Standard +0.3 This is a standard M3 equilibrium problem requiring resolution of forces, friction law (F = μR), and Hooke's law (T = λx/l). While it involves multiple steps and careful algebra to reach the specific extension value of 17cm, the techniques are routine for M3 students and the question clearly signposts what to show, making it slightly easier than average.
The diagram shows a particle of mass \(0.7\) kg resting on a rough horizontal table. The coefficient of friction between the particle and the table is \(0.25\). A light elastic string, of natural length \(50\) cm and modulus of elasticity \(6.86\) N, is attached to the particle. The string is kept at an angle of \(60°\) to the horizontal and is gradually extended by pulling on it until the particle moves. Show that the particle starts to move when the extension in the string is \(17\) cm.
\includegraphics{figure_2}
[8 marks]
The diagram shows a particle of mass $0.7$ kg resting on a rough horizontal table. The coefficient of friction between the particle and the table is $0.25$. A light elastic string, of natural length $50$ cm and modulus of elasticity $6.86$ N, is attached to the particle. The string is kept at an angle of $60°$ to the horizontal and is gradually extended by pulling on it until the particle moves. Show that the particle starts to move when the extension in the string is $17$ cm.
\includegraphics{figure_2}
[8 marks]
\hfill \mbox{\textit{Edexcel M3 Q2 [8]}}