Friday 8 May 2020

newtonian mechanics - Stretch length of horizontal and vertical springs


If the spring in Figure A is stretched a distance d, how far will the spring in Figure B stretch? The spring constants are the same.


The answer is "by half". I don't get it, to me it's the same.



springs



Answer



Think on the equilibrium position:




  1. in figure A you have a force $mg$ exerted at the lower end and an identical force pushing the opposite direction exerted by the wall (if this force didn't exist, the spring with mass attached would just fall down by gravity).

  2. In figure B you have a force $mg/2$ exerted on the right end of the spring and an identical force of $mg/2$ on the other end.


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