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If I stretch a spring, is the spring retaining its mass?

Qmechanic
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sarah
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  • Newton's Second Law is an equation for a particle. So if we apply it to a macroscopic composite object, we are really considering external forces causing center-of-mass acceleration. See my answer to this question. So, I would say yes, the center of mass of the spring could be accelerating (but it could also simply be moving with constant velocity). If the force applied by your left hand has larger magnitude than the force applied by your right hand, at some moment, then there will be an acceleration of the center of mass. – Ben H Feb 15 '23 at 04:33
  • what is $F(t)$? The force with which you pull, as a function of time? – JEB Feb 15 '23 at 04:34
  • Tangentially related to the slinky drop problem – Ben H Feb 15 '23 at 04:55
  • The question has just changed significantly, so all of the answers and comments are not really related to the question! – Ben H Feb 15 '23 at 16:28

2 Answers2

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Answer is yes, spring will accelerate with respect to you. As you hold spring in one hand, you will act as fix support to spring. Spring also have some mass so it will become spring-mass system (Assume mass of spring acting at end of spring, after calculation it will be mass of spring/3). After giving some initial displacement it will start vibrating (So free vibration case). Equation of motion will be $-k x = \frac{m}{3} a$ ➡️ So acceleration will be there but it is variable acceleration which is maximum at extreme end of vibration and zero at mean position.

ZaellixA
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Mr. Mechanical
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It depends on whether or not your hand is moving with constant velocity.
Consider three portions of the spring, at the fixed end, in the middle, and at end you are holding.
The centre of mass of the spring is located at the middle of the spring.
If your hand is moving at a constant velocity of $2\,\rm cm/s$ relative to your eyes then the middle of the spring, and its centre of mass, will be moving at a constant velocity of $1\,\rm cm/s$.
However if you hand is accelerating so will the middle of the spring, and hence its centre of mass, be accelerating.

Farcher
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