A spring has a constant k = 10.32 N/m and is hung vertically. A 0.400kg mass is suspended from the spring. What is the displacement of the end of the spring due to the weight of the. 400kg mass?

displacement (x) = 0.003798 meters

Explanation:

from the fact that the string is hung vertically we can deduce that:

Total force acting on the mass = Fs (by spring) + Fg (by gravity)

where

Fs = k*x, x is the displacement ...

Fg = m*g

then:

Ftot = m*a, but a = 0 m / (s^2) because the mass becames stationary.

Ftot = 0

Fs + Fg = 0

by direction, take down as negative.

Fs - Fg = 0

k*x = m*g

x = m*g/k = [ (0.400) (9.8) ] / (10.32)

= 0.3798 meters