> Thursday 7 October 2021 – Afternoon AS Level Further Mathematics B (MEI) Y411/01 Mechanics a. GRADED A+

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Answer all the questions. 1 The specific energy of a substance has SI unit J kg-1 (joule per kilogram). (a) Determine the dimensions of specific energy. [2] A particular brand of protein powder con... tains approximately 345 Calories (Cal) per 4 ounce (oz) serving. An athlete is recommended to take 40 grams of the powder each day. You are given that 1oz = 28.35 grams and 1 Cal = 4184J. (b) Determine, in joules, the amount of energy in the athlete’s recommended daily serving of the protein powder. [2] 2 The vertices of a triangular lamina, which is in the x-y plane, are at the origin O and the points A(4, 0) and B(0,3). Forces, of magnitude T1 N, T2 N and 10N, whose lines of action are in the x-y plane, are applied to the lamina at O, A and B respectively, as shown in the diagram. x y T2 N T1 N O 10 N 4 A B 3 a i (a) (i) Show that sin 0 a = .6. [1] (ii) Write down the value of cos a. [1] The lamina is in equilibrium. (b) Determine the values of T1, T2 and i. [7]3 © OCR 2021 Y411/01 Oct21 Turn over 3 Three small uniform spheres A, B and C have masses 2kg, 3kg and 5 kg respectively. The spheres move in the same straight line on a smooth horizontal table, with B between A and C. Sphere A moves towards B with speed 7 m s-1, B is at rest and C moves towards B with speed um s-1, as shown in the diagram. 7ms–1 ums–1 2kg 3 kg A B 5 kg C Spheres A and B collide. Collisions between A and B can be modelled as perfectly elastic. (a) Determine the magnitude of the impulse of A on B in this collision. [5] (b) Use this collision to verify that in a perfectly elastic collision no kinetic energy is lost. [1] After the collision between A and B, sphere B subsequently collides with C. The coefficient of restitution between B and C is 14 . (c) Show that, after the collision between B and C, B has a speed of ( . 1 225-0. ) 78125u m s-1 towards C. [4] (d) Determine the range of values for u for there to be a second collision between A and B. [2]4 © OCR 2021 Y411/01 Oct21 4 The diagram shows the path of a particle P of mass 2 kg as it moves from the origin O to C via A and B. The lengths of the sections OA, AB and BC are given in the diagram. The units of the axes are metres [Show More]

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