Standard +0.8 This M3 question requires setting up and solving a work-energy equation involving elastic potential energy, friction work, and the constraint that the particle comes to rest. It demands careful consideration of the string's compression/extension states and whether friction opposes motion throughout, requiring solid mechanics intuition beyond routine application of formulas.
A particle \(P\) of mass \(m\) is held at a point \(A\) on a rough horizontal plane. The coefficient of friction between \(P\) and the plane is \(\frac{2}{3}\). The particle is attached to one end of a light elastic string, of natural length \(a\) and modulus of elasticity \(4mg\). The other end of the string is attached to a fixed point \(O\) on the plane, where \(OA = \frac{3}{4}a\). The particle \(P\) is released from rest and comes to rest at a point \(B\), where \(OB < a\).
Using the work-energy principle, or otherwise, calculate the distance \(AB\). [6]
A particle $P$ of mass $m$ is held at a point $A$ on a rough horizontal plane. The coefficient of friction between $P$ and the plane is $\frac{2}{3}$. The particle is attached to one end of a light elastic string, of natural length $a$ and modulus of elasticity $4mg$. The other end of the string is attached to a fixed point $O$ on the plane, where $OA = \frac{3}{4}a$. The particle $P$ is released from rest and comes to rest at a point $B$, where $OB < a$.
Using the work-energy principle, or otherwise, calculate the distance $AB$. [6]
\hfill \mbox{\textit{Edexcel M3 2003 Q1 [6]}}