OCR Tuesday 19 October 2021 – Afternoon AS Level Further Mathematics A Y533/01 Mechanics. GRADED A+

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Answer all the questions. 1 One end of a light inextensible string of length 2.8m is attached to a fixed point O on a smooth horizontal table. The other end of the string is attached to a particle P... which moves on the table, with the string taut, in a circular path around O. The speed of P is constant and P completes each circle in 0.84 seconds. (a) Find the magnitude of the angular velocity of P. [2] (b) Find the speed of P. [2] (c) Find the magnitude of the acceleration of P. [2] (d) State the direction of the acceleration of P. [1] 2 A car has a mass of 800kg. The engine of the car is working at a constant power of 15kW. In an initial model of the motion of the car it is assumed that the car is subject to a constant resistive force of magnitude RN. The car is initially driven on a straight horizontal road. At the instant that its speed is 20 ms-1 its acceleration is 0 4 . ms-2. (a) Show that R = 430. [3] (b) Hence find the maximum constant speed at which the car can be driven along this road, according to the initial model. [2] In a revised model the resistance to the motion of the car at any instant is assumed to be 60v where v is the speed of the car at that instant. The car is now driven up a straight road which is inclined at an angle a above the horizontal where sin 0 a = .2. (c) Determine the speed of the car at the instant that its acceleration is 0 1 . m 5 s-2 up the slope, according to the revised model. [4]3 © OCR 2021 Y533/01 Oct21 Turn over 3 A particle A of mass 0.5kg is moving with a speed of 3 1 . m 5 s-1 on a smooth horizontal surface when it collides directly with a particle B of mass 0.8 kg which is at rest on the surface. The velocities of A and B immediately after the collision are denoted by vAms-1 and vBms-1 respectively. You are given that vB = 2vA. (a) Find the values of vA and vB. [3] (b) Find the coefficient of restitution between A and B. [2] (c) Explain why the coefficient of restitution is a dimensionless quantity. [1] (d) Calculate the total loss of kinetic energy as a result of the collision. [3] (e) State, giving a reason, whether or not the collision is perfectly elastic. [1] (f) Calculate the impulse that B exerts on A in the collision. [3] 4 A small box B of mass 4.2kg is initially at rest at a point O on rough horizontal ground. A horizontal force of magnitude 35N is applied to B. B moves in a straight line until it reaches the point S which is 2.4m from O. At the instant that B [Show More]

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