# Chapter 8 - Potential Energy and Conservation of Energy - Problems - Page 204: 28b

$v_{1}=\sqrt {\dfrac {k}{m}\left( x^{2}-x^{2}_{1}\right) }\approx 2,71\dfrac {m}{s}$

#### Work Step by Step

Firstly lets calculate spring constant from the graph: $k=\dfrac {\Delta F}{\Delta x}=\dfrac {0,4N}{4\times 10^{-2}m}=10\dfrac {N}{m}$ Lets think cork and spring as a system So initialy this system has only potential energy stored in spring so $E_{tot}=\dfrac {kx^{2}}{2}\left( 1\right)$ the cork leaves spring when spring stretched so at this time potential energy of the system will not be zero So lets write total energy equation when cork leaves spring: $E_{tot}=\dfrac {mv^{2}_{1}}{2}+\dfrac {kx^{2}_{1}}{2}\left( 2\right)$ ($x_{1}$ is the stretched disctance ) so from (1) and (2) we get $v_{1}=\sqrt {\dfrac {k}{m}\left( x^{2}-x^{2}_{1}\right) }\approx 2,71\dfrac {m}{s}$

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