Standard +0.8 This M3 question involves elastic strings with geometry (particle pulled perpendicular to AB), requiring Hooke's law, Pythagoras for extensions, vector resolution for equilibrium, and energy conservation. Part (a) is routine, but parts (b) and (c) require careful geometric reasoning and multi-step application of mechanics principles, making it moderately challenging but still within standard M3 scope.
The ends of a light elastic string, of natural length 0.4 m and modulus of elasticity \(\lambda\) newtons, are attached to two fixed points \(A\) and \(B\) which are 0.6 m apart on a smooth horizontal table. The tension in the string is 8 N .
Show that \(\lambda = 16\)
A particle \(P\) is attached to the midpoint of the string. The particle \(P\) is now pulled horizontally in a direction perpendicular to \(A B\) to a point 0.4 m from the midpoint of \(A B\). The particle is held at rest by a horizontal force of magnitude \(F\) newtons acting in a direction perpendicular to \(A B\), as shown in Figure 5 below.
\begin{figure}[h]
\begin{enumerate}
\item The ends of a light elastic string, of natural length 0.4 m and modulus of elasticity $\lambda$ newtons, are attached to two fixed points $A$ and $B$ which are 0.6 m apart on a smooth horizontal table. The tension in the string is 8 N .\\
(a) Show that $\lambda = 16$
\end{enumerate}
A particle $P$ is attached to the midpoint of the string. The particle $P$ is now pulled horizontally in a direction perpendicular to $A B$ to a point 0.4 m from the midpoint of $A B$. The particle is held at rest by a horizontal force of magnitude $F$ newtons acting in a direction perpendicular to $A B$, as shown in Figure 5 below.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{698b44b5-801c-45ec-b9de-021e44487edb-18_623_796_792_573}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{center}
\end{figure}
(b) Find the value of $F$.
The particle is released from rest. Given that the mass of $P$ is 0.3 kg ,\\
(c) find the speed of $P$ as it crosses the line $A B$.
\hfill \mbox{\textit{Edexcel M3 2017 Q6 [13]}}