You are assuming no dissipation. Then there will be some kinetic energy as
m moves through the equilibrium point.
Bob Sciamanda
Physics, Edinboro Univ of PA (Em) http://www.winbeam.com/~trebor/
trebor@winbeam.com
----- Original Message -----
From: "Savinainen Antti" <antti.savinainen@KUOPIO.FI>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Saturday, December 11, 2004 3:16 PM
Subject: 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/>
|
|
|
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