A box C C\,C of mass 3 kg is held at rest on a rough surface inclined at an angle α \alpha\,α to the horizontal, where cosα=0.8\cos \alpha = 0.8cosα=0.8. It is connected to a box D D\,D of mass 7 kg by a light inextensible string passing over a smooth pulley. D D\,D hangs vertically. The string is parallel to the slope. The coefficient of friction between C C\,C and the plane is 0.25. The system is released from rest.
Find the tension in the string as the boxes accelerate.
Once D D\,D reaches the floor, C C\,C continues to move up the plane until it stops. Determine whether box C C\,C will remain at rest in its highest position.
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.