Answer
$P_{min}=400N$
Work Step by Step
Let's examine the forces deciding whether the small cubes slide downward or not:
- Its weight $mg=4\times9.8=39.2N$, which forces the cube to slide down.
- Static friction $f_s=\mu_s F_N=0.71F_N$, which opposes the downward movement.
To be able to keep the cube from sliding, these forces at least need to balance each other. $$f_s=0.71F_N=39.2N$$ $$F_N^{min}=55.2N$$
$F_N$ here is the horizontal force that causes the cube's acceleration: $$F_N=ma$$ $$a_{min}=\frac{55.2}{4}=13.8m/s^2$$
Now, to find $P$, we consider the whole system. It has acceleration $a=13.8m/s^2$ and its total weight $M=4+25=29kg$. Thus, $$P_{min}=Ma=400N$$
