Friction: static, kinetic and rolling
Friction opposes relative sliding of surfaces in contact. fₛ(max) = μₛFₙ and fₖ = μₖFₙ; rolling friction is the smallest.
What friction is, and why it is a necessary evil
Hit a ball along the ground and it slows down and stops. A force has taken away its momentum. That force is friction. Friction is a contact force. It acts along the surfaces in contact and opposite to the relative motion (or to the motion that is about to start). It comes mainly from the roughness of the surfaces. Friction is called a necessary evil. It wears out machine parts and wastes energy as heat. But without it we could not walk, hold a pen, drive a car or stop a bicycle.
Static, limiting and kinetic friction
Push a heavy box gently and it does not move. The floor's static friction fₛ grows to match your push exactly. It can grow only up to a maximum, the limiting friction fₛ(max) = μₛFₙ. Here Fₙ is the normal force of the floor on the box; on a level floor with a sideways push, Fₙ = mg. Push harder than this and the box starts to slide. Now kinetic friction fₖ = μₖFₙ acts. Since μₖ < μₛ, it is smaller than limiting friction. That is why starting a box moving is harder than keeping it moving. While at rest, fₛ ≤ μₛFₙ.
How to draw the graph of friction against applied force
- Draw the applied force on the horizontal axis and the force of friction on the vertical axis.
- From the origin, draw a straight line rising at 45°, since friction equals the push. Label this part static friction (body at rest).
- Stop the line at a peak and label it fₛ(max), limiting friction.
- From the peak, drop slightly to a horizontal line. Label it fₖ, kinetic friction (body sliding).
- Write fₖ < fₛ(max) beside the drop.
Static, kinetic and rolling friction compared
| Type | When it acts | Formula | Size |
|---|---|---|---|
| Static | Body at rest; a force tries to move it | fₛ ≤ μₛFₙ | Adjusts itself, up to the limiting value |
| Kinetic (sliding) | Body sliding over a surface | fₖ = μₖFₙ | Less than limiting friction |
| Rolling | Wheel or ball rolling on a surface | Coefficient of rolling friction μᵣ | Smallest: μᵣ is about 0.006 for steel on steel and 0.02 to 0.04 for rubber on concrete |
What friction depends on, and how to reduce it
- Normal force: limiting and kinetic friction are both proportional to Fₙ. A heavier box is harder to push.
- Surfaces: roughness, cleanliness, temperature and humidity change μₛ and μₖ.
- Not the area of contact: a brick needs the same push on its broad face or its narrow face.
- Fluid friction (in air or water) depends on the shape and grows quickly with speed. Fish-like streamlined shapes reduce it.
- To reduce friction: use wheels or rollers. Fit ball bearings in fans, cycles and motors. Apply lubricants like oil and grease: they turn dry friction into much smaller fluid friction and keep parts cool. Blow a cushion of clean compressed air between the surfaces, or polish them.
- Try it: push a pile of books across a table with your fingers. Now put three or four round pencils under the books and push again. You need much less force: rolling friction is smaller than sliding friction.
Worked example: will the box move, and how fast does it speed up?
A 4 kg box rests on a level floor. μₛ = 0.5 and μₖ = 0.4. (a) Find the largest horizontal push that will not move it. (b) The box is pushed with 25 N. Find its acceleration. Take g = 9.8 m s⁻².
- Normal force Fₙ = mg = 4 kg × 9.8 m s⁻² = 39.2 N.
- (a) Limiting friction fₛ(max) = μₛFₙ = 0.5 × 39.2 N = 19.6 N.
- (b) 25 N is more than 19.6 N, so the box slides. Kinetic friction fₖ = μₖFₙ = 0.4 × 39.2 N = 15.68 N.
- Net force = 25 N − 15.68 N = 9.32 N.
- a = F/m = 9.32 N ÷ 4 kg = 2.33 m s⁻².
(a) Up to 19.6 N the box stays at rest. (b) With a 25 N push it accelerates at about 2.3 m s⁻²
Bicycle brakes work by friction between rubber pads and the rim, so oil on the rim makes them useless. Ball bearings in ceiling fans and oil in a motorcycle engine cut friction and save energy.
2 marks: “Why is it easier to keep a heavy box moving than to start it moving?” To start it, the push must exceed limiting friction μₛFₙ. Once it slides, only kinetic friction μₖFₙ acts. Since μₖ < μₛ, a smaller push keeps it moving.
3 marks: “A 10 kg block on a level floor is pulled by a horizontal force of 40 N and slides. μₖ = 0.2. Find its acceleration. (g = 9.8 m s⁻²)” Method: fₖ = μₖmg, net force = F − fₖ, a = net force/m. fₖ = 0.2 × 10 × 9.8 = 19.6 N. Net force = 40 − 19.6 = 20.4 N. a = 20.4 ÷ 10 = 2.04 m s⁻².
2 marks: “Why is friction called a necessary evil? Give two ways of reducing it.” Evil: it wears out parts and wastes energy as heat. Necessary: we need it to walk, grip things and brake. Reduce it with ball bearings, lubricants (oil, grease), wheels or polishing.
Starting is harder than sliding, and rolling is easiest: limiting > kinetic > rolling.