Friction
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 4 practice questions.
Kinetic friction is fk = μkN and opposes sliding. Static friction is only as big as it needs to be to prevent sliding, up to a maximum of μsN. Always find the normal force first; it isn’t always mg.
1. The two kinds
2. Static or kinetic?
First check whether the object slides: compare the applied force with the maximum static friction, μsN. If the push is smaller, friction just matches it and nothing moves.
Once sliding starts, switch to μkN, usually a bit smaller.
A force pulling up at an angle reduces N (and friction); one pushing down at an angle increases it. Write the perpendicular equation first, then use μN.
3. Example, then try it
A 10 kg crate sits on a floor with μs = 0.50 and μk = 0.30. What is the friction force when you push horizontally with 30 N? With 60 N?
Maximum static friction: (0.50)(100) = 50 N. At 30 N it doesn’t move, so f = 30 N.
At 60 N it slides: f = (0.30)(100) = 30 N, and a = (60 − 30) ÷ 10 = 3.0 m/s².
A 2.0 kg block is on a 37° incline (sin 37° = 0.60, cos 37° = 0.80) with μs = 0.50 and μk = 0.25. Will it start sliding on its own? Find its acceleration down the slope, and the force along the slope needed to pull it up at constant speed.
Will it slip? tan 37° = 0.75 > μs = 0.50, so yes.
Acceleration: a = 10(0.60 − 0.25 × 0.80) = 10(0.40) = 4.0 m/s².
Pulling up: friction now points down the slope: F = mg sin θ + μkmg cos θ = 12 + 4.0 = 16 N.
Answer: it slips; 4.0 m/s² down; 16 N to pull it up steadily.
4. Common mistakes
You pull a sled with a rope at an upward angle instead of horizontally, with the same tension. How does the kinetic friction on the sled change?
The upward part of the pull lifts some of the sled’s weight, so N, and fk = μkN, decrease.
Ready to practice?
4 questions on Friction, each with a hint and an explanation for every wrong answer.