Question #43904

A block of mass $m = 2 \text{ kg}$ is placed on a rough inclined plane making an angle $\theta = 37^\circ$ with the horizontal. The coefficient of static friction between the block and the plane is $\mu_s = 0.8$. An electromagnet is fixed such that it exerts a time-varying magnetic force $F_{mag} = \alpha i(t)$ on the block in a direction perpendicular to and away from the inclined plane, where $\alpha = 0.5 \text{ N/A}$ and $i(t)$ is the current. The electromagnet circuit has a total inductance $L = 4 \text{ H}$, total resistance $R = 2 \text{ }\Omega$, and is connected to a battery of emf $V = 10 \text{ V}$ via a switch. If the switch is closed at $t = 0$, at what time $t$ will the block just begin to slide down the incline? (Take $g = 10 \text{ m/s}^2$, $\sin 37^\circ = 0.6$, $\cos 37^\circ = 0.8$)