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I was asked the question of a situation in which the static frictional force that a surface exerts on an object is not equal to μs times the normal force that the surface exerts on the object.

I know that the equation for static friction is equal to coefficient of static friction * Net force, so I am confused on how it could ever not be true. Any suggestions?

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Imagine that you have a block of mass $m$ at rest on a horizontal table.
The normal reaction force $N=mg$.
The block and the table have rough surfaces and the coefficient of static friction for the two surfaces is $\mu _{\rm s}$.

What is the static frictional force?
The answer is zero otherwise because the static frictional force would be the only horizontal force on the block, the block would accelerate which is certainly not what one observes.

Now apply a small horizontal force $F$ on the block.
The block does not move because the frictional force on the block adjusts itself to be equal in magnitude and opposite in direction to the force $F$.

As the force $F$ is increased the frictional force increases by the same amount as the applied force and the block does not move.

There come a time when the applied force is $\mu_{\rm s}N =\mu_{\rm s}mg$ in this case, which the maximum possible static frictional force.
The block will still not move but any increase in the applied force above the value $\mu_{\rm s}mg$ will mean that there is a net force on the block and so it will move relative to the table.

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