Question 26.3.44: Two identical springs labelled as 1 and 2 are arranged in se...

A Textbook Of Strength Of Materials: Mechanics of Solids

Two identical springs labelled as 1 and 2 are arranged in series and subjected to force F as shown in Fig. 12. Assume that each spring constant is k. The strain energy stored in spring 1 is

(a) $\frac{F^2}{2k}$ (b) $\frac{F^2}{4k}$ (c) $\frac{F^2}{8k}$ (d) $\frac{F^2}{16k.}$

26.12

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(c)

EXPLANATION

Strain energy stored in spring 1,

$U_1=\frac{1}{2} \times F_1 \times \delta_1 =\frac{1}{2} \times \frac{F}{2} \times \frac{F}{2 k} \\ \space \\ =\pmb{\frac{ F ^2}{8 k }.}$

\text { where } F_1=\text { force carried by spring } 1 \\ \space \\  =\frac{F}{2}(\because \text { both springs are identical }) \\ \space \\  \delta_1=\text { Deflection of spring } 1 \\ \space \\ =\frac{F_1}{k} \\ \space \\=\frac{F}{2 k} \quad\left(\because F_1=\frac{F}{2}\right)

26.21

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