Equilibrium of rigid bodiesEdexcel International A Level Further Maths: Mind map

Exam questions on Equilibrium of rigid bodies

1. A uniform rod $AB$ of mass $6$ kg and length $2$ m is freely hinged to a fixed point at $A$. A horizontal force of magnitude $P$ newtons is applied at $B$, and the rod rests in equilibrium inclined at an angle $\theta$ to the downward vertical, where $\tan\theta=\frac12$. Take $g=9.8$ m s$^{-2}$.
   Find the angle that the force exerted by the hinge makes with the vertical.2 marks
2. A uniform solid cylinder of radius $0.2$ m and height $0.6$ m is placed with its circular base on a plane inclined at an angle $\theta$ to the horizontal. The plane is rough. The angle $\theta$ is increased slowly from zero.
   The coefficient of friction between the cylinder and the plane is $0.5$. Find the angle at which the cylinder first begins to move, and state how it moves.2 marks
3. A uniform ladder $AB$ of mass $20$ kg and length $5$ m rests in equilibrium with its end $A$ on rough horizontal ground and its end $B$ against a smooth vertical wall. The ladder is in a vertical plane perpendicular to the wall, and makes an angle of $60^\circ$ with the horizontal. Take $g=9.8$ m s$^{-2}$.
   Find the magnitude of the frictional force at $A$.3 marks