Kinetic and Static Friction Practice Test

A student wants to determine the coefficient of static friction $$\mu_s$$ between a block and a wooden board. The student places the block on the board and slowly raises one end of the board, increasing the angle of inclination $$\theta$$ until the block just begins to slide. Which of the following expressions represents $$\mu_s$$ in terms of the angle $$\theta_{max}$$ at which the block starts to slide?

Consider a block of mass $$M$$ on a rough horizontal surface. It is acted upon by a horizontal force $$F$$. If the static friction force acting on the block is $$f_s$$, which of the following inequalities must be true if the block remains at rest?