Problem $2$

Mass $)=(20(kg)$ is a collar that slides smoothly on a vertical bar $($hint: there's no friction between the collar and the bar, but there is a normal force$).$ Mass B $(m_B=10kg)$ is attached to a rope and a spring that obeys Hooke's Law. When the spring is unstretched, $h=0\mathrm{.}1m.$ The system is in equilibrium when $h=0\mathrm{.}3$ m $.$ What is the spring constant $k?$

$(0\mathrm{.}3-0\mathrm{.}1)k=F_{\text{s}\text{p}\text{i}\text{n}\text{g}}$

$F_{\text{s}\text{p}\text{r}\text{i}\text{n}\text{g}}=10(9\mathrm{.}81)+T$

$T\frac{6}{\sqrt[\phantom{2}]{41}}=mg$

$T=20(9\mathrm{.}81)\frac{\sqrt[\phantom{2}]{41}}{4}$

$=255\mathrm{.}4(N)$

$0,2k=98\mathrm{.}1+255,4$

$=353,5(N)$

$k=353\mathrm{.}55(\frac{N}{m})$

$=1748(\frac{N}{m})$