Verify that the k I1 scaling law for the spring constant ap

Verify that the k ~ I^1 scaling law for the spring constant applies for both rod extension and cantilever springs.

Solution

The rod extension and cantilever springs are the two types of spring constant. The cantilever spring is constant at one end of the spring. Note that the spring constant k=EA0/L0 where E is the Young\'s modulus of the material (constant, at least in one direction), A0 is the unstretched cross sectional area, and L0 is the unstretched length of the ideal spring. This indicates that k is inversely proportional to the original length of the spring, with all else (material, cross section) being same. Therefore, spring is a quarter of the length will have a spring constant four times as high.