| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Elastic string equilibrium and statics |
| Difficulty | Standard +0.8 This M3 question requires understanding of elastic strings (Hooke's law), equilibrium of forces with symmetry, and geometric reasoning about extensions. While the equilateral triangle setup is elegant, students must correctly identify the extension, resolve forces in 2D, and apply λ = (T×l₀)/x. The geometry is non-trivial and the multi-step nature with elastic string theory makes this moderately challenging, though it follows a standard M3 pattern. |
| Spec | 3.03b Newton's first law: equilibrium3.03m Equilibrium: sum of resolved forces = 06.02g Hooke's law: T = k*x or T = lambda*x/l6.02h Elastic PE: 1/2 k x^2 |
| Answer | Marks |
|---|---|
| (a) \(T = \frac{\lambda(0-1)}{0-2} = -\frac{\lambda}{-2}\) | M1 A1 M1 A1 |
| \(T = 3.96\) | M1 A1 |
| Resolve vertically: \(2T \cos 30° = 0.7g\) | |
| \(\lambda = 2T = 7.92\) | |
| (b) Assumed \(P\) is a particle, e.g. a single point at vertex of the \(\triangle\) | B1 |
| Total: 7 marks |
**(a)** $T = \frac{\lambda(0-1)}{0-2} = -\frac{\lambda}{-2}$ | M1 A1 M1 A1 |
$T = 3.96$ | M1 A1 |
Resolve vertically: $2T \cos 30° = 0.7g$ | |
$\lambda = 2T = 7.92$ | |
**(b)** Assumed $P$ is a particle, e.g. a single point at vertex of the $\triangle$ | B1 |
| | **Total: 7 marks** |A thin elastic string, of modulus $\lambda$ N and natural length 20 cm, passes round two small, smooth pegs $A$ and $B$ on the same horizontal level to form a closed loop. $AB = 10$ cm. The ends of the string are attached to a weight $P$ of mass 0.7 kg.
When $P$ rests in equilibrium, $APB$ forms an equilateral triangle.
\includegraphics{figure_2}
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\lambda$. [6 marks]
\item State one assumption that you have made about the weight $P$, explaining how you have used this assumption in your solution. [1 mark]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 Q2 [7]}}