> Tuesday 19 October 2021 – Afternoon AS Level Further Mathematics B (MEI) Y415/01 Mechanics b

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Answer all the questions. 1 The end O of a light elastic string OA is attached to a fixed point. Fiona attaches a mass of 1kg to the string at A. The system hangs vertically in equilibrium and the ... length of the stretched string is 70cm. Fiona removes the 1kg mass and attaches a mass of 2 kg to the string at A. The system hangs vertically in equilibrium and the length of the stretched string is now 80cm. Fiona then removes the 2kg mass and attaches a mass of 5kg to the string at A. The system hangs vertically in equilibrium. (a) Use the information given in the question to determine expected values for • the length of the stretched string when the 5kg mass is attached, • the elastic potential energy stored in the string in this case. [7] Fiona discovers that, when the mass of 5kg is attached to the string at A, the length of the stretched string is greater than the expected length. (b) Suggest a reason why this has happened. [1] 2 A particle, Q, moves so that its velocity, v, at time t is given by v i = - ( ) 6 6 t t + - ( ) 3 2 + + t2 j k 4 , where 0 6 G G t . (a) Explain how you know that Q is never stationary. [1] When Q is at a point A the direction of the acceleration of Q is parallel to the i direction. When Q is at a point B the direction of the acceleration of Q makes an angle of 45° with the i direction. (b) Determine the straight-line distance AB. [7]3 © OCR 2021 Y415/01 Oct21 Turn over 3 In this question you must show detailed reasoning. [In this question you may use the formula: Volume of cone = 3 1 # base area # height.] The region between the line y x =-3 3 + a, where a 2 0, the x-axis and the y-axis is rotated about the y-axis to form a uniform right circular cone C with base radius a. (a) Show that the centre of mass of C is 4 3 a from its base. [5] The cone C is fixed on top of a uniform cube, B, of edge length 2a, so that there is no overlap. Fig. 3.1 shows a side view of C and B fixed together; Fig. 3.2 shows a view of C and B from above. C B 2a 2a 3a 2a 2a Fig. 3.1 Fig. 3.2 The centre of mass of the combined shape lies on the boundary of C and B. The density of B is not equal to the density of C. (b) Determine the exact value of density of C density of B [Show More]

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