| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2011 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Particle at midpoint of string between two horizontal fixed points: horizontal surface motion |
| Difficulty | Standard +0.8 This is a multi-step energy conservation problem involving elastic strings with geometric considerations. Part (i) requires setting up energy equations with Pythagoras to find extensions, while part (ii) needs force analysis at maximum extension. More demanding than routine mechanics questions but follows standard A-level methods without requiring novel insight. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle6.02j Conservation with elastics: springs and strings |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| EE gain \(= 2 \times 24[\sqrt{(0.6^2 + 0.25^2)} - 0.6]^2/(2 \times 0.6)\) | B1 | EE gain \(= 0.1\) |
| \(m \times 0.5^2/2 = 0.1\) | M1 | KE loss \(=\) EE gain |
| \(m = 0.8\) (kg) AG | A1 [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(T = 24 \times (0.65 - 0.6)/0.6\ (= 2)\) | B1 | |
| \(2 \times 2 \times 0.25/0.65 = 0.8a\) | M1 | Newton's Second Law with attempt to resolve \(2T\) |
| \(a = 1.92\) | A1 [3] |
## Question 3:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| EE gain $= 2 \times 24[\sqrt{(0.6^2 + 0.25^2)} - 0.6]^2/(2 \times 0.6)$ | B1 | EE gain $= 0.1$ |
| $m \times 0.5^2/2 = 0.1$ | M1 | KE loss $=$ EE gain |
| $m = 0.8$ (kg) **AG** | A1 [3] | |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $T = 24 \times (0.65 - 0.6)/0.6\ (= 2)$ | B1 | |
| $2 \times 2 \times 0.25/0.65 = 0.8a$ | M1 | Newton's Second Law with attempt to resolve $2T$ |
| $a = 1.92$ | A1 [3] | |
---3\\
\includegraphics[max width=\textwidth, alt={}, center]{18398d27-15eb-4515-8210-4f0f614d5b28-2_247_839_1375_653}
A light elastic string of natural length 1.2 m and modulus of elasticity 24 N is attached to fixed points $A$ and $B$ on a smooth horizontal surface, where $A B = 1.2 \mathrm {~m}$. A particle $P$ is attached to the mid-point of the string. $P$ is projected with speed $0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ along the surface in a direction perpendicular to $A B$ (see diagram). $P$ comes to instantaneous rest at a distance 0.25 m from $A B$.\\
(i) Show that the mass of $P$ is 0.8 kg .\\
(ii) Calculate the greatest deceleration of $P$.
\hfill \mbox{\textit{CAIE M2 2011 Q3 [6]}}