What is the maximum static friction value for a surface with normal force N and coefficient μ_s?

What is the maximum static friction value for a surface with normal force N and coefficient μ_s?

• A. f_s,max = μ_s N.
• B. f_s,max = μ_k N.
• C. f_s,max = N.
• D. f_s,max = μ_s^2 N.

Answer: (A)

The maximum static friction is μ_s times the normal force N. Static friction can adjust to match the applied tangential force up to this limit, so it resists motion with a force f_s that can range from 0 up to f_s,max = μ_s N. If the tangential push exceeds that limit, motion begins and friction becomes kinetic, with magnitude μ_k N. The other options don’t fit because μ_k N applies only during sliding, N alone isn’t the friction value in general, and μ_s^2 N has no basis in the standard friction law.

The maximum static friction is μ_s times the normal force N. Static friction can adjust to match the applied tangential force up to this limit, so it resists motion with a force f_s that can range from 0 up to f_s,max = μ_s N. If the tangential push exceeds that limit, motion begins and friction becomes kinetic, with magnitude μ_k N. The other options don’t fit because μ_k N applies only during sliding, N alone isn’t the friction value in general, and μ_s^2 N has no basis in the standard friction law.