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.
139 exam-style questions on AQA A Level Maths 3.3 R: Forces and Newton's laws, covering 3.3.1 Concept of a force and Newton's first law, 3.3.2 Newton's second law, 3.3.3 Weight and motion under gravity, 3.3.4 Newton's third law and equilibrium, 3.3.5 Addition of forces and resultants (A-level only), and 3.3.6 Friction (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.