Answer
Newton's law in the horizontal direction leads to
$$
F+F_{2}>f_{s, \max } \Rightarrow 110 \mathrm{N}+F_{2}>126.9 \mathrm{N}
$$
which leads (after appropriate rounding) to $$F_{2, \min }=17 \mathrm{N}$$
Work Step by Step
Newton's law in the horizontal direction leads to
$$
F+F_{2}>f_{s, \max } \Rightarrow 110 \mathrm{N}+F_{2}>126.9 \mathrm{N}
$$
which leads (after appropriate rounding) to $$F_{2, \min }=17 \mathrm{N}$$