[Phys-L] Re: Spring question

[jlu at HEP.ANL.GOV (Jack Uretsky)]

How did you get the block to hang motionless?
                                        Regards.
                                                Jack

On Sat, 11 Dec 2004, Savinainen Antti wrote:

> Hi,
>
> a friend of mine asked a very simple question which could be formulated in the following way:
>
> A vertical spring (spring constant k) is hanging freely.
> A block of mass m is attached to the spring and the spring
> streches. At the equilibrium position of the block, where it hangs motionless, the spring has streched by x. Determine the mass of the block.
>
> Solution 1:
>
> At the equilibrium the net force on the block is zero
> and hence kx = mg which gives m = kx/g.
>
> Solution 2:
>
> The change in gravitational potential energy of the block
> is mgx. This energy must be in the mass-spring system and
> equals 1/2kx*x (assuming no friction in the spring).
> But this calculation gives m = 1/2* kx/g!!
>
> Which solution is correct? What's wrong with the other
> solution?
>
> Regards,
>
> Antti
>
> Antti Savinainen, Ph.D.
> Senior Lecturer in Physics and Mathematics
> Kuopio Lyseo High School
> Finland
> E-mail: <antti.savinainen@kuopio.fi>
> Website: <http://kotisivu.mtv3.fi/physics/>

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