Question

Consider a spring of force constant $0.9kN/m$ which is struck by a $4kg$ mass with a speed of $6m{s}^{-1}$ . Now, find the compression in the spring:

• A. $4cm$
• B. $40cm$
• C. $20cm$
• D. None of these

Answer 1

Answer: (B)

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.
$\Rightarrow \frac{1}{2}m{v}^2=\frac{1}{2}k{x}^2$
$\Rightarrow x=v\sqrt{\frac{m}{k}}$
$=6\sqrt{\frac{4}{900}}=6\times \frac{2}{30}\times 100cm$
$=40cm$