On an incline, the magnitude of friction is given by which expression?

• A. f = mu * m g * cos theta
• B. f = mu * m g * sin theta
• C. f = mu_k * m g
• D. f = mu * m g

Answer: (A)

Friction on a slope depends on the normal force between the object and the surface. The maximum friction force is f = μ N, where μ is the coefficient of friction and N is the normal force. For an object on an incline, the normal force is N = m g cos θ, since only a portion of the weight acts perpendicular to the plane. Substituting gives f = μ m g cos θ. This is why that expression is the correct one: it uses the actual normal force on the incline, and friction scales with that, not with the along-the-slope component of gravity. The along-slope component, m g sin θ, drives motion, not the friction magnitude. The other options either miss the cos θ factor or replace N with m g or m g sin θ, which isn’t correct for the friction on an incline. If the object is static, friction can be up to μ_s N; if it’s sliding, friction is f_k = μ_k N, but in both cases N = m g cos θ.