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.
