A light elastic string $S_1$, with modulus of elasticity $20\,\text{N}$ and natural length $0.5\,\text{m}$, has one end fixed at point $O$. Its other end is fastened to a particle $P$ of mass $0.4\,\text{kg}$, and $P$ hangs in equilibrium directly beneath $O$.
(i)[2]
Find the value of the distance $OP$.
(ii(a))[4]
Find the tension in the inextensible string $S_2$ when $l < 0.5$.
(ii(b))
Find the tension in the inextensible string $S_2$ when $l > 0.6$.
(ii(c))
Find the tension in the inextensible string $S_2$ when $l = 0.54$.
(iii)[3]
In the situation $l = 0.54$, the inextensible string $S_2$ suddenly breaks and $P$ starts to move down vertically. Calculate the greatest speed of $P$ during the motion that follows.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies the weight-extension relation $0.4g = \lambda e/L$” …