Two particles C C\,C of mass 3 kg and D D\,D of mass 5 kg are connected by a light inextensible string. The string passes over a smooth pulley fixed at the top of a rough inclined plane. The plane is inclined at an angle of 35∘ 35^\circ\,35∘ to the horizontal. C C\,C lies at rest on the plane and D D\,D hangs freely from the edge of the plane with the string taut. Particle C C\,C is released from rest and accelerates up the plane at 2 ms-2.
Find the tension in the string
Find the coefficient of friction between C C\,C and the plane
Find the force exerted on the pulley by the string
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.