(Solved): Consider a \( 20 \mathrm{~kg} \) wheel resting on a horizontal surface and acted upon by a string ...

Consider a \( 20 \mathrm{~kg} \) wheel resting on a horizontal surface and acted upon by a string \( S \) and a wedge that is being pushed downward by a force \( P \), as depicted in the accompanying figure. The spring force of \( 100 \mathrm{~N} \) is applied to the wheel via a light weight rod and ideal bearing. If the friction coefficient at point \( A \) is \( 0.25 \), while for both wedge surfaces it is \( 0.3 \), determine the minimum magnitude of \( P \) to move the wheel.