Friction worked problems connect force diagrams, Newton's second law, and real motion. They matter because almost every real surface resists sliding, from shoes on floors to crates on ramps. The main skill is deciding whether friction is static or kinetic before choosing the correct equation.
A clear free-body diagram usually makes the solution much easier.
Key Facts
- Static friction adjusts up to a maximum: 0 <= fs <= μsN.
- Maximum static friction is fs,max = μsN.
- Kinetic friction has magnitude fk = μkN and acts opposite relative sliding.
- On a horizontal surface with no vertical acceleration, N = mg.
- On an incline with no acceleration perpendicular to the surface, N = mg cos θ.
- Along an incline, the component of weight down the slope is mg sin θ, so use ΣFparallel = ma.
Vocabulary
- Friction
- Friction is a contact force that resists relative motion or attempted relative motion between two surfaces.
- Static friction
- Static friction is friction between surfaces that are not sliding past each other, and it can change in size up to a maximum value.
- Kinetic friction
- Kinetic friction is friction between surfaces that are sliding past each other, with magnitude fk = μkN.
- Normal force
- The normal force is the contact force exerted perpendicular to a surface.
- Coefficient of friction
- The coefficient of friction is a unitless number that describes how strongly two surfaces resist sliding.
Common Mistakes to Avoid
- Using μsN automatically for static friction is wrong because static friction only equals the amount needed to prevent slipping until it reaches fs,max.
- Pointing friction opposite the velocity is wrong in some static friction cases because friction opposes relative motion or the tendency to slip, not always the motion of the object itself.
- Using N = mg on an incline is wrong because the normal force is perpendicular to the ramp and equals mg cos θ when no other perpendicular forces act.
- Forgetting to split weight into components is wrong because mg acts vertically, while incline problems are usually solved along and perpendicular to the ramp.
Practice Questions
- 1 A 12 kg box is pushed horizontally with a 40 N force on a floor where μs = 0.45 and μk = 0.30. Does it move, and if it moves, what is its acceleration? Use g = 9.8 m/s^2.
- 2 A 6.0 kg block slides down a 25 degree incline with μk = 0.20. Find its acceleration down the ramp. Use g = 9.8 m/s^2.
- 3 A block rests on a rough incline and does not move as the angle is slowly increased. Explain how the static friction force changes before the block starts sliding, and state what condition is met at the instant slipping begins.