The variation with extension x of the force F applied to a spring is shown in Fig. 4.1. [Figure 4.1] The spring has an unstretched length of 0.080 m and is suspended vertically from a fixed point, as shown in Fig. 4.2. [Figure 4.2] A block is attached to the lower end of the spring. The block hangs in equilibrium at position X when the length of the spring is 0.095 m, as shown in Fig. 4.3. [Figure 4.3] The block is then pulled vertically downwards and held at position Y so that the length of the spring is 0.120m, as shown in Fig. 4.4. The block is then released and moves vertically upwards from position Y back towards position X. [Figure 4.4]

1. (a)Use Fig. 4.1 to determine the spring constant of the spring. spring constant = ............................................... Nm⁻¹ [2][2]
2. (b)Use Fig. 4.1 to show that the decrease in elastic potential energy of the spring is 0.055 J when the block moves from position Y to position X. [2][2]
3. (c)The block has a mass of 0.122kg. Calculate the increase in gravitational potential energy of the block for its movement from position Y to position X. increase in gravitational potential energy = ................................................. J [2][2]
4. (d)Use the decrease in elastic potential energy stated in (b) and your answer in (c) to determine, for the block, as it moves through position X:
5. (d)(i)its kinetic energy kinetic energy = ................................................. J [1][1]
6. (d)(ii)its speed. speed = .................................................... ms⁻¹ [2][2]

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