For kinetic friction on a plane, which formula gives the frictional force?

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

Answer: (C)

When an object slides on a plane, friction opposing the motion is proportional to how hard the surfaces are pressed together, quantified by the normal force, and depends on a coefficient that applies to motion. For sliding, the appropriate coefficient is the kinetic friction coefficient, μ_k, giving the frictional force as F_k = μ_k F_N, directed opposite the velocity.

On a flat horizontal surface with no extra vertical forces, the normal force equals the weight, so this becomes F_k = μ_k mg. This distinguishes it from static friction, which uses μ_s and can vary up to μ_s F_N before motion starts. A formula like F_k = F_N would imply μ_k = 1 in general, which isn’t true for most surfaces, and a division form like μ_k / F_N would have wrong units and physical meaning. The correct relationship is F_k = μ_k F_N.