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Suppose 2 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 42 cm.Then how much work is needed to stretch it from 30 cm to 40 cm.

$\begin{array}{1 1}\large\frac{1}{18}\\\large\frac{1}{28}\\18\\28\end{array} $

1 Answer

Answer : $\large\frac{1}{18}$
From Hooke's law : $F=kx$ where $x$ is the distance the spring is stretched from its natural length,and $k$ is the (usually unknown) spring constant.
The spring's natural length is 30 cm,so it is stretched 12 cm from the natural length,we can use
$W=\int dW=\int F dx$
$2J=\int_0^{.12m}kx dx$
Once we have k,we can calculate the work done as follows
$W=\int dW$
$\;\;\;\;=\int\limits_0^{.1}F dx$
$\;\;\;\;=\int\limits_0^{.1} \large\frac{100}{9}$$xdx$
answered Sep 2, 2014 by sreemathi.v
edited Sep 2, 2014 by sreemathi.v

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