Answer
The cube will slide when $~~0 \leq \mu_s \lt 0.57$
Work Step by Step
If the cube begins to tip, the rotation axis will be along the bottom edge of one side of the cube.
Let $M$ be the mass of the cube.
We can find the required value of $P$ to make the cube start to tip:
$(7.0~cm)~P = (4.0~cm)~Mg$
$P = \frac{(4.0~cm)(9.8~m/s^2)~M}{7.0~cm}$
$P = 5.6~M$
We can find the minimum value of $\mu_s$ that will cause the cube to tip:
$Mg~\mu_s = P$
$\mu_s = \frac{P}{Mg}$
$\mu_s = \frac{(5.6)~(M)}{(M)(9.8)}$
$\mu_s = 0.57$
Thus, the cube will slide when $~~0 \leq \mu_s \lt 0.57$
