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.
49 exam-style questions on OCR (MEI) A Level Maths 3.5 Newton's Laws of Motion, covering 3.5.1 Meaning of Newton's three laws, 3.5.2 Equation of motion, 3.5.3 Equation of motion for a particle in a straight line, 3.5.4 Model a system of connected particles, 3.5.5 Equations of motion for individual particles, 3.5.6 System with no relative motion as a single particle, and 3.5.7 Equation of motion in a straight line or plane (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.