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.
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.