State two conditions for an object to be in equilibrium. 1. .................................................................................................................................... 2. ....................................................................................................................................

1. (a)State two conditions for an object to be in equilibrium. 1. .................................................................................................................................... 2. ....................................................................................................................................[2]
2. (b)(i)A sphere of weight 2.4N is suspended by a wire from a fixed point P. A horizontal string is used to hold the sphere in equilibrium with the wire at an angle of 53° to the horizontal, as shown in Fig. 3.1. [Figure 3.1] Calculate: 1. the tension T in the wire T = ..................................................... N 2. the force F exerted by the string on the sphere. F = ..................................................... N[2]
3. (b)(ii)The wire has a circular cross-section of diameter 0.50 mm. Determine the stress σ in the wire. σ = ..................................................... Pa[3]
4. (c)(i)The string is disconnected from the sphere in (b). The sphere then swings from its initial rest position A, as illustrated in Fig. 3.2. [Figure 3.2] The sphere reaches maximum speed when it is at the bottom of the swing at position B. The distance between P and the centre of the sphere is 75cm. Air resistance is negligible and energy losses at P are negligible. Show that the vertical distance h between A and B is 15 cm.[1]
5. (c)(ii)Calculate the change in gravitational potential energy of the sphere as it moves from A to B. change in gravitational potential energy = ..................................................... J[2]
6. (c)(iii)Use your answer in (c)(ii) to determine the speed of the sphere at B. Show your working. speed = ..................................................... m s⁻¹[3]

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