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.
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.