Question #42435

A wedge of mass $M = 3 \text{ kg}$ rests on a smooth horizontal floor. Its inclined surface makes an angle $\theta = 37^\circ$ with the horizontal and is oriented such that its outward normal vector points upwards and to the left. A block of mass $m = 1 \text{ kg}$ rests on the incline. A horizontal force $F(t) = 40t \text{ N}$ ($t$ in seconds) is applied to the wedge towards the left. The coefficient of static friction between the block and the wedge is $\mu_s = 0.5$. Find the work done by the static friction force on the block in the ground frame from $t = 0$ until the moment the block just begins to slip. (Take $g = 10 \text{ m/s}^2$, $\sin 37^\circ = 0.6$, $\cos 37^\circ = 0.8$)