# Conceptual question on superposition of forces holding a specific mass in equilibrium

Consider a point mass $x$ (like for example the earth in space) and let $A$ and $B$ be two sets of point masses which each hold the point mass $x$ in equilibrium, meaning the acceleration induced by $A$ on $x$ is zero, and the same for $B$. Now if I put the point masses of both $A$ and $B$ in space then (by superposition) the accelaration exerted by all the point masses in $A$ and $B$ together would still be zero on $x$. This seems quite obvious, but in this article on p. 485 something different seems to be suggested, to quote

If we restrict to partial configurations that do not $a$ include the weight of the sphere, then the obvious superposition law fails. In fact let $\hat E$ denote the subset of partial configurations, excluding the weight of the sphere, for which the sphere has no observed acceleration.

Then it is claimed that $\hat E$ is not closed under superposition (i.e. addition of force configurations)? Does I understand something wrong?

## 1 Answer

He is not counting the Earth in $A$ or $B$. $A$ counters the Earth and so does $B$. Having them both is overkill and gives you an upward force.