Two blocks X X\,X of mass 5 kg and Y Y\,Y of mass 10 kg are connected by a light inextensible string. Block X X\,X is on a rough plane inclined at angle β \beta\,β to the horizontal where tanβ=5/12\tan \beta = 5/12tanβ=5/12. The string passes over a smooth pulley and Y Y\,Y hangs vertically. The coefficient of friction between X X\,X and the plane is 0.1. The blocks are released from rest with X X\,X moving up the plane.
Find the tension in the string.
After Y Y\,Y hits the floor, X X\,X comes to rest. Determine whether X X\,X will stay at rest.
Suggest two refinements to the model that would make it more realistic.
130 exam-style questions on Edexcel A Level Maths Applications of Forces, covering 7.1 Static Particles, 7.2 Modelling with Statics, 7.3 Friction and Static Particles, 7.4 Static Rigid Bodies, 7.5 Dynamics and Inclined Planes, and 7.6 Connected Particles 2. Each one has a worked solution and a mark scheme showing where the marks go.