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So after putting in some research effort into the math, it seems like this should be possible under the right criteria.

Say I have a spring with a mass of 1500kg and a spring constant of 100N/cm and a total length of 30cm.

Given the formula:

F = -kx

I think that if I want to compress my spring 15cm it will have 1500N of potential energy.

With this understanding I move on to calculating the minimum mass required to negate this force with the formula:

F = ma

To get the mass, I divide the force exerted by the compressed spring of 1500N by a desired acceleration, let’s say 3cm/s. Which gives me a mass of 500kg.

This is where I get stuck, but I believe the next step is to convert the mass into Newtons by multiplying by 9.8 which gives me 4900N.

I believe I may be going about this the wrong way, so can someone help me by explaining the following:

  • Is it possible to compress a spring to half of its length without moving it?
    • If so, how do I show that mathematically?
    • If not, how do I show that mathematically?

To clarify “without moving it”, let’s say that a constant force equivalent to or less than a 3000kg vehicle traveling at 200km/h coming to a dead stop by impacting an obstacle wouldn’t be able to physically move the spring through space. The spring would simply compress. Think of it like trying to move a heavy boulder by pushing on it with your bare hands, it seems like you can’t because you can’t exert enough force to move it.

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  • $\begingroup$ Potential energy is measured in Joules, not Newtons. The potential energy of a compressed spring is $U = \frac{1}{2}kx^2$. Also, what does it mean to compress a spring without moving it? $\endgroup$ – J. Murray Jul 16 '19 at 23:05
  • $\begingroup$ Please be more specific about what you mean by not moving it. $\endgroup$ – Alaz Cig Jul 16 '19 at 23:09
  • $\begingroup$ I’ll edit the question to clarify. $\endgroup$ – Perpetual J Jul 16 '19 at 23:13
  • $\begingroup$ @PerpetualJ your clarification is unclear. A 3000 kg vehicle traveling at 200 km/h coming to a "dead stop by impacting an obstacle" does not characterize a constant force. $\endgroup$ – Andrew Paul Jul 16 '19 at 23:24
  • $\begingroup$ I think you're implying that a free spring, when acted on by a force under a certain threshold, will only compress and the entire spring itself will not move? If so, this is false. Compression will only occur when one of the ends of the spring is fixed. $\endgroup$ – Andrew Paul Jul 16 '19 at 23:32
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I believe you want to compress a spring and make it stay there using a mass.

First of all, you can't theoretically put a mass in front horizontally to hold it since no force is exerted by the block to the spring in this direction, other than static friction, which will depend on the surface types. If you want this approach, you will need to solve $-k\Delta x=mg\mu_s$, where $\mu_s$ is the static friction coefficient.

What you want is to place a mass on top of the spring. So, there has to be $F_{net}=0$ for there to be no movement. Energy is irrelevant. Weight acts downwards and the elastic force acts upwards. Thus: $$F_{net}=F_e-F_W=0$$ $$F_e=F_W$$ Putting in your formulas: $$-k\Delta x=mg$$ Solving for mass: $$\frac{-k\Delta x}{g}=m$$ Your spring constant of $100\space N/cm$ sounds too big. $1\space N/cm$ sounds more like it. $$m=\frac{-1\cdot (-15)}{9.81}=1.53\space kg$$ For this example, you should place a $1.53\space kg$ object on top.

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  • $\begingroup$ I'm not sure that this is what the OP means. It seems that OP is implying that a free spring, when acted on by a force under a certain threshold, will only compress and the entire spring itself will not move (which is false). $\endgroup$ – Andrew Paul Jul 16 '19 at 23:31
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    $\begingroup$ @mathysics I hope not. It wouldn't be a spring at that point. $\endgroup$ – Alaz Cig Jul 16 '19 at 23:33
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This question is a bit odd. It is not entirely clear what is meant by compressing a spring without moving it. If you want a spring to give an outwards force without pushing it in you could try heating it up. The metal will expand with heat. If you want instead for it to give an inwards force you could lower its temperature.

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