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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?
 

Grade:10

2 Answers

Jitender Pal
askIITians Faculty 365 Points
8 years ago
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Rishi Sharma
askIITians Faculty 646 Points
3 years ago
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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