Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A smooth bead $B$ of mass $0.3\,\text{kg}$ is fixed to a light inextensible string of length $0.9\,\text{m}$. One end of the string is fastened at the fixed point $A$, while the other end is fastened at the fixed point $C$, which lies vertically beneath $A$. The string has tension $T\,\text{N}$, and the bead moves with angular speed $\omega\,\text{rad s}^{-1}$ in a horizontal circle about the vertical axis through $A$ and $C$.
(i)[5]
Since $B$ travels in a circle with centre $C$ and radius $0.2\,\text{m}$, calculate $\omega$, and then determine the kinetic energy of $B$.
(ii)[6]
With angle $ABC = 90^{\circ}$ instead, and $AB$ making an angle $\tan^{-1}\!\left(\tfrac{1}{2}\right)$ with the vertical, calculate $T$ and $\omega$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Determine the angle: $\theta = \sin^{-1}(0.2/0.7) = 16.6^\circ$ to the vertical” …