(i)[4]
Show that the tension in the string is $\frac{3}{\cos\theta}\,\text{N}$ and hence determine $m$.
(ii)[4]
Show that $\omega$ is independent of $\theta$.
(iii)[4]
Find this value of $\theta$.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
One end of a light elastic string with modulus of elasticity $15\,\text{N}$ has its top end fastened at point $A$, which lies $2\,\text{m}$ directly above a fixed small smooth ring $R$. The string’s natural length is $2\,\text{m}$ and it passes through $R$. The other end is connected to a particle $P$ of mass $m\,\text{kg}$, and $P$ travels with constant angular speed $\omega\,\text{rad s}^{-1}$ in a horizontal circle whose centre is $0.4\,\text{m}$ below the ring. $PR$ makes an acute angle $\theta$ with the vertical (see diagram).
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Uses $T=\dfrac{\lambda e x}{2}$ to give $T=\dfrac{15(0.4/\cos\theta)}{2}$” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI