Understanding the Force on a Spring: Why is it 1.2 - 9x?

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The discussion focuses on understanding the force equation for a spring in a scenario involving two blocks and a spring with a constant of 9 lb/ft. The user is confused about the expression F = 1.2 - 9x, specifically the reasoning behind the 1.2 term and its relationship to the spring's extension. They seek clarification on the initial energy of the spring when both blocks are present and the energy when only the 0.5 lb block is on the spring. Additionally, there is a question about how the change in elastic energy of the spring is defined in the context of the problem. Understanding these concepts is crucial for determining the maximum velocity of the 0.5 lb block after the upper block is removed.
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Homework Statement


a .7 lb block rests on top of a .5 lb block supported by but not attached to a spring of constant 9 lb/ft. the upper block is suddenly removed. determine the maximum velocity reached by the .5 lb block.



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The Attempt at a Solution


i have already solved the probelm. my question is, why is the expression for the force on the spring F = 1.2 - kx =>> 1.2 - 9x.

i get the 1.2 part but I am not understanding why its 1.2 minus 9x. I am trying to understand this visually with arrows but its not quite working...pls help!
 
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So when both blocks are on the spring, what is the extention? (What is the initial energy of the spring?)

When the 0.5lb block is on the spring alone, what is the extension? (What the energy it has due to the 0.5lb block alone?)

What is the change in elastic energy of the spring converted to?
 
it doesn't say in the question...the solution manual calls it x.
 
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