Edexcel M3 Specimen — Question 2 7 marks

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
SessionSpecimen
Marks7
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Mark schemeDownload PDF ↗
TopicHooke's law and elastic energy
TypeParticle at midpoint of string between two horizontal fixed points: vertical motion
DifficultyStandard +0.3 This is a standard M3 equilibrium problem with elastic strings requiring resolution of forces and Hooke's law. The symmetry simplifies the problem significantly, and the method is routine for this topic. While it involves multiple steps (geometry, extensions, force resolution, Hooke's law), these are all standard techniques that follow a predictable pattern, making it slightly easier than average.
Spec3.03m Equilibrium: sum of resolved forces = 06.02h Elastic PE: 1/2 k x^2

2. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{e256678d-89e8-48eb-aa8a-b8e027b62ef1-2_310_1122_1178_466}
\end{figure} Two elastic ropes each have natural length 30 cm and modulus of elasticity \(\lambda \mathrm { N }\). One end of each rope is attached to a lead weight \(P\) of mass 2 kg and the other ends are attached to two points \(A\) and \(B\) on a horizontal ceiling, where \(A B = 72 \mathrm {~cm}\). The weight hangs in equilibrium 15 cm below the ceiling, as shown in Fig. 2. By modelling \(P\) as a particle and the ropes as light elastic strings,
  1. find, to one decimal place, the value of \(\lambda\).
  2. State how you have used the fact that \(P\) is modelled as a particle.

2.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 2}
  \includegraphics[alt={},max width=\textwidth]{e256678d-89e8-48eb-aa8a-b8e027b62ef1-2_310_1122_1178_466}
\end{center}
\end{figure}

Two elastic ropes each have natural length 30 cm and modulus of elasticity $\lambda \mathrm { N }$. One end of each rope is attached to a lead weight $P$ of mass 2 kg and the other ends are attached to two points $A$ and $B$ on a horizontal ceiling, where $A B = 72 \mathrm {~cm}$. The weight hangs in equilibrium 15 cm below the ceiling, as shown in Fig. 2. By modelling $P$ as a particle and the ropes as light elastic strings,
\begin{enumerate}[label=(\alph*)]
\item find, to one decimal place, the value of $\lambda$.
\item State how you have used the fact that $P$ is modelled as a particle.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M3  Q2 [7]}}