ANSWER
• The constant of proportionality is the ,coefficient of static friction, 0.2
,
• The ,equation, is:
[tex]f_{s\max }=0.2\cdot F_N[/tex]
EXPLANATION
The maximum static frictional force is proportional to the normal force,
[tex]f_{s\max }=k\cdot F_N[/tex]
The constant of proportionality is called the coefficient of static friction,
[tex]f_{s\max }=\mu_s\cdot F_N[/tex]
To find it, we have to use the measurements of the forces. The coefficient of static friction is the quotient between the maximum static frictional force and the normal force,
[tex]\mu_s=\frac{f_{s\max}}{F_N}[/tex]
For each of the measurements we have, rounded to the nearest tenth,
Hence, the coefficient of static friction is 0.2, and the equation is
[tex]f_{s\max }=0.2\cdot F_N[/tex]
The constant of proportionality is unitless because it is from the quotient of two magnitudes with the same unit.
