1.
\begin{figure}[h]
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\caption{Figure 1}
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A light elastic string \(A B\) has natural length \(4 a\) and modulus of elasticity \(\lambda\). The end \(A\) is attached to a fixed point and the end \(B\) is attached to a particle of mass \(m\). The particle is held in equilibrium, with the string stretched, by a horizontal force of magnitude \(k m g\).
The line of action of the horizontal force lies in the vertical plane containing the elastic string.
The string \(A B\) makes an angle \(\alpha\) with the vertical, where \(\tan \alpha = \frac { 4 } { 3 }\)
With the particle in this position, \(A B = 5 a\), as shown in Figure 1.
- Show that \(\lambda = \frac { 20 m g } { 3 }\)
- Find the value of \(k\).