| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2004 |
| Session | June |
| Marks | 7 |
| 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: vertical motion |
| Difficulty | Standard +0.8 This is a multi-step energy conservation problem requiring: (1) geometric analysis to find string extensions at two positions using tan α = 4/3, (2) elastic potential energy calculations for two strings, (3) gravitational potential energy change, and (4) algebraic manipulation to find λ. While the energy method is standard M3 content, the symmetric two-string geometry and the need to carefully track extensions at both positions elevates this above routine exercises. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
2.
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Two light elastic strings each have natural length $a$ and modulus of elasticity $\lambda$. A particle $P$ of mass $m$ is attached to one end of each string. The other ends of the strings are attached to points $A$ and $B$, where $A B$ is horizontal and $A B = 2 a$. The particle is held at the mid-point of $A B$ and released from rest. It comes to rest for the first time in the subsequent motion when $P A$ and $P B$ make angles $\alpha$ with $A B$, where $\tan \alpha = \frac { 4 } { 3 }$, as shown in Fig. 1.
Find $\lambda$ in terms of $m$ and $g$.\\
\hfill \mbox{\textit{Edexcel M3 2004 Q2 [7]}}