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Q.
Consider a spring of force constant $0.9kN/m$ which is struck by a $4kg$ mass with a speed of $6ms^{- 1}$ . Now, find the compression in the spring:
NTA AbhyasNTA Abhyas 2020
Solution:
Object moving with a certain velocity possesses kinetic energy and loses as it comes to rest. Hence, all the kinetic energy of the object is converted into elastic potential energy of spring.
$\Rightarrow \frac{1}{2}mv^{2}=\frac{1}{2}kx^{2}$
$\Rightarrow x=v\sqrt{\frac{m}{k}}$
$=6\sqrt{\frac{4}{900}}=6\times \frac{2}{30}\times 100cm$
$=40cm$