Question

A block of mass ' $m$ ' (as shown in figure) moving with kinetic energy E compresses a spring through a distance $25\, cm$ when, its speed is halved. The value of spring constant of used spring will be $nE Nm ^{-1}$ for $n =$ ___

Answer 1

Using work - energy theorem
$ W _\text{ net }=\left( K _{ f }- K _{ i }\right)$
$ \Rightarrow-\frac{1}{2} Kx ^2=\frac{1}{2} m \left(\frac{ v }{2}\right)^2-\frac{1}{2} mv ^2=\frac{ E }{4}- E$
$ \Rightarrow \frac{1}{2} Kx ^2=\frac{3 E }{4} \Rightarrow K =\frac{3 E }{2 x ^2} $
$\Rightarrow K =\frac{3 E }{2 \times\left(\frac{1}{4}\right)^2}=24 E $
$ n =24$