Short on time? This page is the recap for the calculus-based course (separate from Physics 1, which uses the same friction model without calculus). For explanations, diagrams and worked examples, use the full study guide.
Recap
- A contact force has a normal part F_N (perpendicular, pointing away from the surface) and a friction part (parallel to the surface).
- Kinetic friction acts when the surfaces slide relative to each other. On each surface it points opposite that surface’s motion relative to the other.
- Static friction acts when they do not slide. It takes the size and direction needed to prevent slipping, up to a maximum.
- μ_k and μ_s have no unit and depend on the two materials. Usually μ_s > μ_k.
- Friction does not depend on the area of contact.
Key relationships
| Relationship | When it applies |
|---|---|
| F_f,k = μ_k F_N | surfaces sliding |
| |F_f,s| ≤ μ_s F_N | surfaces not sliding |
| F_f,s,max = μ_s F_N | slipping about to start |
| F_N = mg cos θ | block on a slope at θ, no other force perpendicular to it |
| at rest on a slope needs tan θ ≤ μ_s | static, mass cancels |
| a_x = g(sin θ − μ_k cos θ) | sliding down a slope, +x down the slope |
Assumptions behind the numbers
- g = 9.8 m/s². Objects are treated as point objects or rigid blocks.
- μ_k does not depend on speed, and μ values are constant over the surface unless stated.
- Strings are light, and floors described as frictionless have μ = 0.
Mistakes to avoid
- F_N = mg without checking. Angled pulls, extra pushes, slopes and lifts all change F_N.
- Writing F_f,s = μ_s F_N when slipping is not about to start.
- “Friction opposes motion.” It opposes relative motion; it can speed an object up.
- Skipping the slip test. Assume no slip, find the friction needed, compare with μ_s F_N.
- Constant-a equations when the force changes with time. Integrate a_x(t) from the moment slipping starts.
- Forgetting the third-law partner on the other surface.
Quick self-check
- A 2.0 kg block on a level bench (μ_s = 0.60) is pulled horizontally with 10 N and stays still. What is the friction? (10 N, opposite the pull; the maximum would be 11.76 N)
- A block slides down a 30° slope with μ_k = 0.20. What is its acceleration? (g(sin 30° − 0.20 cos 30°) ≈ 3.2 m/s² down the slope)
- A 1.0 kg block on a level floor (μ_s = 0.50) is pushed with P = (3.0 N/s)t. When does it start to slide? (0.50 × 9.8 ÷ 3.0 ≈ 1.6 s)
Next: practice questions.