question_answer

Springs A and B are identical except that A is stiffer than B. In which spring is more work expended if they are stretched by the same force?

Answer:

                As \[F=kx,\] so \[x=\frac{F}{k}\]                 For same \[F,{{W}_{A}}=\frac{1}{2}{{k}_{A}}{{x}^{2}}=\frac{1}{2}{{k}_{A}}{{\left( \frac{F}{{{k}_{A}}} \right)}^{2}}=\frac{{{F}^{2}}}{2{{k}_{A}}}\]                 and        \[{{W}_{B}}=\frac{{{F}^{2}}}{2{{k}_{B}}}\]                 \[\therefore \]  \[\frac{{{W}_{A}}}{{{W}_{B}}}=\frac{{{k}_{B}}}{{{k}_{A}}}\]                 As           \[{{k}_{A}}>{{k}_{B}}\]  therefore, \[{{W}_{A}}<{{W}_{B}}.\]