Question

The total length of a spring when a mass of 20g is hung from its end is 14cm while its total leggings 16cm when a mass of 30g os hung from the same end . calculate the instructed length of the spring assuming hooked laws is obeyed

Answer 1

$m_2-m_1=\Delta m;\\l_2-l_1=\Delta l;\\Newton's\; second\; law\;and\;Hooke's\; law\\\\|\Delta m g|=|-k\Delta l|;\\We\; are\; not\; interested\; in\; the\; sign;\\k=\frac{|\Delta m g}{\Delta l}=\frac{0.01\times 9.8}{0.02}=4.9\frac{N}{m};\\for\; a\; weight \;of\; 1:\\|m_1g|=|-k\Delta l'|(We\; are\; not\; interested\;\\ in\; the\; sign\;again)\\\Delta l'=\frac{m_1g}{k}=\frac{0.02\times 9.8}{4.9}=0.04m;\\0.14-0.04=0.1m=10cm.\\Answer:the \;instructed\; length\;\\ of \;the \;spring \;is\; equal \;to\;10cm$