Two light springs and having force constants and respectively are connected in series…

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

Two light springs

S_1

and

S_2

having force constants

k_1=300\,\text{N\,m}^{-1}

and

k_2=200\,\text{N\,m}^{-1}

respectively are connected in series between two rigid supports along a common straight line. The combination is pulled so that the total extension produced is

8.0\,\text{cm}

. Answer the following: (i) Derive the expression for the effective force constant

k_{\text{series}}

of two springs connected in series. (ii) Using the derivation of part (i), calculate the numerical value of

k_{\text{series}}

for the given data. (iii) Determine the total elastic potential energy stored in the spring combination for the stated extension. (iv) If instead the springs were connected in parallel and stretched by the same amount of

8.0\,\text{cm}

, calculate the total elastic potential energy stored and compare it with the answer obtained in part (iii).

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