Answer
$\mu_s=0.0721$
Work Step by Step
To find the maximum force of static friction, use the equation that $$F_{s,max}=\mu_sN$$ where $N$ is the normal force. Since the backpack isn't on an incline, the normal force is equal to the weight, $52.0N$. Substituting the known value of $N=52.0N$ yields a maximum force of friction of $$F_{s,max}=52.0\mu_s$$ This force of friction must be equal to the spring force, which is equal to $kx$. Substituting known values of $k=150N/m$ and $\Delta x=2.50cm=0.0250m$ yields a spring force of $$F_{spring}=(150N/m)(0.0250m)=3.75N$$ Substituting this value into the $F_{max}$ equation yields $$3.75=52.0\mu_s$$ Solving for $\mu_s$ yields a value of $$\mu_s=0.0721$$
