The spring will come to rest 4.9 m below the natural length
Explanation:
The mass-spring system will come to rest when the restoring force on the spring (pulling upward) balances the weight of the mass (pulling downward). Mathematically, this can be written as
[tex]F_x = W\\kx = mg[/tex]
where
k is the spring constant
x is the elongation of the spring
m is the mass
g is the acceleration of gravity
In this problem, we have:
[tex]m = 8 kg[/tex] is the mass
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
[tex]k=16 N/m[/tex] is the spring constant
Solving the equation for x,
[tex]x=\frac{(8)(9.8)}{16}=4.9 m[/tex]
Therefore, the spring will come to rest 4.9 m below the natural length.
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