Ahelical compression spring is wound using 2.5-mm-diameter music wire. the spring has an outside diameter of 31 mm with plain ground ends, and 14 total coils. (a) estimate the spring rate. (b) what force is needed to compress this spring to closure? (c) what should the free length be to ensure that when the spring is compressed solid the torsional stress does not exceed the yield strength? (d) is there a possibility that the spring might buckle in service?

Asheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200oc and is permitted to achieve a steady-state diffusion condition. the diffusion coefficient for nitrogen in steel at this temperature is 6 x 10- 11 m2 /s, and the diffusion flux is found to be 1.2 x 10-7 kg/m2 -s. also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3 . how far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3 ? assume a linear concentration profile.