Two masses M1 M_1\,M1 of 2 kg and M2 M_2\,M2 of 4 kg are connected by a light inextensible string. The string passes over a smooth pulley at the top of a rough plane inclined at 45∘ 45^\circ\,45∘ to the horizontal. M1 M_1\,M1 rests on the plane and M2 M_2\,M2 hangs freely. The system is released from rest and M1 M_1\,M1 accelerates up the plane at 2.5 ms-2.
Find the tension in the string
Find the coefficient of friction between M1 M_1\,M1 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.