| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2010 |
| Session | January |
| Marks | 10 |
| 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 resolving forces in equilibrium with an elastic string, then using the elastic energy formula to form a quadratic equation. It combines statics, Hooke's law, and energy concepts in a non-routine way that requires careful algebraic manipulation—more challenging than standard equilibrium problems but accessible to well-prepared M3 students. |
| Spec | 3.03n Equilibrium in 2D: particle under forces6.02h Elastic PE: 1/2 k x^2 |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \(\uparrow \quad T\cos\theta = 40\) | M1 A1 | M1 attempt at both equations |
| \(\rightarrow \quad T\sin\theta = 30\) | A1 | |
| leading to \(T = 50\) | M1 A1 | |
| \(E = \frac{\lambda x^2}{2a} = 10\) | B1 | |
| HL: \(T = \frac{\lambda x}{a} = 50\) | M1 | |
| leading to \(x = 0.4\) | M1 A1 | |
| \(OP = 0.5 + 0.4 = 0.9 \text{ (m)}\) | A1ft | (10) |
| Total | [10] |
# Question 4:
| Working/Answer | Marks | Guidance |
|---|---|---|
| $\uparrow \quad T\cos\theta = 40$ | M1 A1 | M1 attempt at both equations |
| $\rightarrow \quad T\sin\theta = 30$ | A1 | |
| leading to $T = 50$ | M1 A1 | |
| $E = \frac{\lambda x^2}{2a} = 10$ | B1 | |
| HL: $T = \frac{\lambda x}{a} = 50$ | M1 | |
| leading to $x = 0.4$ | M1 A1 | |
| $OP = 0.5 + 0.4 = 0.9 \text{ (m)}$ | A1ft | (10) |
| **Total** | **[10]** | |4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{d831556d-fdf3-4639-9a89-6d3b372d3446-08_388_521_279_710}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
A particle $P$ of weight 40 N is attached to one end of a light elastic string of natural length 0.5 m . The other end of the string is attached to a fixed point $O$. A horizontal force of magnitude 30 N is applied to $P$, as shown in Figure 3. The particle $P$ is in equilibrium and the elastic energy stored in the string is 10 J .
Calculate the length $O P$.
\hfill \mbox{\textit{Edexcel M3 2010 Q4 [10]}}