Equilibrium, sliding and topplingAQA A-Level Further Maths: Mind map

Exam questions on Equilibrium, sliding and toppling

1. A uniform horizontal rod $AB$ of length $4$ m and mass $6$ kg rests in equilibrium, supported by two vertical strings. One string is attached at $A$ and the other at the point $C$ on the rod, where $AC=3$ m. Take $g=9.8$ m s$^{-2}$.
   A particle of mass $3$ kg is now attached to the rod at $B$. Find the new tension in the string at $A$.2 marks
2. A uniform rectangular lamina $ABCD$ has $AB=0.9$ m, $AD=0.6$ m and mass $3$ kg. It hangs freely in equilibrium from a smooth pivot at $A$. Take $g=9.8$ m s$^{-2}$.
   The lamina is now held in equilibrium with $AB$ horizontal by a vertical string attached at $B$. The lamina can still rotate freely about $A$. Find the tension in the string.2 marks
3. A uniform ladder $AB$ of length $5$ m and mass $20$ kg rests in equilibrium in a vertical plane with its upper end $B$ against a smooth vertical wall and its lower end $A$ on rough horizontal ground. The foot $A$ is $3$ m from the wall. Take $g=9.8$ m s$^{-2}$.
   Find the magnitude of the force exerted by the wall on the ladder.3 marks