A box M1 M_1\,M1 of mass 5 kg and a weight M2 M_2\,M2 of mass 8 kg are joined by a light inextensible string. The string passes over a small smooth pulley at the top of a rough ramp. The ramp is inclined at an angle ϕ \phi\,ϕ to the horizontal where tanϕ=0.75\tan \phi = 0.75tanϕ=0.75. The coefficient of friction between the box and the ramp is 0.3. M1 M_1\,M1 is placed on the ramp and M2 M_2\,M2 is suspended 3 m above the floor. The system is released from rest with the string taut. Assume M2 M_2\,M2 hits the floor before M1 M_1\,M1 reaches the pulley.
Find the speed at which M2 M_2\,M2 hits the floor.
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.