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How relativity could explain this engineering problem.

  1. Dec 25, 2011 #1
    This is a thought experiment but not very academic.

    Assume a satellite solar panel was critically designed in such a way that even 10% increase in mass would result in hinge attachment failure.
    Assume some inertial frame (A) in a distant planet or space ship, at some part of its course it sees the satellite solar panel is at a relative velocity very close to light speed and when they measure the mass it is twice than that of the designed mass.
    So, mass measured from earth is design mass 'm'. Mass measured from inertial frame A is '2m'. According to engineers in earth solar panel should work fine, but engineers at inertial frame A would say it should fail.

    What will happen to solar panel?
    My answer is solar panel will not fail. Then how physicist in the inertial frame A could explain this.
     
  2. jcsd
  3. Dec 25, 2011 #2

    Dale

    Staff: Mentor

    Hi duri, welcome to PF!

    My answer is that it will fail since anything designed with only a 10% margin of safety will inevitably fail. However, my answer has nothing to do with relativistic effects, and is just a comment on engineering.

    Your instincts are correct as far as relativity goes. If it does not fail at rest then it will not fail travelling inertially at any speed. This is guaranteed by the first postulate of relativity without even having to do any further detailed analysis.

    One thing to note is that structures are designed to handle a certain stress, not a certain mass. The material stress is part of the stress-energy tensor, which is a very important object in relativity, particularly general relativity. Because it is a tensor, you should be able to express the failure condition in terms of tensors, which would guarantee that all frames will agree on the failure condition. The mass condition is just a simplification of the real failure condition, and only applies at rest.

    Also, you may not be aware, but the concept of relativistic mass has pretty much been discarded by modern physicists. The term "mass" usually refers to "invariant mass" which is the same in all frames.
     
  4. Dec 25, 2011 #3
    Please don't bother about how mass acts as load. This is possible in several scenarios. Assume solar panel attached to circular rod, which can take some centrifugal stress (Tensile stress to the rod). Or vibrating solar panel. Solar panel as load and connecting rod as beam. In all cases mass is the contributor to stress and additional mass will add to stress.



    Hi Dale, I can't agree this, tensor is a mathematical concept and its a tool to handle few class of problem. Just because of tensor nature i can't assume relativity equations can handle this kind of stress. Because take fluid and solid, though both enjoys the same tensor quantities like normal and shear their behavior is very different in nature.

    Yes Dale, I not aware of this. Do you mean mass will not change with speed?. Then, is reaching speed of light possible?.
     
  5. Dec 25, 2011 #4
    If you bolt a chair to the satellite and go with it to carefully monitor the mass and mechanical performance of the panel and hinge, you will not be able to measure any differences among any of the reference frames the craft finds itself in.
     
    Last edited: Dec 25, 2011
  6. Dec 25, 2011 #5

    Dale

    Staff: Mentor

    So is everything in physics and engineering. This argument could be applied to every aspect.

    Yes, mass (in modern usage) does not change with speed. No, you cannot reach light speed: the energy required would be infinite, even with constant mass.
     
    Last edited: Dec 26, 2011
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