Two particles P P\,P and Q Q\,Q of mass 4 kg and 6 kg respectively are connected by a light inextensible string. Particle P P\,P is placed on a rough plane inclined at an angle θ \theta\,θ to the horizontal, where tanθ=4/3\tan \theta = 4/3tanθ=4/3. The string passes over a smooth fixed pulley at the top of the plane, and Q Q\,Q hangs freely. The part of the string between P P\,P and the pulley is parallel to the line of greatest slope of the plane. The coefficient of friction between P P\,P and the plane is 0.5. The system is released from rest with P P\,P moving up the plane.
Calculate the tension in the string during the motion.
When Q Q\,Q hits the ground, P P\,P continues to move up the plane until it momentarily comes to rest. Determine, with justification, whether P P\,P will remain at rest or slide back down the plane.
Suggest two refinements to the model that would make it more realistic.
136 exam-style questions on CCEA A Level Maths 2.3 Forces and Newton's laws, covering 2.3.1 Forces and Newton's laws, 2.3.2 Forces and Newton's laws, 2.3.3 Forces and Newton's laws, 2.3.4 Forces and Newton's laws, 2.3.5 Forces and Newton's laws, 2.3.6 Forces and Newton's laws, 2.3.7 Forces and Newton's laws, 2.3.8 Forces and Newton's laws, 2.3.9 Forces and Newton's laws, 2.3.10 Forces and Newton's laws, 2.3.11 Forces and Newton's laws, 2.3.12 Forces and Newton's laws, and 2.3 Forces and Newton's laws. Each one has a worked solution and a mark scheme showing where the marks go.