A steel strip of length $L=200$ mm is fixed at end $A$ and rests at $B$ on a vertical spring of stiffness, $k=2 \: N/mm$. The steel strip is $5$ mm wide and $10$ mm thick. A vertical load, $P=50$ N is applied at $B$, as shown in the figure. Considering $E=200$ GPa, the force (in N) developed in the spring is ________.
