Static and Kinetic Friction Force
Friction is the contact force that opposes motion, and it acts along the surface. Push a box and the floor pushes back. That is the whole of it.
What makes friction worth a chapter is that it comes in two kinds that behave completely differently, and that one of its three properties is something almost nobody believes until they measure it.
Static and kinetic, and why static is the strange one
You have felt this without knowing it has a name. A heavy box is hard to start moving and easier to keep moving. The moment it goes, it gets lighter under your hands.
| When it acts | How big it is | |
|---|---|---|
| Static friction, fs | The object is not moving | It varies. It matches whatever force is trying to move the object, up to a maximum |
| Kinetic friction, fk | The object is moving | Constant for a given pair of surfaces and a given load |
Static friction is the one that catches people out, because it is not a fixed number.
Push a heavy box gently and it does not move, so friction must be exactly equal to your push. Push twice as hard and it still does not move, so friction has doubled to match you. Keep going and you eventually pass a maximum, and the box goes.
And at that instant friction drops, because you have switched from static to kinetic. That drop is why the box suddenly feels easier, and it is the thing this practical puts a number on.
The normal force, because friction depends on it
The normal force is the contact force a surface exerts on an object at right angles to the surface. On a horizontal bench it is what holds the object up, so it is equal in size to the object's weight.
Normal and friction are really two parts of one contact force the surface exerts. It is only convenient bookkeeping that we split them: one perpendicular to the surface, one parallel to it.
Why it matters here: friction is proportional to the normal force and to nothing else about the load. Press harder and friction rises. Take weight off and it falls.
The two relationships
fs ≤ μsFN for an object at rest
fk = μkFN for a moving object
Look at which one has the "less than or equal to". Static friction is not fixed at μsFN. That is only the maximum it can reach, and it only gets there at the instant the object breaks away.
Writing fs = μsFN is the commonest mistake in this topic, and it is wrong everywhere except at the point of slipping.
μ has no unit. It is a force divided by a force, so the units cancel. Learners invent one and it costs a mark every single time.
Three properties, and one of them is hard to swallow
Friction force is:
- proportional to the normal force
- independent of the area of contact
- independent of the speed at which the object slides
Nobody believes the middle one. Twice the contact area sounds like it must mean twice the friction. It does not, and you can disprove it in two minutes with a block of wood.
Why friction happens at all, and it answers the area question
Under an electron microscope, even polished glass is a landscape of ridges. When two surfaces touch, only the microscopic high points actually meet, and the real area of contact is a tiny fraction of the area you can see.
That is the answer. Stand the block on its narrow edge and the same weight is carried by a smaller area, so the pressure is higher and the high points are squashed flatter. More real contact per square millimetre, over fewer square millimetres. The two effects cancel.
It also explains lubricants: oil fills the valleys so the high points cannot interlock.
Where this fits in the curriculum
| Subject | Physical Sciences |
|---|---|
| Grade | 11 |
| Term | 1 |
| Topic | Mechanics, Newton's laws |
| Status | A practical demonstration. Not a formal assessment |
| Marks | 40 on our worksheet. None is prescribed |
Measure the angle, not the height
The standard version of this demonstration has a flaw worth knowing about before you run it.
It tells you to tilt a plank until the object slides and then measure how high the raised end is. The trouble is that the height depends on how long your plank is. A school with a 400 mm plank and a school with a 900 mm plank get different numbers for the same two surfaces, so nothing can be compared and nothing can be checked against a published value.
Measure the angle instead. An object on a slope slips at exactly the point where
μs = tan θ
which drops straight out of fs ≤ μsFN. At the moment of slipping, the component of gravity down the slope equals maximum static friction, the weight cancels from both sides, and you are left with the tangent.
You do not even need a protractor. Measure the height of the raised end and the horizontal base, and tan θ is height divided by base. That is better teaching than reading a scale, because the learner has to see where the tangent comes from.
The practical
Two measurements, and together they prove something the theory only asserts.
Apparatus
| Item | Qty |
|---|---|
| Friction ramp, hinged, with a folding support | 1 |
| Surface samples: rough pine, varnished pine, acrylic, laminate, rubber | 5 |
| Hardwood block with a screw eye, flat faces of different area | 1 |
| Newton meter, 2,5 N | 1 |
| Newton meter, 5 N, for the rubber surface | 1 |
| Mass set, 9 x 10 g with a 100 g hanger | 1 |
| Tape measure, 5 m | 1 |
| Protractor and cord | 1 |
Nothing is supplied by the school. No chemicals, no consumables, no store cupboard dependency. A bench and a calculator.
Practical A: drag it, to find the coefficient of kinetic friction
- Rough pine on the bench, block on top, largest face down
- Hook the 2,5 N meter to the screw eye so the pull is horizontal
- Pull steadily until the block moves at a slow constant speed, and read the meter while it is moving. That reading is fk
- Three trials, then average
- Add 100 g and repeat. Then 200 g, 300 g, 400 g
- Work out FN for each load, remembering to include the block's own mass
- Plot fk against FN. A straight line through the origin, and the gradient is μk
The graph is the whole point of Practical A. One reading gives you one number. Five readings and a straight line prove the proportionality, and the gradient is a better value than any single measurement.
Practical B: tilt it, to find the coefficient of static friction
- Same surface on the ramp, block near the top
- Raise the free end slowly until the block just begins to slide, and stop there
- Measure the height h of the raised end and the base b, the horizontal distance
- μs = h ÷ b
- Three trials, then average
Use the horizontal base, not the length of the ramp. The ramp's own length gives you sin θ, and sin θ is not tan θ.
Practical C: does the area matter?
Repeat one drag with the block on its narrow edge. Same block, same mass, same surface, about a third of the contact area.
The reading does not change. Get the class to predict first.
What you should see
Practical A, a 200 g block on rough pine
| Added mass | Total mass | FN | fk |
|---|---|---|---|
| 0 g | 200 g | 1,96 N | about 0,40 N |
| 100 g | 300 g | 2,94 N | about 0,58 N |
| 200 g | 400 g | 3,92 N | about 0,80 N |
| 300 g | 500 g | 4,90 N | about 0,98 N |
| 400 g | 600 g | 5,88 N | about 1,20 N |
Gradient, and therefore μk, about 0,20.
All five surfaces
| Surface | μs | Slips at about | μk |
|---|---|---|---|
| Rubber | 0,6 to 0,8 | 31° to 39° | 0,5 to 0,7 |
| Rough pine | 0,4 to 0,5 | 22° to 27° | 0,3 to 0,4 |
| Varnished pine | 0,25 to 0,35 | 14° to 19° | 0,2 to 0,3 |
| Laminate | 0,2 to 0,3 | 11° to 17° | 0,15 to 0,25 |
| Acrylic | 0,2 to 0,3 | 11° to 17° | 0,15 to 0,25 |
Those ranges are wide on purpose. A coefficient depends on the exact timber, the finish, how clean the surfaces are and how humid the room is. A class that gets the surfaces in the right order has succeeded. A class matching a published figure to two decimals has been lucky.
The two results worth the whole lesson
μk comes out smaller than μs on every surface. The theory says maximum static friction exceeds kinetic friction. Here the class has measured both and proved it, which is a different thing from being told it.
And the area result. Same block on its edge, same reading. Let them predict, let them be wrong, then explain it.
A note on glass, and why the kit ships acrylic
The usual apparatus list suggests a length of glass shelving or a mirror as the smooth surface.
A sheet of glass sliding off a tilted plank onto a classroom floor is not a risk worth taking to measure a coefficient of 0,25.
3 mm cast acrylic gives a very similar value, it does not shatter, and it costs about the same.
If it does not work
| What you see | What caused it |
|---|---|
| The block judders instead of sliding | Pulling too fast or in jerks. Slow and steady. Some juddering on rubber is normal and has a name, stick-slip |
| The reading drifts and will not settle | The cord is not horizontal. Even 20° of lift reduces the normal force and drops the reading |
| fk goes off the top of the scale | You are on rubber with masses added. Switch to the 5 N meter |
| The graph misses the origin | The block's own mass was left out of FN |
| μ comes out above 1 | Almost certainly rubber, and it is legitimate. Unusual, not impossible |
| μ has a unit on it | It has none. Force divided by force |
| The block will not slide at any angle | The ramp does not tilt far enough, or it is the rubber surface |
| Every surface gives the same angle | They are dusty, or the same sample got used twice |
| Two groups get very different numbers | Expected. Compare the order of the surfaces, not the values |
The failure worth keeping
A group pulling at an angle rather than horizontally gets a low, drifting value and has no idea why.
Lifting the cord even slightly adds an upward component that reduces the normal force, so friction falls with it. It is a clean demonstration that fk depends on FN and not on how hard you pull, and it lands far harder discovered than warned about.
Why this matters outside the classroom
ABS braking is this practical, at 120 km/h.
A rolling tyre's contact patch is momentarily stationary against the road, so the grip available is static friction. Lock the wheels and the tyre slides, which switches it to kinetic friction, which is smaller. Less friction, less retarding force, longer stopping distance, and no steering.
Anti-lock brakes release and reapply to stop the wheel locking, keeping the tyre in the static regime where the coefficient is higher. That is the entire idea, and it is Grade 11 friction.
It is also why worn smooth tyres are dangerous, why a mountain bike has knobbly tyres and a racing bike does not, and why you put a branch under a wheel stuck in mud.
How the 40 marks are made up
| Section | Marks |
|---|---|
| Aim, variables and method | 5 |
| Practical A results table | 8 |
| The fk against FN graph | 8 |
| Practical B, μs by tilting | 7 |
| Comparing the surfaces | 5 |
| Area of contact | 3 |
| Conclusion | 4 |
No mark allocation is prescribed. This is set as a demonstration with no marks attached, so the worksheet and this split are ours.
The graph carries 8 on its own, because drawing it correctly is the skill actually being tested: axes the right way round, a sensible scale, a line of best fit rather than dot-to-dot, and a gradient read off the line rather than off a data point.
The mark most often dropped is giving μ a unit. Close behind is leaving the block's own mass out of the normal force, which shifts every point on the graph.
If you have time
One drop of cooking oil on the laminate. The coefficient collapses. Thirty seconds, and it is what a lubricant does.
Three faces, three areas. Face, edge and end, all tabulated. Nobody believes the area result once, and three readings settle it.
Work out the stopping distance. With μk for rubber on your ramp and a bit of Newton's second law, a class can estimate how far a car slides from 60 km/h with the wheels locked. It is longer than they expect.
Free worksheet and marking memo
Both free, no sign up, straight to the PDF.
- Learner worksheet, 40 marks, with both results tables, a gridded space for the graph, the five surface comparison and the area test
- Marking memorandum, with a worked sample set, the full derivation of μs = tan θ, expected ranges for all five surfaces and the six places learners most often drop marks
Related practicals
- Newton's Second Law, Grade 11. The same chapter, and a formal assessment
- Conservation of linear momentum, Grade 12. Where the mechanics goes next
- Vertical projectile motion, Grade 12. Motion without friction, for contrast
Buy this experiment
We are putting together a Friction Kit for Grade 11 with the hinged ramp, five interchangeable surface samples, the hardwood block, both Newton meters, a mass set, tape measure and protractor in one box, plus a printed teacher guide and the marking memo. Coming shortly.
The Newton meters are the part to check your store cupboard for, and they are in the force, motion and dynamics range at R70 in six ranges from 2,5 N to 50 N. A 200 g block on wood needs about 0,6 N to drag, so the 2,5 N is the one this practical wants, with the 5 N as backup for rubber.