Teacher sheet · Ages 15–16 · about 45–50 minutes
Friction: coefficients and calculations
Lesson page: echoesof.science/school/friction/ages-15-16/ · Pupil worksheet: echoesof.science/school/friction/ages-15-16/print/
Learning aims
- Distinguish static and kinetic friction.
- Use f_s ≤ μ_s·N and f_k = μ_k·N, and μ_k = tan θ on a slope.
- Know that friction is an approximate model, nearly independent of contact area.
- Link friction to work done and thermal energy; measure μ and evaluate uncertainty.
Lesson plan
| Time | Activity |
|---|---|
| 5 min | Starter: why is it harder to start pushing a car than to keep it rolling? |
| 10 min | Read the text; work through the 100 kg crate example. |
| 25 min | Measure μk with the force meter and with the tilted board. |
| 5 min | Compare methods and discuss the uncertainty. |
| 5 min | Quiz, or the game as homework. |
Materials for the experiment
- Wooden block with a hook (about 200–500 g)
- Force meter (0–5 N or 0–10 N)
- Balance
- A board about 1 m long that can be tilted
- Protractor (or metre rule to measure height and length)
- Slotted masses to load the block
Safety: Keep the board low and clamp or hold it so it cannot slip; stand to the side so the block cannot slide onto feet. Don't overload the force meter.
Common misconceptions
| Pupils may think… | Actually… |
|---|---|
| Friction is always equal to μ·N. | Static friction only rises to μs·N; below that it equals the applied force. |
| A bigger contact area gives more friction. | Friction is nearly independent of the apparent contact area. |
| μ can never be more than 1. | μ is just a ratio of two forces; rubber on dry concrete already has μs ≈ 1.0. |
Worksheet answers
- Weight down, normal force up (equal); pulling force forwards and kinetic friction backwards (equal), because the velocity is constant.
- N = 40 × 9.8 = 392 N. To start: more than 0.6 × 392 ≈ 235 N. To keep moving: 0.4 × 392 ≈ 157 N.
- Answers vary; values typically agree within about 10–20%. The slope method avoids reading a moving force meter, while the pulling method allows several loads and a graph. Uncertainty from the spread of the repeats.
- KE = ½·m·v² = ½ × 1000 × 20² = 200 000 J (200 kJ). It appears mainly as heat in the brakes (and some in the tyres and road).
Quiz answers
- A 5 kg block slides on a floor with μk = 0.30 (g = 9.8 m/s²). What is the kinetic friction? About 15 N. N = 5 × 9.8 = 49 N; f = 0.30 × 49 ≈ 15 N.[1]
- Wood on wood has μs = 0.5. What is the largest static friction on a 2 kg wooden block on a level wooden table? About 9.8 N. f_s,max = 0.5 × (2 × 9.8) ≈ 9.8 N.[1]
- A block slides down a 17° slope at constant velocity. What is μk? (tan 17° ≈ 0.31) About 0.31. At constant velocity μk = tan θ.[1]
- You turn a brick onto its narrow side, with the same weight. The sliding friction… stays about the same. Friction is nearly independent of the contact area.[1][2]
- Oiling dry steel parts changes μk from about 0.3 to about… 0.03. Oiled steel on steel has μk ≈ 0.03.[1]
- A sliding box stops after 4 m with a friction force of 20 N. How much kinetic energy became thermal energy? 80 J. Work done by friction = f·d = 20 × 4 = 80 J.[5]
Going further
Plot f against N for your loads. Does the line pass through the origin? What would it mean if it did not? Research why anti-lock brakes (ABS) try to stop the wheels from skidding.
Sources used in this lesson
- [1] University Physics Volume 1, 6.2 Friction (OpenStax, Rice University): reliability High
- [2] Friction (Encyclopaedia Britannica): reliability High
- [5] College Physics 2e, 7.5 Nonconservative Forces (OpenStax, Rice University): reliability High
Full list with links and a note on each source's reliability: echoesof.science/school/friction/sources/
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