Physics - NLM Question with Solution | TestHub

The forces acting on the block are the applied force $F$, gravity $mg$, normal force $N$, and kinetic friction $f_k$. Resolving forces vertically: $N+F\sin \theta =mg$. So, $N=mg-F\sin \theta$. The kinetic friction force is $f_k={\mu }_{k}N={\mu }_k(mg-F\sin \theta )$. Resolving forces horizontally: $F\cos \theta -f_k=ma$. Substituting $f_k$: $F\cos \theta -{\mu }_k(mg-F\sin \theta )=ma$. Therefore, $a=\frac{F\cos \theta -{\mu }_k(mg-F\sin \theta )}{m}$.