8. A horse is trapped in a well. Its owner attaches one end of a light,...

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8. A horse is trapped in a well. Its owner attaches one end of a light, inextensible rope to the horse, and the other end to her tractor. The tractor has a mass of 2100 kg and the horse has a mass of 800 kg. The rope passes over a smooth pulley, as illustrated to the right. Between the tractor and the pulley the rope is horizontal. Between the pulley and the horse the rope is vertical. Initially, the rope is taut and the tractor and the horse are at rest. The tractor begins to move away from the well with its engine providing a constant forward force of 10,200 N. A constant resistance of 1200 N opposes the tractor's forward motion. There is no force resisting the horse's motion. (a) Draw separate diagrams showing the forces acting on: (i) the horse while it is being lifted (ii) the tractor while it is lifting the horse (b) Show that the tractor accelerates at 0.4 m s (c) Find the tension in the rope (d) Suggest one refinement that could be made to the model A Level Edexcel Mathematics Set B Paper 3 Page 7 of 70 ZigZag Education, 2019 9. A ladder PQ of length / and weight W is placed on a rough horizontal floor and propped against a smooth vertical wall, as sketched to the right. The acute angle between the ladder and the ground, 0, satisfies tan = 2. 1 The coefficient of friction between the ladder and the ground is A painter of weight 4W stands at a point R on the ladder such that PR has length x/ for some 0x1. The ladder rests in equilibrium. The ladder is modelled as a uniform rod, and the painter is modelled as a particle. P W (a) Show that the normal reaction of the wall on the ladder at Q has magnitude (8x+1) (b) Find the range of values of x for which the ladder remains in equilibrium The painter places some heavy paint cans on the bottom rung of the ladder at P. (c) Explain how this allows the painter to climb higher before the ladder slips 4 (5) (5) (3) 8. A horse is trapped in a well. Its owner attaches one end of a light, inextensible rope to the horse, and the other end to her tractor. The tractor has a mass of 2100 kg and the horse has a mass of 800 kg. The rope passes over a smooth pulley, as illustrated to the right. Between the tractor and the pulley the rope is horizontal. Between the pulley and the horse the rope is vertical. Initially, the rope is taut and the tractor and the horse are at rest. The tractor begins to move away from the well with its engine providing a constant forward force of 10,200 N. A constant resistance of 1200 N opposes the tractor's forward motion. There is no force resisting the horse's motion. (a) Draw separate diagrams showing the forces acting on: (i) the horse while it is being lifted (ii) the tractor while it is lifting the horse (b) Show that the tractor accelerates at 0.4 m s (c) Find the tension in the rope (d) Suggest one refinement that could be made to the model A Level Edexcel Mathematics Set B Paper 3 Page 7 of 70 ZigZag Education, 2019 9. A ladder PQ of length / and weight W is placed on a rough horizontal floor and propped against a smooth vertical wall, as sketched to the right. The acute angle between the ladder and the ground, 0, satisfies tan = 2. 1 The coefficient of friction between the ladder and the ground is A painter of weight 4W stands at a point R on the ladder such that PR has length x/ for some 0x1. The ladder rests in equilibrium. The ladder is modelled as a uniform rod, and the painter is modelled as a particle. P W (a) Show that the normal reaction of the wall on the ladder at Q has magnitude (8x+1) (b) Find the range of values of x for which the ladder remains in equilibrium The painter places some heavy paint cans on the bottom rung of the ladder at P. (c) Explain how this allows the painter to climb higher before the ladder slips 4 (5) (5) (3)