| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2017 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Two strings, two fixed points |
| Difficulty | Standard +0.3 This is a standard circular motion problem with two strings requiring resolution of forces in vertical and horizontal directions. The setup is clearly defined, and students need to apply Newton's second law in both directions plus the centripetal force formula. While it involves multiple steps and careful angle work, it follows a routine problem-solving pattern for M2 circular motion with no novel insights required. |
| Spec | 6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Notes |
| \(6\cos60 = 4\cos60 + mg\) | M1 | Resolve vertically |
| \(m = 0.1\) kg | A1 | |
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Notes |
| \(\text{radius} = 0.7\sin60\) | B1 | |
| \(6\sin60 + 4\sin60 = 0.1v^2/(0.7\sin60)\) | M1 | Uses Newton's Second Law horizontally with 3 terms |
| \(v = 7.25\) m s\(^{-1}\) | A1 | |
| Total: 3 |
## Question 2:
**Part (i)**
| Answer | Marks | Notes |
|--------|-------|-------|
| $6\cos60 = 4\cos60 + mg$ | M1 | Resolve vertically |
| $m = 0.1$ kg | A1 | |
| **Total: 2** | | |
**Part (ii)**
| Answer | Marks | Notes |
|--------|-------|-------|
| $\text{radius} = 0.7\sin60$ | B1 | |
| $6\sin60 + 4\sin60 = 0.1v^2/(0.7\sin60)$ | M1 | Uses Newton's Second Law horizontally with 3 terms |
| $v = 7.25$ m s$^{-1}$ | A1 | |
| **Total: 3** | | |
---2\\
\begin{tikzpicture}[>=Stealth, scale=1.8]
% Define coordinates based on the 60-degree angle and 0.7m length
% Let 0.7m be represented by 4 units for better visibility
\pgfmathsetmacro{\len}{4}
\coordinate (A) at (0, {\len*cos(60)});
\coordinate (B) at (0, {-\len*cos(60)});
\coordinate (P) at ({\len*sin(60)}, 0);
\coordinate (M) at (0, 0);
% Draw dashed lines
\draw[thick, dashed] (A) -- (B);
\draw[thick, dashed] (M) -- (P);
% Draw solid lines with mid-way arrowheads
\draw[thick, decoration={
markings,
mark=at position 0.6 with {\arrow{>}}
}, postaction={decorate}] (P) -- (A);
\draw[thick, decoration={
markings,
mark=at position 0.6 with {\arrow{>}}
}, postaction={decorate}] (P) -- (B);
% Draw point P
\fill (P) circle (2pt) node[right=5pt, font=\Large] {$P$};
% Node labels A and B
\node[left=3pt, font=\Large] at (A) {$A$};
\node[left=3pt, font=\Large] at (B) {$B$};
% Draw angles with labels
\draw (0, 1.4) arc (-90:-30:0.6);
\node at (0.35, 1.25) {\Large $60^\circ$};
\draw (0, -1.4) arc (90:30:0.6);
\node at (0.35, -1.25) {\Large $60^\circ$};
% Distance labels (0.7 m)
\node[above] at ($(A)!0.2!(P)+(0.1, .1)$) {$0.7{ m}$};
\node[below] at ($(B)!0.2!(P)+(0.1, -.1)$) {$0.7{ m}$};
% Force labels (6 N and 4 N)
\node[below] at ($(P)!0.6!(A)+(0,-.1)$) {$6{ N}$};
\node[above] at ($(P)!0.6!(B)+(0,.1)$) {$4{ N}$};
\end{tikzpicture}
The ends of two light inextensible strings of length 0.7 m are attached to a particle $P$. The other ends of the strings are attached to two fixed points $A$ and $B$ which lie in the same vertical line with $A$ above $B$. The particle $P$ moves in a horizontal circle which has its centre at the mid-point of $A B$. Both strings are inclined at $60 ^ { \circ }$ to the vertical. The tension in the string attached to $A$ is 6 N and the tension in the string attached to $B$ is 4 N (see diagram).\\
(i) Find the mass of $P$.\\
(ii) Calculate the speed of $P$.\\
\hfill \mbox{\textit{CAIE M2 2017 Q2 [5]}}