Edexcel M3 2006 January — Question 1 8 marks

Exam BoardEdexcel
ModuleM3 (Mechanics 3)
Year2006
SessionJanuary
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicHooke's law and elastic energy
TypeElastic string equilibrium and statics
DifficultyModerate -0.3 This is a straightforward equilibrium problem requiring resolution of forces and application of Hooke's law. While it involves three parts and elastic strings (M3 content), the solution follows a standard template: resolve horizontally and vertically to find F and tension, use Hooke's law for extension, then apply elastic energy formula. No novel insight or complex problem-solving required, making it slightly easier than average.
Spec3.03m Equilibrium: sum of resolved forces = 06.02h Elastic PE: 1/2 k x^2

1. \section*{Figure 1}
\includegraphics[max width=\textwidth, alt={}]{67a9cf74-833f-4b4a-9fde-3c62dcc08e8c-2_515_1157_276_516}
A particle \(P\) of mass 0.8 kg is attached to one end of a light inelastic string, of natural length 1.2 m and modulus of elasticity 24 N . The other end of the string is attached to a fixed point \(A\). A horizontal force of magnitude \(F\) newtons is applied to \(P\). The particle \(P\) in in equilibrium with the string making an angle \(60 ^ { \circ }\) with the downward vertical, as shown in Figure 1. Calculate
  1. the value of \(F\),
  2. the extension of the string,
  3. the elasticity stored in the string.

1.

\section*{Figure 1}
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{67a9cf74-833f-4b4a-9fde-3c62dcc08e8c-2_515_1157_276_516}
\end{center}

A particle $P$ of mass 0.8 kg is attached to one end of a light inelastic string, of natural length 1.2 m and modulus of elasticity 24 N . The other end of the string is attached to a fixed point $A$. A horizontal force of magnitude $F$ newtons is applied to $P$. The particle $P$ in in equilibrium with the string making an angle $60 ^ { \circ }$ with the downward vertical, as shown in Figure 1.

Calculate
\begin{enumerate}[label=(\alph*)]
\item the value of $F$,
\item the extension of the string,
\item the elasticity stored in the string.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M3 2006 Q1 [8]}}