• # question_answer A block of mass m is pushed across a rough surface by an applied force F, directed at an angle $\theta$ relative to the horizontal as shown. The block experiences a friction force $f$ in the opposite direction. What is the coefficient of friction between the block and the surface? A) $\frac{mg}{F\,\,\sin \phi }$ B) $\frac{f}{F\,\,\sin \phi +mg}$ C) $\frac{f}{mg}$  D) $\frac{mg}{f}$

 the key to finding the coefficient of friction $\mu$is in calculating the correct normal force acting on the block $\sum{Fy=m{{a}_{y}}}$ Free body diagram Block does not move in y direction $\therefore {{a}_{y}}=0$ $\therefore N=F\sin \phi +mg$ $\mu =\frac{{{F}_{friction}}}{N}=\frac{f}{F\sin \phi +mg}$