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 AQA A Level Maths 3.3 R: Forces and Newton's laws, covering 3.3.1 Concept of a force and Newton's first law, 3.3.2 Newton's second law, 3.3.3 Weight and motion under gravity, 3.3.4 Newton's third law and equilibrium, 3.3.5 Addition of forces and resultants (A-level only), and 3.3.6 Friction (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.