Understanding Energy Conservation in a Hanging Spring System

[divineyang]

Homework Statement

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

Homework 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

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?

 

[tiny-tim]

hi divineyang!

(try using the X² icon just above the Reply box )

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?

yes, you've lost your bounce!

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! )

 

[divineyang]

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?

 

[tiny-tim]

what exactly is the original question?

 

[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.

I want to know why its possible to derive an expression for x by using energy.

 

[tiny-tim]

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)

 

[divineyang]

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