echoesof.science · Ages 15–16
Friction: coefficients and calculations
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Friction opposes relative motion between surfaces in contact. While the surfaces do not slide, static friction matches the applied force up to a maximum: fs ≤ μs·N. Once sliding, kinetic friction is fk = μk·N, where N is the normal force and μ is the dimensionless coefficient of friction.
Typical values (static / kinetic): rubber on dry concrete 1.0 / 0.7; wood on wood 0.5 / 0.3; dry steel on steel 0.6 / 0.3 but oiled 0.05 / 0.03; ice on ice 0.1 / 0.03; waxed wood on wet snow 0.14 / 0.1. This is an approximate empirical model, so the values are given to only one or two significant figures.
μs is usually larger than μk. Friction is nearly independent of the apparent contact area, because only the high spots of the rough surfaces actually touch; adhesion between surface molecules also contributes.
Experiment: Measuring the coefficient of friction two ways
- Method 1: measure the mass of the block and calculate N = m·g. Pull it along the level board at a slow, steady speed and read the force meter: this is f_k. Calculate μ_k = f_k / N.
- Repeat with two or three different loads on the block and plot f_k against N. The gradient is μ_k.
- Method 2: put the block on the board and slowly raise one end. Each time, give the block a small nudge. Find the angle θ at which it just keeps sliding at a steady speed after the nudge.
- Calculate μ_k = tan θ (or height ÷ horizontal length).
- Repeat each method at least three times. Compare the two values of μ_k and estimate the uncertainty in each.
- Optional: also record the force (method 1) or angle (method 2) at which the block first starts to move without a nudge, and compare with μ_k.
| Load: N (N) | f_k try 1 (N) | f_k try 2 (N) | f_k try 3 (N) | μ_k = f/N |
|---|---|---|---|---|
Questions
Draw a free-body diagram for a box pulled at constant speed across a level floor. Label all four forces.
🍎A 40 kg crate is on a level floor, μs = 0.6 and μk = 0.4. Calculate the force needed to start it moving and to keep it moving at constant speed.
Your experiment: compare your values of μk from the two methods. Which method do you trust more, and why? Estimate the uncertainty.
A 1000 kg car travelling at 20 m/s brakes to a stop. How much energy is converted into heat? Where does this heat appear?
Sources for every fact on this sheet: echoesof.science/school/friction/sources/