A particle A A\,A of mass 3 kg and a particle B B\,B of mass 6 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 coefficient of friction between the particle A A\,A and the plane is 0.25. The plane is inclined at an angle of α∘ \alpha^\circ\,α∘ to the horizontal such that cosα=0.6\cos \alpha = 0.6cosα=0.6. A A\,A lies on the plane and B B\,B hangs freely from the edge of the plane 1.5 m above the ground with the string taut. The system is released from rest. Assume B B\,B hits the ground before A A\,A reaches the pulley.
Find the speed at which B B\,B hits the ground.
139 exam-style questions on OCR A Level Maths 3.3 Forces and Newton's Laws, covering 3.3.1 Concept and vector nature of a force, 3.3.2 Newton's first law, 3.3.3 Newton's second law in a straight line, 3.3.4 Newton's second law with vectors (A-level only), 3.3.5 Newton's second law with resolved forces (A-level only), 3.3.6 Weight, 3.3.7 Gravitational acceleration, 3.3.8 Newton's third law, 3.3.9 Normal reaction force, 3.3.10 Smooth contact model, 3.3.11 Equilibrium with connected particles and pulleys, 3.3.12 Newton's third law with resolved forces (A-level only), 3.3.13 Equilibrium by resolving (A-level only), 3.3.14 Equilibrium of forces in two dimensions using vectors (A-level only), 3.3.15 Resolving forces for advanced problems (A-level only), 3.3.16 Resultant forces and components (A-level only), 3.3.17 Dynamics of a particle in a plane (A-level only), 3.3.18 Concept of a frictional force (A-level only), 3.3.19 Contact force components (A-level only), 3.3.20 Coefficient of friction (A-level only), 3.3.21 Static and limiting equilibrium on a rough surface (A-level only), 3.3.22 Motion of a body on a rough surface (A-level only), and 3.3 Forces and Newton's Laws. Each one has a worked solution and a mark scheme showing where the marks go.