A particle of mass m m\,m kg rests on a rough plane inclined at an angle of 30° 30°\,30° to the horizontal. The particle is on the point of sliding down the plane.
Show that the coefficient of friction between the particle and the plane is 33\displaystyle \frac{\sqrt{3}}{3}33.
A force of magnitude P P\,P newtons is now applied to the particle up a line of greatest slope. Find, in terms of m m\,m and ggg, the set of values of P P\,P for which the particle remains at rest.
87 exam-style questions on OCR (MEI) A Level Maths 3.4 Forces, covering 3.4.1 Language relating to forces, 3.4.2 Acceleration due to gravity, 3.4.3 Identify forces and draw force diagrams, 3.4.4 Resultant of concurrent forces, 3.4.5 Equilibrium of a particle, 3.4.6 Resolve a force into components (A-level only), 3.4.7 Equilibrium condition for resultant zero (A-level only), 3.4.8 Forces in equilibrium sum to zero (A-level only), 3.4.9 Equations for a particle in equilibrium (A-level only), 3.4.10 Frictional force and normal contact force (A-level only), 3.4.11 Model friction with F ≤ μR (A-level only), and 3.4.12 Apply Newton's Laws to friction problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.