| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2017 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Elastic string – conical pendulum (string inclined to vertical) |
| Difficulty | Standard +0.8 This is a multi-step circular motion problem requiring resolution of forces (tension, weight), Hooke's law for elastic strings, and energy calculations. It combines several M2 topics (circular motion, elastic strings, energy) and requires careful geometric reasoning to relate the angle, radius, and extension. The two-part structure with 9 total marks and the need to find multiple unknowns simultaneously places it above average difficulty, though the techniques are standard for M2. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| 6(i) | T = 12 × 0.1 / 0.4 ( = 3 N) | B1 |
| 3sinθ = 0.15ω2(0.5sinθ) | M1 | Uses Newton's Second Law horizontally |
| ω = 6.32 rads−1 | A1 | |
| Tcosθ = 0.15g (cosθ = 0.5) | M1 | Resolves vertically |
| θ = 60 | A1 | |
| Total: | 5 |
| Answer | Marks | Guidance |
|---|---|---|
| 6(ii) | v = 6.32 × 0.5sin60 | B1 FT |
| KE = 0.15(6.32 × 0.5sin60)2 / 2 (=0.5625J) | B1 | |
| Difference = 0.5625 – 12 × 0.12 / (2 × 0.4) | M1 | Uses EE = λx2 / (2L) |
| Difference = 0.4125 J | A1 | |
| Total: | 4 |
Question 6:
--- 6(i) ---
6(i) | T = 12 × 0.1 / 0.4 ( = 3 N) | B1 | Uses T = λx / L
3sinθ = 0.15ω2(0.5sinθ) | M1 | Uses Newton's Second Law horizontally
ω = 6.32 rads−1 | A1
Tcosθ = 0.15g (cosθ = 0.5) | M1 | Resolves vertically
θ = 60 | A1
Total: | 5
--- 6(ii) ---
6(ii) | v = 6.32 × 0.5sin60 | B1 FT | Uses v = rω and r = 0.5sin60
KE = 0.15(6.32 × 0.5sin60)2 / 2 (=0.5625J) | B1
Difference = 0.5625 – 12 × 0.12 / (2 × 0.4) | M1 | Uses EE = λx2 / (2L)
Difference = 0.4125 J | A1
Total: | 4A particle $P$ of mass $0.15$ kg is attached to one end of a light elastic string of natural length $0.4$ m and modulus of elasticity $12$ N. The other end of the string is attached to a fixed point $A$. The particle $P$ moves in a horizontal circle which has its centre vertically below $A$, with the string inclined at $θ°$ to the vertical and $AP = 0.5$ m.
\begin{enumerate}[label=(\roman*)]
\item Find the angular speed of $P$ and the value of $θ$. [5]
\item Calculate the difference between the elastic potential energy stored in the string and the kinetic energy of $P$. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2017 Q6 [9]}}