10 12 In a conical spring the diameter of the coils increases over its length. The spring can be designed so that each coil fits into the inner diameter of the next coil so they take up minimal space when fully compressed. (Source: © Anatolii Riabokon/Alamy Stock Vector) A conical spring is compressed against a flat surface. The graph shows the force‑displacement graph for the spring as the compression force increases from 0 N to the point when the spring is fully compressed. 800 700 600 500 400 300 200 100 0 130 120 110 100 90 80 70 60 50 40 30 20 10 0 Displacement / mm Force / N The spring obeys Hooke’s law for small compression forces. (a) Determine a value for the spring constant of the spring for compression forces up to 60 N. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. Spring constant = ....................................................... 11 Turn over (b) The compression force is increased from 60 N to 220 N. Determine a value for the additional energy stored in the spring due to this increase in force. (3) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... Additional energy = ....................................................... (c) When fully compressed all the coils lie flat inside each other. h d unloaded fully compressed The height h of the spring when unloaded is 126 mm. Calculate the diameter d of the wire in the spring. (2) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... Diameter = ....................................................... (Total for Question 12 = 7 marks)