Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A uniform lamina $ABC$ takes the form of a major segment of a circle with centre $O$ and radius $0.35\,\text{m}$. The straight boundary of the lamina is $AB$, and angle $AOB=\frac{2\pi}{3}$ radians. The lamina weighs $14\,\text{N}$. It is positioned on a rough horizontal surface with $A$ vertically above $B$, and the lowest point of the arc $BC$ touching the surface. The lamina is maintained in equilibrium in a vertical plane by a force of magnitude $F\,\text{N}$ applied at $A$.
(i)[6]
Show that the lamina has its centre of mass $0.0600\,\text{m}$ from $O$, correct to $3$ significant figures.
(ii(a))[2]
Find $F$ when the force of magnitude $F\,\text{N}$ is applied along $AB$.
(ii(b))[3]
Find $F$ when the force of magnitude $F\,\text{N}$ is applied along the tangent to the circular arc at $A$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Determines $OG$ for the sector: $\dfrac{2\times0.35\sin(2\pi/3)}{3\times2\pi/3}$” …