Max Distance Calculated for Spring Mass System of K=450N/m, m=2.2kg

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A spring with a spring constant of 450 N/m is analyzed with a mass of 2.2 kg attached to it. The net force acting on the mass is calculated to be 21.56 N, leading to a displacement of 0.05 m. The equilibrium position is determined by setting the spring force equal to the weight of the mass, resulting in a distance x below the initial position. The block will fall until the spring force overcomes its momentum, and due to the system's symmetry, the maximum distance fallen before moving upward is twice the equilibrium distance. The discussion clarifies the relationship between the forces and the maximum displacement of the block.
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A spring with K=450N/m hangs vertically. You attach 202kg block to it and allow the mass to fall. What is the maximum distance the block will fall before it begins moving upward?

ans-
k=450N/m
m=2.2kg
x=?

Fnet=mg
=2.2kg*9.8N/m
=21.56 N

F=+/- kx
x=f/k
x=0.05m

Is this the max distance I calcul;ated or the new equilibrium distance? Can u give me a hint.
 
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The equilibrium position will be where the force equals the weight:
450x= 2.2(9.8), measured below the initial position. Since the mass gains momentum as it falls, it will have its maximum velocity when it passes there, a distance x below it's initial position. It will continue to fall until the spring overcomes that momentum. Because of the symmetry of the situation, that distance below equilibrium will also be x. The "maximum distance the block will fall before it begins moving upward" will be 2x where x satisfies 450x= 2.2(9.8).
 
HallsofIvy, I don't understand what you are saying.
 
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