Kinetic and Static Friction
Introduced| English |
|---|
| kinetic friction/kɪˈnetɪk ˈfrɪkʃn/ |
| static friction/ˈstætɪk ˈfrɪkʃn/ |
| normal force/ˈnɔːml fɔːs/ |
| coefficient of friction/ˌkəʊɪˈfɪʃənt ɒv ˈfrɪkʃn/ |
The force that lets you walk -- and stop
- Without friction you could not walk, drive, or even hold a pencil.
- Yet the same force wastes energy and wears out brakes.
- Friction always fights sliding between two surfaces.
- It comes in two flavours -- one before things slide, one during.
Static versus kinetic friction
- Static friction 静摩擦 acts before sliding starts. It adjusts itself to match your push, up to a maximum.
- Kinetic friction 动摩擦 acts while surfaces slide, with a fixed value.
- The peak static friction is usually a little larger than the kinetic -- which is why something is hardest to get moving at the first shove.
How big is it?
- Maximum static friction: $f_s \le \mu_s N$.
- Kinetic friction: $f_k = \mu_k N$.
- Here $N$ is the normal force 法向力 pressing the surfaces together, and $\mu$ the coefficient of friction 摩擦系数.
Applied force vs friction
Increase the applied force and watch friction resist until the box breaks free and accelerates.
A box has normal force $N = 50\ \text{N}$ and $\mu_s = 0.6$. What is the maximum static friction (in N)?
$f_s^{max} = \mu_s N = 0.6 \times 50 = 30\ \text{N}$.
Kinetic friction equals the coefficient times the ____ force.
$f_k = \mu_k N$, where $N$ is the normal force.
A sliding box has $N = 40\ \text{N}$ and $\mu_k = 0.25$. Find the kinetic friction (in N).
$f_k = \mu_k N = 0.25 \times 40 = 10\ \text{N}$.
What it depends on -- and doesn't
- Friction depends on the normal force and the coefficient $\mu$.
- It does not depend on the contact area -- a brick slides the same on its side or its end.
- Press harder (bigger $N$) and friction grows.
Sliding a brick on its small end gives more friction than on its large flat side.
Friction does not depend on contact area -- only on the normal force and $\mu$. Both orientations give the same friction.
Select all things the friction force depends on.
Friction $= \mu N$ -- it depends on $\mu$ and $N$, not on how much area is touching.
Friction on a ramp
- On a slope, the normal force is only $N = mg\cos\theta$ (not the full weight).
- So the friction available is $\mu\,mg\cos\theta$.
- Compare it with the along-slope pull $mg\sin\theta$ to see whether the object slides.
You push a heavy crate with $18\ \text{N}$ and it does not move. The static friction acting on it is...
Static friction matches the push, so it is $18\ \text{N}$ -- it only reaches $\mu_s N$ at the instant of slipping.
A $10\ \text{kg}$ box sits on the floor with $\mu_s = 0.4$.
- Normal force: $N = mg = 98\ \text{N}$.
- Maximum static friction: $f_s = \mu_s N = 0.4 \times 98 \approx 39\ \text{N}$.
- Push with less than $39\ \text{N}$ and it stays put; push harder and it breaks free.
Static friction is not a fixed number -- it is whatever it needs to be, up to $\mu_s N$. If you push a heavy box with $20\ \text{N}$ and it does not move, the friction is $20\ \text{N}$, not $\mu_s N$. Only at the instant of slipping does it reach its maximum.
Friction opposes sliding. Static friction ($f_s \le \mu_s N$) rises to match a push until slipping; kinetic friction ($f_k = \mu_k N$) is fixed once sliding. Both depend on the normal force $N$ and the coefficient of friction $\mu$ -- never on contact area.