The coefficient of friction tells how strongly two surfaces resist sliding against each other. It is written with the Greek letter mu, μ, and it has no units because it is a ratio of forces. This idea matters in everyday physics, from shoes gripping a floor to tires stopping a car to a box sliding down a ramp.
A larger coefficient means more friction for the same normal force.
Key Facts
- Friction force is modeled by f = μN, where N is the normal force.
- Static friction adjusts up to a maximum value: fs ≤ μsN.
- Kinetic friction during sliding is fk = μkN.
- For most surface pairs, μs is greater than μk, so starting motion takes more force than keeping motion going.
- On a flat surface with no vertical acceleration, N = mg.
- For a block on an incline at the threshold of sliding, μs = tan θ.
Vocabulary
- Coefficient of friction
- A unitless number that describes how much friction acts between two surfaces.
- Static friction
- The friction force that prevents two surfaces from starting to slide past each other.
- Kinetic friction
- The friction force that acts while two surfaces are already sliding past each other.
- Normal force
- The support force exerted perpendicular to a surface.
- Inclined plane
- A sloped surface, such as a ramp, used to analyze forces at an angle.
Common Mistakes to Avoid
- Using f = μmg on a ramp, which is wrong because the normal force is not mg on an incline. On a ramp, N = mg cos θ if no other perpendicular forces act.
- Treating static friction as always equal to μsN, which is wrong because static friction only reaches μsN at the instant just before slipping. Before that, it matches the needed opposing force up to its maximum.
- Confusing μs and μk, which gives the wrong force for starting or continuing motion. Use μs for objects not yet sliding and μk for objects already sliding.
- Adding units to μ, which is wrong because μ is a ratio of friction force to normal force. Since both forces are measured in newtons, the units cancel.
Practice Questions
- 1 A 12 kg box rests on a horizontal floor with μs = 0.50 and μk = 0.35. What is the maximum static friction force, and what is the kinetic friction force once the box is sliding?
- 2 A block just begins to slide down a ramp when the ramp angle reaches 28 degrees. Estimate the coefficient of static friction using μs = tan θ.
- 3 A student says a heavier box always has a larger coefficient of friction because it has more friction force. Explain why this reasoning is incorrect.