Physics - Kinematics Question with Solution | TestHub

For $0<\mathrm{F}<40$, there is no slipping anywhere. Between 6 kg and the ground, slipping starts for $\mathrm{F}\ge 40$. Between the two blocks, slipping starts for $\mathrm{F}\ge 72\mathrm{N}$. So for:

$$\begin{array}{rl}& \mathrm{F}=36\mathrm{N},{\mathrm{f}}_1=0,{\mathrm{f}}_2=36\mathrm{N}\\ & \mathrm{F}=48\mathrm{N},{\mathrm{f}}_1=4\mathrm{N},{\mathrm{f}}_2=32\mathrm{N}\\ & \mathrm{F}=64\mathrm{N},{\mathrm{f}}_1=8\mathrm{N},{\mathrm{f}}_2=32\mathrm{N}\\ & \mathrm{F}=96\mathrm{N},{\mathrm{f}}_1=8\mathrm{N},{\mathrm{f}}_2=32\mathrm{N}\end{array}$$