Short on time? This page is the recap. For explanations, diagrams and worked examples, use the full study guide. This is the algebra-based course: no calculus is needed.
Recap
- A surface exerts a contact force with two components: the normal force (perpendicular, pointing away from the surface) and friction (parallel to the surface).
- Kinetic friction acts when the surfaces slide relative to each other. On each surface it points opposite to that surface’s motion relative to the other.
- Static friction acts when the surfaces do not slide. It takes whatever size and direction stops slipping, up to a maximum.
- The coefficients μ_k and μ_s have no units and depend on the materials in contact. For one pair of surfaces, μ_s is usually larger than μ_k.
- In this model friction does not depend on contact area.
Key relationships
| Relationship | When to use it | Note |
|---|---|---|
| F_f,k = μ_k F_n | surfaces sliding | sizes only; friction ⟂ F_n |
| F_f,s ≤ μ_s F_n | surfaces not sliding | find the actual value from Newton’s second law |
| F_f,s,max = μ_s F_n | on the point of slipping | the threshold for starting to slide |
| F_n = mg | level surface, no other vertical forces | not true in general |
| F_n = mg cos θ | slope at angle θ, no other perpendicular forces | gravity along the slope is mg sin θ |
| μ_s = tan θ_slip | block just slips on a tilted plane | mass cancels |
Assumptions behind the numbers
- μ_k is the same at every sliding speed.
- Contact area does not affect friction.
- The object is a point; tipping over is ignored.
- g = 9.8 m/s² near Earth’s surface.
Mistakes to avoid
- F_f,s = μ_s F_n for an object at rest. That is only the maximum. Use the force balance.
- F_n = mg every time. Check for angled forces and slopes.
- Friction drawn against the velocity in every case. Static friction on a walking foot points forwards.
- Using μ_s once the object is sliding. Switch to μ_k.
- Adding friction and F_n as if parallel. They are perpendicular components of one contact force.
- Forgetting the third-law partner. Friction on the floor from a sliding box points in the box’s direction of motion.
Quick self-check
- A 12 kg box slides across a level floor with μ_k = 0.25. What is the kinetic friction on it? (0.25 × 12 × 9.8 = 29 N, opposite to its motion)
- A crate has F_n = 200 N and μ_s = 0.45. A 60 N horizontal push does not move it. What is the static friction? (60 N, opposite to the push: 60 N is below the 90 N maximum)
- A coin on a tilted book just starts to slip at 22°. What is μ_s? (tan 22° = 0.40)
Next: practice questions.