Question

A uniform spring has an unstretched length l and force constant k. The spring is cut into two parts of unstretched length l1 and l2 such that l1 = nl2, where n is an integer, then the respective force constant of the broken springs are

Answer 1

A uniform spring has an unstretched length l and force constant k. The spring is cut into two parts of unstretched length l1 and l2 such that l1 = nl2.

then, k1l1 = k2l2 = F { force will be same in both case }

or, k1nl2 = k2l2

or, k2 = nk1 .......(1)

now force will be same in both springs

then, we have to apply series combination where k will be equivalent spring constant.

e.g., 1/k = 1/k1 + 1/k2

or, 1/k = 1/k1 + 1/nk1

or, 1/k =(n + 1)/nk1

or, k = nk1/(n + 1)

or, k1 = (n + 1)k/n

Putting k1 in equation (1),

k2 = (n + 1)k

hence, answer is (n + 1)k/n and (n + 1)k

Answer 2

Explanation:

here's the answer

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