A rubber band (two parallel strands of elastic material forming a closed loop) has an effective spring constant of 10 N/m. If the band is cut in one place such that it now forms a single long strand o

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A rubber band (two parallel strands of elastic material forming a closed loop) has an effective spring constant of 10 N/m. If the band is cut in one place such that it now forms a single long strand of elastic material, what is its new effective spring constant?

TestHub · Accepted Answer

Closed band = two identical strands in parallel: $k_{e q} = 2 k = 10 \Rightarrow k = 5 N/m$ .

After cutting, the two strands join end to end (series): $\frac{1}{k ^{'}} = \frac{1}{k} + \frac{1}{k} \Rightarrow k^{'} = \frac{k}{2} = 2.5 N/m$ . Answer: (D).

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