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Pearson Edexcel Level 3 GCE., Further Mathematics Advanced Subsidiary Further Mathematics options 26: Further Mechanics 2 (Part of option J).

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A uniform rod of length 72a is cut into pieces. The pieces are used to make two rigid squares, ABCD and PQRS, with sides of length 10a and 8a respectively. The two squares are joined to form the rig... id framework shown in Figure 1. The squares both lie in the same plane with the rod AB parallel to the rod PQ. Given that • AD cuts PQ in the ratio 3: 5 • DC cuts QR in the ratio 5:3 (a) explain why the centre of mass of square ABCD is at Q. (1) (b) Find the distance of the centre of mass of the framework from B. (5 A small smooth ring P, of mass m, is threaded onto a light inextensible string of length 4a. One end of the string is attached to a fixed point A on a smooth horizontal table. The other end of the string is attached to a fixed point B which is vertically above A. The ring moves in a horizontal circle with centre A and radius a, as shown in Figure 2. The ring moves with constant angular speed 2 3 ga about AB. The string remains taut throughout the motion. (a) Find, in terms of m and g, the magnitude of the normal reaction between P and the table. (6) The angular speed of P is now gradually increased. (b) Find, in terms of a and g, the angular speed of P at the instant when it loses contact with the table. (3) (c) Explain how you have used the fact that P is smooth. (1 [Show More]

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