A particle $P$ with mass $0.6\,\text{kg}$ is fastened to one end of a light elastic string whose natural length is $1.5\,\text{m}$ and whose modulus of elasticity is $9\,\text{N}$. The string is threaded through a small smooth ring $R$, fixed $0.4\,\text{m}$ above a rough horizontal plane. The other end of the string is attached to a fixed point $O$ that lies $1.5\,\text{m}$ vertically above $R$. Points $A$ and $B$ lie on the horizontal surface, with $B$ directly below $R$. When $P$ is on the surface between $A$ and $B$, $RP$ makes an acute angle $\theta^\circ$ with the horizontal (see diagram).
(i)[3]
Show that the magnitude of the normal force on $P$ from the surface is $3.6\,\text{N}$ for every value of $\theta$.
(ii)[4]
A particle $P$ is projected towards $B$ at a speed of $2.5\,\text{m s}^{-1}$ from its starting position at $A$, where $\theta = 30^\circ$. When $P$ passes through $B$, its speed is $3\,\text{m s}^{-1}$. Find the work done against friction as $P$ travels from $A$ to $B$.
(iii)[2]
Calculate the coefficient of friction between $P$ and the surface.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the general angle $\theta$ to form $T = 9(0.4/\sin\theta)/1.5” …