A block of mass m, lying on a smooth horizont | vedclass

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Question

When $\,{v_{\max }}$ $\Rightarrow $ acceleration $= 0$

$ \Rightarrow \,x = \frac{F}{K}$

Apply work energy theorem 

$\,{W_{sp}}$ + $w_f$

Vedclass · Accepted Answer

$\frac{F}{{\sqrt {mk} }}$

Vedclass · Answer

When $\,{v_{\max }}$ $\Rightarrow $ acceleration $= 0$

$ \Rightarrow \,x = \frac{F}{K}$

Apply work energy theorem 

$\,{W_{sp}}$ + $w_f$ = $\Delta K.E$

$\begin{array}{l}
 - \frac{1}{2}K{x^2} + F.x = \Delta K.E\,\,\,;\,\, - \frac{1}{2}K\frac{{{F^2}}}{{{K^2}}} + \frac{{{F^2}}}{K}\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{2}mu_{\max }^2\
\frac{{{F^2}}}{{2K}} = \frac{1}{2}mu_{\max }^{2\,}\,\,\,;\,\,\,\frac{F}{{\sqrt {mK} }} = {V_{\max }}
\end{array}$

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