Equilibrium, toppling and slidingEdexcel A-Level Further Maths: Mind map

Exam questions on Equilibrium, toppling and sliding

1. A uniform rectangular lamina $ABCD$ has $AB=12$ cm and $BC=8$ cm. It is freely suspended from the vertex $A$ and hangs in equilibrium.
   Find the distance from $A$ to the centre of mass of the lamina.2 marks
2. A uniform solid block has a rectangular cross-section 0.4 m wide and 0.6 m high. It rests on a rough plane inclined at an angle $\alpha$ to the horizontal, with its 0.4 m wide face in contact with the plane and the width lying along a line of greatest slope.
   Find the range of values of the coefficient of friction $\mu$ for which the block topples before it slides.2 marks
3. A uniform rod $AB$, of mass 12 kg and length 4 m, has its end $A$ on rough horizontal ground and its end $B$ against a smooth vertical wall. The rod lies in a vertical plane perpendicular to the wall and is inclined at $60^\circ$ to the horizontal. Take $g=9.8$ m s⁻².
   Find the magnitude of the force exerted on the rod by the wall.3 marks