Which expression gives the maximum static friction force that must be overcome to initiate motion?

• A. mu_s * F_N
• B. mu_k * F_N
• C. F_N / mu_s
• D. F_N

Answer: (A)

Static friction can oppose motion up to a maximum value. That maximum is found by multiplying the normal force by the coefficient of static friction: f_max = mu_s N. To just start moving, you must overcome this maximum static friction, so the force you need to apply is mu_s times the normal force. Once motion starts, friction becomes kinetic and is mu_k N, which is typically smaller than the static maximum. The other expressions don’t represent the threshold to start sliding: mu_k N describes friction during motion, F_N alone is just the normal force, and F_N divided by mu_s doesn’t correspond to the initiating resistance.