Standard +0.3 This is a straightforward elastic string equilibrium problem requiring application of Hooke's law to two string segments and resolving forces vertically. While it involves multiple steps (finding extensions, applying Hooke's law twice, and resolving forces), the method is standard and well-practiced in M2. The setup is clear with given numerical values, making it slightly easier than average A-level mechanics questions.
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\includegraphics[max width=\textwidth, alt={}, center]{6fe2c5e0-0496-4fb4-95d2-354b90607b5b-2_643_218_264_959}
A particle \(P\) of mass \(m \mathrm {~kg}\) is attached to the mid-point of a light elastic string of natural length 0.8 m and modulus of elasticity 8 N . One end of the string is attached to a fixed point \(A\) and the other end is attached to a fixed point \(B\) which is 2 m vertically below \(A\). When the particle is in equilibrium the distance \(A P\) is 1.1 m (see diagram). Find the value of \(m\).
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\includegraphics[max width=\textwidth, alt={}, center]{6fe2c5e0-0496-4fb4-95d2-354b90607b5b-2_643_218_264_959}
A particle $P$ of mass $m \mathrm {~kg}$ is attached to the mid-point of a light elastic string of natural length 0.8 m and modulus of elasticity 8 N . One end of the string is attached to a fixed point $A$ and the other end is attached to a fixed point $B$ which is 2 m vertically below $A$. When the particle is in equilibrium the distance $A P$ is 1.1 m (see diagram). Find the value of $m$.
\hfill \mbox{\textit{CAIE M2 2005 Q1 [4]}}