Static and kinetic friction

TL;DR:

• Friction opposes sliding. Static friction holds an object still and can be any size up to μs N. Kinetic friction acts once it slides and equals μk N.

• Usually μs is larger than μk, which is why starting is harder than keeping going.

• Friction depends on the normal force, not (to a good approximation) on contact area.

You lean on a heavy couch and nothing happens. You push harder, still nothing, then suddenly it lurches forward and keeps going with less effort than it took to start. That lurch is the switch from one kind of friction to another. Seeing the two kinds apart clears up a lot of confusing homework problems.

The idea in plain words

Friction is a contact force along the surface that opposes sliding, or the tendency to slide. Static friction acts while the surfaces are not slipping. Kinetic friction acts while they are slipping.

Static friction is clever: it adjusts. Push gently and it pushes back gently. Push twice as hard and it pushes back twice as hard, matching you exactly so that nothing moves. It can only do that up to a maximum value. Past that, the object breaks free.

The formulas and the coefficients

• Static friction, at most: f_s ≤ μs N. The equals sign holds only at the brink of slipping.

• Kinetic friction, always: f_k = μk N.

• Normal force: on a flat floor with no vertical push, N = mg.

The coefficients μs and μk are numbers with no units. They describe the pair of surfaces, such as wood on carpet, not either surface alone. The values used below are examples, not measurements of any specific couch.

Why starting is harder than keeping going

The usual picture is that surfaces are rough at a tiny scale, and while they sit still the microscopic bumps settle and bond more firmly. Once sliding, the contacts have less time to lock together, so the resistance is lower. You do not need the microscopic story for exams, only the result: typically μs > μk.

Worked example: pushing a heavy couch

A couch of mass 60 kg sits on a floor with μs = 0.60 and μk = 0.40. Use g = 9.8 m/s².

1. Normal force: N = mg = 60 × 9.8 = 588 N.

2. Maximum static friction: 0.60 × 588 = 352.8 N.

3. Kinetic friction once sliding: 0.40 × 588 = 235.2 N.

4. Push with 300 N. That is less than 352.8 N, so the couch does not move, and static friction is exactly 300 N, not 352.8 N. Net force zero.

5. Push with 400 N. That is more than 352.8 N, so it breaks free. Now friction drops to 235.2 N.

6. Net force while sliding: 400 − 235.2 = 164.8 N. Acceleration: 164.8 / 60 ≈ 2.75 m/s².

To keep the couch moving at a steady speed you only need to push with 235.2 N, since steady speed means zero net force. That is 117.6 N less than the push needed to start it (352.8 − 235.2).

A good way to feel the difference is a graph of friction against your push. From zero up to 352.8 N the friction line rises along with your push, one for one, a straight diagonal. At the break-free point it drops suddenly to 235.2 N and then stays flat, no matter how hard you push after that. Extra push beyond 235.2 N does not increase friction, it just produces acceleration.

That flat line is also why the jolt happens. At the moment of breaking free, your push of about 353 N suddenly faces only 235 N of resistance. The unbalanced 118 N makes the couch jump forward before you can ease off.

How to check your answer

• Which type? If the object is not moving, use static friction, which equals whatever is needed to balance, not μs N. Only use μs N for the instant of breaking free.

• Units. Friction is in newtons. The coefficient has no units.

• Reasonableness. Kinetic friction must be less than the maximum static value. 235.2 < 352.8.

• Direction. Friction points opposite to the sliding (or to the push).

Common mistakes

• Always using μs N, even when the object is at rest below the limit.

• Using weight when the normal force is different, for example on a ramp or when someone pulls upward on a rope. If you pull upward at an angle, N decreases and so does friction.

• Believing friction depends on the area. For ordinary solid surfaces, it mostly does not, which is why the brick has the same friction on its wide face as on its narrow one.

• Thinking friction only slows things. Static friction on your shoes pushes you forward when you walk.

• Forgetting to pick a direction for the net force.

Tip: On a test, draw the free-body diagram first and ask "is it moving?". That one question decides which friction formula you use.

Where you will use it next

Friction is the force that makes a car turn, which is the next topic in circular motion and centripetal force. It also explains the energy lost in the roller-coaster example, where friction turns motion into heat. And in ramp problems the normal force shrinks as the angle grows, so friction shrinks too.

Frequently asked questions

Can the coefficient of friction be greater than 1?

Yes. It is just a ratio of friction force to normal force. Some soft, sticky surfaces, like racing tyre rubber on a clean road, can exceed 1.

Does rolling friction count as kinetic friction?

It is a separate effect, usually much smaller. A rolling wheel's contact point is not sliding, so the grip it uses is static friction. Resistance to rolling comes from the wheel and surface deforming.