Aspring 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