## Weight hanging on a spring

1. The problem statement, all variables and given/known data

Scenario: A block of mass m hanging on the end of a vertical spring with spring constant k

2. Relevant equations

When the spring has come to rest:

Vertical eqm: weight = force exerted by spring
mg = kx

Energy conservation: loss in GPE = gain in EPE of spring
mgx = 0.5*kx^2

3. The attempt at a solution

canceling x on both sides of the energy conservation equation will give me mg = 0.5*kx, which does not tally with the equation of vertical equilibrium. Why is this so?

Is there a problem with my understanding of energy conservation?

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hi divineyang!

(try using the X2 icon just above the Reply box )
 Quote by divineyang When the spring has come to rest: Vertical eqm: weight = force exerted by spring mg = kx Energy conservation: loss in GPE = gain in EPE of spring mgx = 0.5*kx^2 … canceling x on both sides of the energy conservation equation will give me mg = 0.5*kx, which does not tally with the equation of vertical equilibrium. Why is this so? Is there a problem with my understanding of energy conservation?

if there's conservation of energy, then the weight will go speeding past the equilibrium position, and bounce happily up and down for ever and ever!

(and zero speed doesn't mean zero acceleration! )

 so I cannot use the energy conservation approach to find the displacement of the mass? other than equilibrium of forces, how else can I find the value of x?

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## Weight hanging on a spring

what exactly is the original question?

 i want to find the extension, x of a spring with spring constant k with a mass of m hanging on its end.. Express x in terms of k, m and g. I want to know why its possible to derive an expression for x by using energy.

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 Quote by divineyang i want to find the extension, x of a spring with spring constant k with a mass of m hanging on its end.. Express x in terms of k, m and g.
but what are the initial conditions?

if you want to use conservation (of anything), you need a before and an after …

if the question gives you an equilibrium position, but no initial position, then there's nothing to conserve, is there?

(and then you simply use ∑F = 0)

 oh there arent any initial conditions haha. i understand now, thanks so much!

 Tags energy conservation, hanging, mass, spring