A block of mass $5\ \text{kg}$ rests on a rough incline that makes $37^\circ$ with the horizontal. The coefficient of friction is $0.75$, both for sticking and for sliding. A force $F$, pointing up the incline at an angle $\varphi$ above its surface, is to drag the block up the incline at a steady speed, as shown in the figure. Take $g = 10\ \text{m/s}^2$, $\sin 37^\circ = 0.6$ and $\cos 37^\circ = 0.8$. What is the smallest force that can do this, and at what angle must it act?

Fig. 1: A block of 5 kg rests on a fixed incline at 37 degrees, with friction coefficient 0.75. A force F acts on the block, pointing up the incline at an angle phi above the surface of the incline.