A special spring exhibits two distinct regions of behaviour. For extensions x≤4.0cm it obeys a force constant k1=150Nm−1. Beyond 4.0cm the coils become stiffer and the force constant suddenly increases to k2=250Nm−1. The spring is initially at its natural length.
Answer the following:
a. (i) Sketch qualitatively the variation of restoring force with extension for the spring and clearly indicate the change in slope at x=4.0cm.
b. (ii) Obtain an expression for the total elastic potential energy stored when the spring is stretched to a total extension of 6.0cm.
c. (iii) Calculate the numerical value of this energy in joule for the given data.