Friction Force
Senior 2 · Physics
Friction Force
Lesson 2 of 4
25 min
Let's begin
Anyone who has pushed a heavy crate of tomatoes knows it is hardest to get it started. Once it is sliding, it is easier to keep it going. That difference is the difference between static and kinetic friction. Engineers who design brakes, tyres and conveyor belts use these ideas every day.
Static friction acts between surfaces that are not sliding over each other. It adjusts itself to match the push, up to a maximum value. Push a crate gently with 50 N and static friction is 50 N. Push with 100 N and it becomes 100 N, so the crate still does not move. The largest static friction possible is called limiting friction:
fs,max = μs N
Here N is the normal reaction, the force pressing the surfaces together. On level ground N equals the object's weight, mg. μs (the Greek letter "mu") is the coefficient of static friction, a number with no unit that depends on the two materials.
Once the surfaces slide, kinetic friction acts. It is roughly constant and is usually smaller than limiting friction:
fk = μk N, with μk < μs
| Surfaces | μs | μk |
|---|---|---|
| Rubber on dry concrete | 1.0 | 0.7 |
| Rubber on wet concrete | 0.7 | 0.5 |
| Wood on wood | 0.5 | 0.3 |
| Steel on steel (dry) | 0.6 | 0.3 |
| Shoes on ice | 0.1 | 0.05 |
A 40 kg wooden crate of tomatoes rests on a wooden floor (μs = 0.50, μk = 0.30). Take g = 9.8 m/s².
When a wheel or ball rolls instead of sliding, the resistance, called rolling friction, is much smaller than sliding friction. That is why a wheelbarrow carries a load that you could never drag across the ground. For the same object, the order is: rolling < kinetic < limiting static.
Liquids and gases are fluids. An object moving through a fluid feels drag (fluid friction). Drag in air is called air resistance. Unlike sliding friction, drag depends strongly on speed: for moving vehicles it grows roughly with the square of the speed, so doubling the speed makes the drag about four times larger. Drag also grows with the area facing the flow and depends on the object's shape.
A falling object speeds up until the upward drag equals its weight. From then on, it falls at a steady terminal velocity. A parachute's large area makes that terminal velocity small enough for a safe landing.
Try the Friction screen of the Forces and Motion: Basics simulation. Push a crate with a slowly increasing force and watch the friction arrow grow, then drop suddenly when the crate starts to slide.
Tip
Static friction is "as much as needed, up to μsN"
If the push is less than the limiting friction, the friction force EQUALS the push, not μsN. Examiners often test this.
A 20 kg box sits on a floor with μs = 0.45 and μk = 0.35 (g = 9.8 m/s²). What force starts it moving, and what force keeps it moving at a steady speed?
Solution: N = 20 × 9.8 = 196 N. To start it you need just over 0.45 × 196 = 88 N. To keep it moving steadily you need 0.35 × 196 = 69 N.
A pull of 90 N keeps a 30 kg crate sliding at a steady speed (g = 10 m/s²). Find μk.
Solution: At steady speed, friction = 90 N. N = 30 × 10 = 300 N. μk = 90 ÷ 300 = 0.30.
The 40 kg crate from the worked example is pushed with 60 N. What is the friction force?
Solution: 60 N is below the limiting friction of 196 N, so the crate does not move and static friction = 60 N.
Why does a raindrop not keep speeding up all the way from a cloud to the ground?
Solution: As it speeds up, the air resistance on it grows until it balances the drop's weight. It then falls at a constant terminal velocity.
Summary
Sources and credits
The Rwandan examples, worked examples and practice items are written by Ganzaa.
