To determine the coefficient of static friction ([tex]\(\mu_s\)[/tex]) for an object on a surface, we need to relate the maximum force of static friction ([tex]\(F_{S, \max}\)[/tex]) and the normal force ([tex]\(F_N\)[/tex]).
The coefficient of static friction is defined by the equation:
[tex]\[
\mu_s = \frac{F_{S, \max}}{F_N}
\][/tex]
Here’s the step-by-step reasoning:
1. Static Friction Force ([tex]\(F_{S, \max}\)[/tex]): This is the maximum force that can be applied to an object at rest before it starts to move. It represents the threshold at which static friction transforms into kinetic friction.
2. Normal Force ([tex]\(F_N\)[/tex]): This is the force exerted by a surface perpendicular to the object resting on it. For a horizontal surface, it equals the weight of the object if no other vertical forces are acting on it.
3. Coefficient of Static Friction ([tex]\(\mu_s\)[/tex]): This dimensionless quantity measures how easily one object moves relative to another while in contact, without motion occurring. It is a ratio of the maximum static friction force to the normal force.
Given that the coefficient of static friction is a ratio of these two forces, the formula that correctly expresses this relationship is:
[tex]\[
\mu_s = \frac{F_{S, \max}}{F_N}
\][/tex]
Among the given options, the correct equation is:
Option A: [tex]$\mu_s=\frac{F_{s, \max }}{F_N}$[/tex]
Thus, the answer is:
[tex]\[
\boxed{1}
\][/tex]
