Question

Answer give me please!!!?​

Answer 1

${\mathfrak{\underline{\purple{\:\:\: Given:-\:\:\:}}}}$

$\:\:\:\:\bullet\:\:\:\sf{ Force \: applied = F}$

$\:\:\:\:\bullet\:\:\:\sf{ Stretched \: length = x}$

${\mathfrak{\underline{\purple{\:\:\:To \:Find:-\:\:\:}}}}$

$\:\:\:\:\bullet\:\:\:\sf{ Potential \: energy \: in \: spring}$

${\mathfrak{\underline{\purple{\:\:\: Solution:-\:\:\:}}}}$

★ Force applied is balanced by spring is constant

$\dashrightarrow\:\: \sf{ F = kx ....... (1)}$

★ Let $\bold{dw}$ be work done for a small interval of time with $\bold{dx}$ displacement in the spring.

$\dashrightarrow\:\: \sf{dw = F \: dx}$

☞ Putting value of (1)

$\sf \dashrightarrow \:\: \int dw = \int kx \: dx \\ \\ \\ \sf \dashrightarrow\:\: \int \limits_{0}^{w} dw = k \int \limits_{0}^{x} x \: dx \\ \\ \\ \sf \dashrightarrow\:\: w = k \bigg( \frac{ {x}^{2} }{2} \bigg) \\ \\ \\ \sf \dashrightarrow\:\: w = \frac{1}{2} k {x}^{2}$

★ Work done by spring is $\bf{Potential\: energy }$ conserved in the spring.

$\therefore \:\bf{Potential \:\: energy \:\: in \:\: spring \:\: is \:\: \frac{1}{2} {kx}^{2} }$