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Consider a system with $1$ degree of freedom. Suppose $2$ particles, each of mass $1$ are placed next to each other. The 1st particle is being acted upon by a $100\text{ N}$ force. In general the equations would be (considering 1st particle $m_1$ second particle $m_2$)$-$ $$100-f_r=m_1a_1=a_1$$ $$f_r=m_2a_2=a_2$$ But consider the case when the second particle cannot give a reactionary force so $f_r$ is $0$. In this case, $$100=m_1a_1=a_1$$ $$m_2a_2=0$$

So what is happening here? Will one ball go through the other?

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Yes, if there is no reaction force then the particles are called non-interacting. One can pass through the other without disturbing it. This happens, for example, with neutrinos which interact only very weakly. They often pass right through a human or even the earth or sun without interacting with anything.

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  • $\begingroup$ @dave Can you also explain how the scenario will change if $f_r$ is not $0$, but less than $50$? $\endgroup$
    – Eisenstein
    Nov 16, 2021 at 17:58
  • $\begingroup$ There is nothing particularly interesting in that case. They are interacting and follow Newton’s laws in the usual way. This could be like pushing a paddle through water or pushing a stick into dirt. $\endgroup$
    – Dale
    Nov 16, 2021 at 19:39

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