Relativity of spring constant

[GRDixon]

Relativity of spring "constant"

Let equal-magnitude, oppositely signed charges be at rest at the Origin and on the y-axis of IRF K. They are held apart by a compressed spring. The force exerted by the spring on either charge is equal and oppositely directed to the electrostatic force.

Viewed from IRF K’, which moves in the positive x-direction of K at speed v, the charges and the spring move in the –x’ direction at common speed v. But according to the general field transformations the Lorentz force on either charge in K’ is less than it is in K by a factor (1-v^2/c^2)^(1/2). Is the spring constant actually a function of the spring’s motion relative to an IRF? And if so, what is the general rule for arbitrary spring orientations in frame K’?

 

[Altabeh]

Let equal-magnitude, oppositely signed charges be at rest at the Origin and on the y-axis of IRF K. They are held apart by a compressed spring. The force exerted by the spring on either charge is equal and oppositely directed to the electrostatic force.

Viewed from IRF K’, which moves in the positive x-direction of K at speed v, the charges and the spring move in the –x’ direction at common speed v. But according to the general field transformations the Lorentz force on either charge in K’ is less than it is in K by a factor (1-v^2/c^2)^(1/2). Is the spring constant actually a function of the spring’s motion relative to an IRF? And if so, what is the general rule for arbitrary spring orientations in frame K’?

If I can understand you correctly, as soon as the spring is released, the charges start to move along the y-axis of IRF K. But the point is that in order to have a relativistic motion, the trajectory of motion in both K and K' must in the the same direction (as is assumed here, the direction of x-axis), while in this example, K' moves in the positive x-direction of K, so it is impossible for an observer in K' to measure any relativistic thing in K.

AB

 

[bcrowell]

This may be helpful: Grøn, Covariant formulation of Hooke's law, Am. J. Phys. 49, 28-30 ( 1981 )

 

[Altabeh]

This may be helpful: Grøn, Covariant formulation of Hooke's law, Am. J. Phys. 49, 28-30 ( 1981 )

It is not going to be helpful that much, since its framework is surely GR and in the SR, unfortunately the matter tensor vanishes so no contribution of the spring constant exists anymore. The same topic can be found in a very better and glib language http://arxiv.org/pdf/gr-qc/0005099".

AB

 

[yuiop]

In this old thread https://www.physicsforums.com/showthread.php?t=207419&highlight=new+angle+right+angle+paradox&page=2 we worked out in simple terms, how the spring constant and modulus of elasticity change for springs parallel and transverse to the motion. See post #17 in particular.

 

[GRDixon]

In this old thread https://www.physicsforums.com/showthread.php?t=207419&highlight=new+angle+right+angle+paradox&page=2 we worked out in simple terms, how the spring constant and modulus of elasticity change for springs parallel and transverse to the motion. See post #17 in particular.

Once again, thanks KEV. That's what I had in mind. It's nice to know that I'm not flailing around solo out here with some of these conclusions.