5
\includegraphics[max width=\textwidth, alt={}, center]{8f8492a7-8a83-4eb2-81ee-99b4a385b704-3_876_483_260_840}
A uniform triangular prism of weight 20 N rests on a horizontal table. \(A B C\) is the cross-section through the centre of mass of the prism, where \(B C = 0.5 \mathrm {~m} , A B = 0.4 \mathrm {~m} , A C = 0.3 \mathrm {~m}\) and angle \(B A C = 90 ^ { \circ }\). The vertical plane \(A B C\) is perpendicular to the edge of the table. The point \(D\) on \(A C\) is at the edge of the table, and \(A D = 0.25 \mathrm {~m}\). One end of a light elastic string of natural length 0.6 m and modulus of elasticity 48 N is attached to \(C\) and a particle of mass 2.5 kg is attached to the other end of the string. The particle is released from rest at \(C\) and falls vertically (see diagram).
- Show that the tension in the string is 60 N at the instant when the prism topples.
- Calculate the speed of the particle at the instant when the prism topples.