Friction
Friction has two modes. Static friction adjusts itself to whatever is needed to prevent slipping, up to a ceiling of $\mu_s F_N$. Kinetic friction takes a definite value $\mu_k F_N$ once surfaces are sliding. The arrow you draw on a free-body diagram for static friction is not the maximum value; it is whatever value cancels the other in-plane forces, until the in-plane forces exceed the ceiling, at which point the surfaces start to slide and the friction force drops to its kinetic value.
Three pitfalls. Quoting $f_s = \mu_s F_N$ as an equation when it is really a ceiling: $f_s \le \mu_s F_N$. Direction: friction opposes relative motion, not absolute motion. A block on a moving conveyor experiences friction in the direction of the conveyor. And the normal force is rarely just $mg$. Pull up on a handle and it drops; press down on it and it rises, both of which change the friction ceiling. The lesson walks all three.
The work
3 ways in · any order
Lesson
Kinetic and Static Friction
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Read the lesson. Two worked examples (the slip angle on an incline, an angled pull and the disappearing normal force) followed by a ten-scenario applet that drills the static-ceiling inequality, the relative-motion direction rule, and the partial-lift effect on normal force.
Diagnostic
10-item topic check
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Ten multiple-choice items on the static-ceiling inequality, friction direction in non-trivial relative-motion setups, and the way a vertical component of an applied force changes the normal force and the friction available.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.