# When an applied force that exactly equals the max static friction is on an object

When an applied force that exactly equals the max static friction is on an object, does the object start moving at this point?

• You cannot answer this because the max static friction is actually not a constant at all. – John Alexiou Nov 7 '14 at 19:22
• Can you just assume that it's a constant tho? – Dani Nov 7 '14 at 20:39
• @ja72, static friction is not constant, but maximum stattic friction is constant (or limit point) – Nikos M. Nov 7 '14 at 22:34
• you should assume a force which is just (infinitesimaly) larger than the max static friction, then move starts – Nikos M. Nov 7 '14 at 22:35
• Maybe not constant is not the right term. "Unstable" or "Unknowable" would describe it better. You cannot know what it is unless you exceed it, and then once it moves it changes. – John Alexiou Nov 8 '14 at 0:48

## 2 Answers

If the applied force equals the max static friction then: $$\boldsymbol F_{applied}-\boldsymbol F_{\max \text{ friction}} = 0 = m\boldsymbol a.$$ From which it can be seen that $\boldsymbol a =0$, taking into account that the forces are opposite. Therefore the object does not move.

In this case, $$\sum F=F_s^{\text{ max}}+F_{\text{ applied}}=ma$$ However, $$F_s^{\text{max}}=F_{\text{ applied}}$$ so $$\sum F=0$$ and $$a=0$$ So the object will not move, if these are the only two forces acting on it (not including forces perpendicular to these).