A uniform ladder ABABAB, with length 4 m and mass 12 kg, rests with its end A A\,A on rough horizontal ground. The ladder is in limiting equilibrium against a fixed smooth horizontal rail at a point CCC, where AC=3AC = 3AC=3 m. The ladder is in a vertical plane perpendicular to the rail and is inclined to the horizontal at an angle α\alphaα, where tanα=4/3\tan \alpha = 4/3tanα=4/3. The coefficient of friction between the ladder and the ground is μ\muμ.
Using the model, find the value of μ\muμ.
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.