A spring is attached at one end to a fixed point and hangs vertically with a cube attached to the other end. The cube is initially held so that the spring has zero extension, as shown in Fig. 3.1. [Figure 3.1] The cube has weight 4.0N and sides of length 5.1cm. The cube is released and sinks into water as the spring extends. The cube reaches equilibrium with its base at a depth of 7.0cm below the water surface, as shown in Fig. 3.2. [Figure 3.2] The density of the water is 1000kgm⁻³.

1. (a)Calculate the difference in the pressure exerted by the water on the bottom face and on the top face of the cube.[2]
2. (b)Use your answer in (a) to show that the upthrust on the cube is 1.3N.[2]
3. (c)Calculate the force exerted on the spring by the cube when it is in equilibrium in the water.[1]
4. (d)The spring obeys Hooke's law and has a spring constant of 30Nm⁻¹. Determine the initial height above the water surface of the base of the cube before it was released.[3]
5. (e)(i)The cube in the water is released from the spring. Determine the initial acceleration of the cube.[2]
6. (e)(ii)Describe and explain the variation, if any, of the acceleration of the cube as it sinks in the water.[2]

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