question_answer

Two springs A and B are identical but A is harder than \[\text{B}\left( {{\text{K}}_{\text{A}}}>{{\text{K}}_{\text{B}}} \right)\]. On which spring more work will be done if : (a) they are stretched through the same distance, (b) they are stretched by same force?

Answer:

                (a) As \[\text{W}=\frac{1}{2}\text{K}{{\text{x}}^{\text{2}}}\], and \[{{\text{K}}_{\text{A}}}>{{\text{K}}_{\text{B}}}\] work done on spring A will be more than work done on spring B (for same x) As F = Kx, therefore, x = F/K As \[{{\text{K}}_{\text{A}}}>{{\text{K}}_{\text{B}}}\] \[{{\text{X}}_{\text{A}}}<{{\text{X}}_{\text{B}}}\] As \[\text{W}=\frac{1}{2}\text{K}{{\text{x}}^{\text{2}}}=\frac{1}{2}\left( \frac{F}{x} \right){{x}^{2}}=\frac{1}{2}Fx\] As \[{{\text{x}}_{\text{A}}}<{{\text{x}}_{\text{B}}}\] \[{{\text{W}}_{\text{A}}}<{{\text{W}}_{\text{B}}}\] or \[{{\text{W}}_{\text{B}}}>{{\text{W}}_{\text{A}}}\] i.e. more work is required in case of spring B than in the case of spring A.