N.
\hfill \mbox{\textit{CAIE M2 2018 Q6 [9]}}