Equilibrium of a particleEdexcel International A Level Maths: Mind map

Exam questions on Equilibrium of a particle

1. A crate of mass 20 kg rests on a rough horizontal floor. A rope attached to the crate is pulled with a force of 50 N at $30^\circ$ above the horizontal, and the crate remains at rest. Take $g=9.8$ m s$^{-2}$ and model the crate as a particle.
   The crate is on the point of slipping. Find the coefficient of friction between the crate and the floor.2 marks
2. A particle of weight 30 N is held in equilibrium on a smooth plane inclined at $30^\circ$ to the horizontal by a force of magnitude $P$ N acting up the slope, parallel to the line of greatest slope.
   The force $P$ is removed and replaced by a horizontal force of magnitude $H$ N, so that the particle is still in equilibrium on the plane. Find $H$.2 marks
3. A particle of weight 80 N is in equilibrium, supported by two light inextensible strings. One string has tension $T_1$ N and makes an angle of $30^\circ$ with the horizontal. The other has tension $T_2$ N and makes an angle of $60^\circ$ with the horizontal, on the opposite side of the particle.
   By resolving horizontally, show that $T_2=\sqrt{3}\,T_1$.3 marks