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[Phys-L] Spring question



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/>