A rough surface is inclined at an angle θ \theta\,θ to the horizontal, where tanθ=815\displaystyle \tan \theta = \frac{8}{15}tanθ=158. A crate of mass k k\,k kg is placed on the surface and allowed to slide. The coefficient of friction between the crate and the surface is 13\displaystyle \frac{1}{3}31.
Find the acceleration of the crate.
A different crate with mass 5k 5k\,5k kg is placed on the same surface. Explain how the acceleration of this crate would compare to your answer in part (a).
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.