Static friction can be much less intuitive than kinetic friction. For a book at rest on a flat table, where the only other forces are the force of gravity and the normal, the static force of friction is zero. If you then push horizontally with a small force, static friction establishes an equal-and-opposite force that keeps the book at rest.

As you steadily increase your force, the force of friction increases to match you. Eventually your force exceeds the maximum force of friction, and the book moves.

The maximum force of static friction, f_s, is given by:

f_{s max} = m_s N

m_s is known as the coefficient of static friction.

m_s ³ m_k. In other words, it is harder to start something moving than it is to keep it moving once it's moving.

Static friction can be difficult to deal with because in general:

f_s £ m_s N

We will often deal with the limiting case, involving the maximum force of static friction, but always think before writing down

f_{s max} = m_s N. We will deal with cases where f_s < m_s N .