Answer:
The total length is 0.65m.
Explanation:
The total length [tex]x_{tot}[/tex] of the spring is equal to its length [tex]x_0[/tex] right now (0.50 m ) plus the amount [tex]x[/tex] by which it is compressed due to weight of the man:
[tex]x_{tot} = x_0+x[/tex]
The spring compression is given by Hooke's law:
[tex]F = -kx[/tex]
which in our case gives
[tex]-Mg = -kx[/tex]
solving for [tex]x[/tex] we get:
[tex]x= \dfrac{Mg}{k }[/tex]
putting in [tex]M = 150kg, g= 10m/s^2[/tex] and [tex]k = 10,000N/m[/tex] we get:
[tex]x= \dfrac{(150kg)(10m/s^2)}{10,000N/m^2}[/tex]
[tex]x = 0.15m[/tex]
Hence, the total length of the spring is
[tex]x_{tot} = 0.50m+0.15m[/tex]
[tex]\boxed{x_{tot} = 0.65m.}[/tex]
