Spring Forces · 弹簧力
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| Hooke's law/hʊks lɔː/ | 胡克定律 | hú kè dìng lǜ |
| restoring force/rɪˈstɔːrɪŋ fɔːs/ | 回复力 | huí fù lì |
| extension/ekˈstenʃn/ | 伸长量 | shēn cháng liàng |
| spring constant/sprɪŋ ˈkɒnstənt/ | 弹簧劲度系数 | tán huáng jìn dù xì shù |
| elastic limit/ɪˈlæstɪk ˈlɪmɪt/ | 弹性极限 | tán xìng jí xiàn |
Pull twice as far, feel twice the pull
- Stretch a spring a little and it tugs back gently; stretch it twice as far and it tugs twice as hard.
- The pull grows in exact step with how far you stretch — a beautifully simple rule.
- That rule is Hooke's law 胡克定律, and it describes springs, rubber, and many materials.
- The spring always pulls back toward its natural length — a restoring force 回复力.
拉长一倍,感到一倍的拉力
- 把弹簧稍微拉长,它轻轻回拉;拉长一倍,它就用两倍的力回拉。
- 拉力与你拉伸的距离严格同步增长——一条美妙而简单的规律。
- 这条规律就是胡克定律,它描述弹簧、橡皮以及许多材料。
- 弹簧总是把力拉回它的自然长度——一个回复力。
Hooke's law
- The spring force is proportional to the extension 伸长量 $x$ from its natural length.
- In size: $F = kx$. The constant $k$ is the spring constant 弹簧劲度系数.
- $k$ measures stiffness — a stiff spring has a large $k$ (needs more force per metre).
- Its units are $\tfrac{\text{N}}{\text{m}}$: newtons of force for each metre of stretch.
胡克定律
- 弹簧力正比于相对自然长度的伸长量 $x$。
- 大小上:$F = kx$。常数 $k$ 是弹簧常数。
- $k$ 量度劲度——劲度大的弹簧 $k$ 大(每米需要更大的力)。
- 它的单位是 $\tfrac{\text{N}}{\text{m}}$:每拉伸一米所需的牛顿力。
Stretch the spring · 拉伸弹簧
Change the force and watch the extension grow in proportion — the slope is the spring constant. · 改变力并观察伸长量成比例增长——斜率即为弹簧常数。
A spring with $k = 200\ \tfrac{\text{N}}{\text{m}}$ is stretched by $0.10\ \text{m}$. What is the spring force, in $\text{N}$? · 劲度系数为 $k = 200\ \tfrac{\text{N}}{\text{m}}$ 的弹簧被拉伸了 $0.10\ \text{m}$。弹簧力是多少，单位为 $\text{N}$？
$F = kx = 200 \times 0.10 = 20\ \text{N}$.
A force of $15\ \text{N}$ stretches a spring by $0.05\ \text{m}$. What is the spring constant, in $\tfrac{\text{N}}{\text{m}}$? · $15\ \text{N}$ 的力使弹簧伸长了 $0.05\ \text{m}$。弹簧常数是多少，单位为 $\tfrac{\text{N}}{\text{m}}$？
$k = F/x = 15 / 0.05 = 300\ \tfrac{\text{N}}{\text{m}}$.
Within the elastic limit, doubling a spring's extension changes its force to: · 在弹性限度内，将弹簧的伸长量加倍，其弹力变为：
$F = kx$ is linear, so doubling $x$ doubles $F$. · $F = kx$F=kx 是线性的，因此加倍$x$x会使$F$F加倍。
The spring constant $k$ measures a spring's ____ (how much force each metre of stretch takes). · 弹簧常数$k$k衡量弹簧的____（每米伸长所需的力）。
A large $k$ means a stiff spring — more force per metre of extension. · 较大的$k$k意味着刚度大的弹簧——每米伸长需要更多的力。
Always a restoring force
- Whichever way you deform the spring, its force points back toward equilibrium.
- Stretch it and it pulls in; compress it and it pushes out.
- That is why we write $F = -kx$ — the minus sign means "opposite to the displacement".
- This restoring behaviour is exactly what makes springs oscillate (Topic 7).
永远是回复力
- 无论你朝哪个方向使弹簧变形,它的力都指向回到平衡位置。
- 拉伸它,它往里拉;压缩它,它往外推。
- 这就是我们写成 $F = -kx$ 的原因——负号表示"与位移相反"。
- 正是这种回复行为使弹簧能够振动(主题 7)。
A stretched spring pushes in the same direction as the stretch. · 拉伸的弹簧沿与拉伸相同的方向推。
It is a restoring force, pointing back toward equilibrium — opposite to the stretch ($F = -kx$). · 它是一个恢复力，指向平衡位置方向——与拉伸方向相反（$F = -kx$F=-kx）。
The elastic limit
- Hooke's law only holds up to the spring's elastic limit 弹性极限.
- Stretch beyond it and the spring deforms permanently — the straight line bends.
- Within the limit, the spring returns to its original length when released.
- Every real spring has a range where $F = kx$ is a faithful description.
弹性极限
- 胡克定律只在弹簧的弹性极限以内成立。
- 拉伸超过它,弹簧就永久变形——那条直线开始弯曲。
- 在极限以内,弹簧松开后会回到原来的长度。
- 每根真实弹簧都有一个范围,在其中 $F = kx$ 是忠实的描述。
Select all · 所有 statements that are true about Hooke's law. · 选择所有关于胡克定律的正确陈述。
Hooke's law is linear, its slope is $k$, and the force restores. But it fails beyond the elastic limit. · 胡克定律是线性的，其斜率是$k$k，且力为恢复力。但在弹性限度之外失效。
The spring force is a restoring force: it points opposite to the stretch, not along it. And Hooke's law is only valid below the elastic limit — push a spring too far and $F = kx$ no longer holds.
弹簧力是一个回复力:它指向与拉伸相反的方向,而非沿拉伸方向。而且胡克定律只在弹性极限以下有效——把弹簧拉得太远,$F = kx$ 就不再成立。
A spring with $k = 200\ \tfrac{\text{N}}{\text{m}}$ is stretched by $x = 0.10\ \text{m}$.
- $F = kx = 200 \times 0.10 = 20\ \text{N}$.
- The spring pulls back with $20\ \text{N}$ toward its natural length.
一根 $k = 200\ \tfrac{\text{N}}{\text{m}}$ 的弹簧被拉伸 $x = 0.10\ \text{m}$。
- $F = kx = 200 \times 0.10 = 20\ \text{N}$。
- 弹簧以 $20\ \text{N}$ 朝它的自然长度回拉。
Hooke's law: a spring's force is proportional to its extension, $F = kx$ (as a restoring force, $F = -kx$). The spring constant $k$ (in $\tfrac{\text{N}}{\text{m}}$) is its stiffness — the slope of the force–extension line. It holds only below the elastic limit.
胡克定律:弹簧力正比于其伸长量,$F = kx$(作为回复力,$F = -kx$)。弹簧常数 $k$(单位 $\tfrac{\text{N}}{\text{m}}$)是它的劲度——力–伸长量直线的斜率。它只在弹性极限以下成立。