Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A uniform triangular prism with weight $20\text{ N}$ is at rest on a horizontal table. $ABC$ is the cross-section through the prism’s centre of mass, with $BC = 0.5\text{ m}$, $AB = 0.4\text{ m}$, $AC = 0.3\text{ m}$ and angle $BAC = 90^\circ$. The vertical plane $ABC$ is perpendicular to the table edge. Point $D$ on $AC$ lies at the table edge, and $AD = 0.25\text{ m}$. One end of a light elastic string of natural length $0.6\text{ m}$ and modulus of elasticity $48\text{ N}$ is fixed to $C$ and a particle of mass $2.5\text{ kg}$ is attached to the other end of the string. The particle is let go from rest at $C$ and moves down vertically.
(i)[3]
Show that the tension in the string is $60\text{ N}$ at the instant when the prism topples.
(ii)[5]
Calculate the speed of the particle at the instant when the prism topples.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “States centre of mass $0.1\,\text{m}$ from $AB$” …