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Springs A and B are identical except that A is stiffer that B; that is, k A > k B . On which spring is more work expended if they are stretched (a) by the same amount and (b) by the same force? Springs A and B are identical except that A is stiffer that B; that is, kA > kB. On which spring is more work expended if they are stretched (a) by the same amount and (b) by the same force?
Dear Student,Please find below the solution to your problem.A is stiffer than B implies that for equal expansion in A and B, more force should be applied on A than B. Hence spring constant of A would be greater than B.Now force applied on both is the same. Thus spring B will expand more than spring A as it's spring constant is less than that of A.Work done by the spring is given by (1/2)(K)(x^2). Talking about A it's spring constant is greater but expansion is less and in the expression, the term for expansion is squared. Hence overall we can say that it did less work.Thus spring B did more work than A.Alternately, we can see that the force applied in both the cases is same. Spring B expands more than A. Since work=force×displacement, hence spring B does more work than A.Thanks and Regards
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