Further Mechanics 1

A van of mass 900 kg is moving along a straight horizontal road. At the instant when the speed of the van is v m s−1, the resistance to the motion of the van is modelled as a force of magnitude (500 + 7v) N. When the engine of the van is working at a constant rate of 18 kW, the van is moving along the road at a constant speed V m s−1 (a) Find the value of V. (5) Later on, the van is moving up a straight road that is inclined to the horizontal at an 1 angle θ , where sin θ = 21 At the instant when the speed of the van is v m s−1, the resistance to the motion of the van from non-gravitational forces is modelled as a force of magnitude (500 + 7v) N. The engine of the van is again working at a constant rate of 18 kW. (b) Find the acceleration of the van at the instant when v = 15 (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ *P66800A0228* _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ *P66800A0428* _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 1 is 9 marks) *P66800A0528* 2. Two particles, A and B, are moving in opposite directions along the same straight line on a smooth horizontal surface when they collide directly. Particle A has mass 5m and particle B has mass 3m. The coefficient of restitution between A and B is e, where e > 0 Immediately after the collision the speed of A is v and the speed of B is 2v. Given that A and B are moving in the same direction after the collision, (a) find the set of possible values of e. (8) Given also that the kinetic energy of A immediately after the collision is 16% of the kinetic energy of A immediately before the collision, (b) find (i) the value of e, (ii) the magnitude of the impulse received by A in the collision, giving your answer in terms of m and v. 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