- 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 \(4 m g\). The other end of the string is attached to a fixed point \(O\) on the plane, where \(O A = \frac { 3 } { 2 } a\). The particle \(P\) is released from rest and comes to rest at a point \(B\), where \(O B < a\).
Using the work-energy principle, or otherwise, calculate the distance \(A B\).
(6)