Kinetic and Static Friction · 动摩擦与静摩擦
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| kinetic friction/kɪˈnetɪk ˈfrɪkʃn/ | 动摩擦 | dòng mó cā |
| static friction/ˈstætɪk ˈfrɪkʃn/ | 静摩擦 | jìng mó cā |
| normal force/ˈnɔːml fɔːs/ | 法向力 | fǎ xiàng lì |
| coefficient of friction/ˌkəʊɪˈfɪʃənt ɒv ˈfrɪkʃn/ | 摩擦系数 | mó cā xì shù |
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.
让你能走路——也能停下的力
- 没有摩擦力,你走不了路、开不了车,甚至握不住铅笔。
- 可是同一个力又浪费能量、磨损刹车。
- 摩擦力总是阻碍两个表面之间的滑动。
- 它有两种——一种在滑动之前,一种在滑动之中。
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.
静摩擦与动摩擦
- 静摩擦在滑动开始之前起作用。它会自我调整以匹配你的推力,直到一个最大值。
- 动摩擦在表面滑动时起作用,大小固定。
- 静摩擦的峰值通常比动摩擦略大——这就是为什么东西在第一推时最难启动。
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.
它有多大?
- 最大静摩擦:$f_s \le \mu_s N$。
- 动摩擦:$f_k = \mu_k N$。
- 这里 $N$ 是把两个表面压在一起的法向力,$\mu$ 是摩擦系数。
Applied force vs friction · 施加的力与摩擦力
Increase the applied force and watch friction resist until the box breaks free and accelerates. · 增大施加的力,看着摩擦力阻抗,直到箱子挣脱并加速。
A box has normal force $N = 50\ \text{N}$ and $\mu_s = 0.6$. What is the maximum static friction (in N)? · 一个箱子的法向力 $N = 50\ \text{N}$,$\mu_s = 0.6$。最大静摩擦是多少(单位 N)?
$f_s^{max} = \mu_s N = 0.6 \times 50 = 30\ \text{N}$. · $f_s^{max} = \mu_s N = 0.6 \times 50 = 30\ \text{N}$。
Kinetic friction equals the coefficient times the ____ force. · 动摩擦等于系数乘以____力。
$f_k = \mu_k N$, where $N$ is the normal force. · $f_k = \mu_k N$,其中 $N$ 是法向力。
A sliding box has $N = 40\ \text{N}$ and $\mu_k = 0.25$. Find the kinetic friction (in N). · 一个滑动的箱子 $N = 40\ \text{N}$,$\mu_k = 0.25$。求动摩擦(单位 N)。
$f_k = \mu_k N = 0.25 \times 40 = 10\ \text{N}$. · $f_k = \mu_k N = 0.25 \times 40 = 10\ \text{N}$。
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.
它取决于什么——又不取决于什么
- 摩擦力取决于法向力和系数 $\mu$。
- 它不取决于接触面积——一块砖侧放或立放,滑动情况相同。
- 压得越重($N$ 越大),摩擦力越大。
Sliding a brick on its small end gives more friction than on its large flat side. · 把砖立在小端滑动,比平放大面滑动摩擦力更大。
Friction does not depend on contact area -- only on the normal force and $\mu$. Both orientations give the same friction. · 摩擦力不取决于接触面积——只取决于法向力和 $\mu$。两种放法摩擦力相同。
Select all · 所有 things the friction force depends on. · 选出摩擦力所有依赖的因素。
Friction $= \mu N$ -- it depends on $\mu$ and $N$, not on how much area is touching. · 摩擦力 $= \mu N$——取决于 $\mu$ 和 $N$,而不是接触面积多大。
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.
斜坡上的摩擦
- 在斜坡上,法向力只有 $N = mg\cos\theta$(不是全部重量)。
- 所以可提供的摩擦力是 $\mu\,mg\cos\theta$。
- 把它与沿坡的拉力 $mg\sin\theta$ 比较,就能判断物体是否滑动。
You push a heavy crate with $18\ \text{N}$ and it does not · 不 move. The static friction acting on it is... · 你用 $18\ \text{N}$ 推一个重板条箱,它没有移动。作用在它上的静摩擦是……
Static friction matches the push, so it is $18\ \text{N}$ -- it only reaches $\mu_s N$ at the instant of slipping. · 静摩擦与推力相匹配,所以是 $18\ \text{N}$——只有在即将打滑那一刻才达到 $\mu_s N$。
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.
一个 $10\ \text{kg}$ 的箱子放在地板上,$\mu_s = 0.4$。
- 法向力:$N = mg = 98\ \text{N}$。
- 最大静摩擦:$f_s = \mu_s N = 0.4 \times 98 \approx 39\ \text{N}$。
- 用小于 $39\ \text{N}$ 的力推,它保持不动;推得更用力,它就挣脱。
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.
静摩擦不是一个固定的数——它是所需的任意值,最多到 $\mu_s N$。如果你用 $20\ \text{N}$ 推一个重箱子而它不动,那么摩擦力就是 $20\ \text{N}$,而不是 $\mu_s N$。只有在即将打滑的那一刻,它才达到最大值。
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.
摩擦力阻碍滑动。静摩擦($f_s \le \mu_s N$)会上升以匹配推力,直到打滑;动摩擦($f_k = \mu_k N$)在滑动后固定。两者都取决于法向力 $N$ 和摩擦系数 $\mu$——绝不取决于接触面积。