Two blocks X X\,X and YYY, of mass 2 kg and 4 kg respectively, are connected by a light inextensible string. The string passes over a smooth pulley at the peak of a rough inclined roof. The roof is inclined at an angle β \beta\,β where cosβ=1213\displaystyle \cos \beta = \frac{12}{13}cosβ=1312. Block X X\,X is on the roof and Y Y\,Y hangs vertically at a height of 2.5 m above the ground. The coefficient of friction between X X\,X and the roof is 0.1. The system is released from rest. Given that Y Y\,Y hits the ground before X X\,X reaches the pulley.
Find the speed of block Y Y\,Y at the instant it 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.