Forces, Newton's laws and moments · 力、牛顿定律与力矩
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| force/fɔːs/ | 力 | lì |
| friction/ˈfrɪkʃn/ | 摩擦力 | mó cā lì |
| extension/ekˈstenʃn/ | 伸长量 | shēn cháng liàng |
| limit of proportionality/ˈlɪmɪt ɒv prəˌpɔːʃəˈnælɪti/ | 比例极限 | bǐ lì jí xiàn |
| spring constant/sprɪŋ ˈkɒnstənt/ | 弹簧常数 | tán huáng cháng shù |
| resultant force/rɪˈzʌltənt fɔːs/ | 合力 | hé lì |
| drag/dræɡ/ | 阻力 | zǔ lì |
| moment/ˈməʊmənt/ | 力矩 | lì jǔ |
| pivot/ˈpɪvət/ | 支点 | zhī diǎn |
| equilibrium/ˌiːkwɪˈlɪbrɪəm/ | 平衡 | píng héng |
| centre of gravity/ˈsentə ɒv ˈɡrævɪti/ | 重心 | zhòng xīn |
Pushes and pulls
- A force 力 is a push or a pull.
- A force can change an object's shape, its speed, or its direction.
- This lesson covers stretching, Newton's laws, friction 摩擦力, turning effects, and balance.
推和拉
- 一个力(force)是一个推或一个拉。
- 一个力能改变一个物体的形状、它的速率,或它的方向。
- 这节课涵盖拉伸、牛顿定律、摩擦、转动效应和平衡。
Stretching: Hooke's law
- Hang a load on a spring and it stretches. The stretch is the extension 伸长量.
- On a load–extension graph the line is straight at first: extension is proportional to load.
- The point where it stops being straight is the limit of proportionality 比例极限.
- The spring constant 弹簧常数 is the force per unit extension:
- A large $k$ means a stiff spring.
拉伸:胡克定律
- 在一个弹簧上挂一个负载,它就拉伸。这个拉伸是伸长(extension)。
- 在一张负载–伸长图上,线起初是直的:伸长与负载成正比。
- 它停止变直的点是比例极限(limit of proportionality)。
- 弹簧常数(spring constant)是每单位伸长的力:
- 一个大的 $k$ 意味着一个硬的弹簧。
Forces & Newton's laws · 力与牛顿定律
F = ma (resultant) · F = ma(合力)
The resultant force sets the acceleration; balanced forces ⇒ none. · 合力决定加速度;平衡的力 ⇒ 没有加速度。
A force of $8.0\ \text{N}$ stretches a spring by $0.040\ \text{m}$ (within the limit of proportionality). What is the spring constant, in N/m? · 一个 $8.0\ \text{N}$ 的力把一个弹簧拉伸 $0.040\ \text{m}$(在比例极限内)。弹簧常数是多少,以 N/m 计?
$k = \dfrac{F}{x} = \dfrac{8.0}{0.040} = 200\ \text{N/m}$. · $k = \dfrac{F}{x} = \dfrac{8.0}{0.040} = 200\ \text{N/m}$。
Resultant force 合力 and Newton's laws
- Add forces along a line to get the resultant force (one way positive, the other negative).
- If the resultant force is zero: the object stays at rest, or keeps moving at constant velocity (Newton's first law).
- If the resultant force is not zero: the object accelerates in the direction of the force:
- Every force comes in a pair: if A pushes B, then B pushes back on A with an equal, opposite force (Newton's third law).
合力与牛顿定律
- 沿一条线相加力以得到合力(resultant force,一个方向为正,另一个为负)。
- 如果合力为零:物体保持静止,或以恒定速度持续运动(牛顿第一定律)。
- 如果合力不为零:物体在力的方向上加速:
- 每个力成对出现:如果 A 推 B,那么 B 以一个相等、相反的力推回 A(牛顿第三定律)。
The resultant force on a moving car is zero. What does the car do? · 一辆运动的车上的合力为零。车会怎样?
Newton's first law: with zero resultant force, an object keeps moving at constant velocity (or stays at rest). · 牛顿第一定律:在合力为零时,一个物体以恒定速度持续运动(或保持静止)。
A resultant force of $6.0\ \text{N}$ acts on a $2.0\ \text{kg}$ trolley. What is its acceleration, in m/s²? · 一个 $6.0\ \text{N}$ 的合力作用在一个 $2.0\ \text{kg}$ 的小车上。它的加速度是多少,以 m/s² 计?
$F = ma$, so $a = \dfrac{F}{m} = \dfrac{6.0}{2.0} = 3.0\ \text{m/s}^2$. · $F = ma$,所以 $a = \dfrac{F}{m} = \dfrac{6.0}{2.0} = 3.0\ \text{m/s}^2$。
Friction
- Friction is the force between two surfaces that touch.
- It always acts against the motion, and it makes surfaces heat up.
- Drag 阻力 (friction in a liquid or gas, like air resistance) slows objects down in the same way.
The four forces on a box pushed along the ground
摩擦
- 摩擦(friction)是接触的两个表面之间的力。
- 它总是对抗运动作用,并使表面变热。
- 阻力(drag,液体或气体中的摩擦,如空气阻力)以相同的方式减慢物体。
被沿地面推的一个盒子上的四个力
Moments 力矩 — the turning effect
- The moment of a force is its turning effect about a pivot 支点:
- The unit is the newton metre (N m).
- Principle of moments: when something is balanced, total clockwise moment = total anticlockwise moment.
- An object is in equilibrium 平衡 when there is no resultant force and no resultant moment.
力矩——转动效应
- 一个力的力矩(moment)是它绕一个支点(pivot)的转动效应:
- 单位是牛顿米(N m)。
- 力矩原理(principle of moments):当某物平衡时,总顺时针力矩 = 总逆时针力矩。
- 当没有合力且没有合力矩时,一个物体处于平衡(equilibrium)。
A spanner is pushed with $20\ \text{N}$ at a perpendicular distance of $0.50\ \text{m}$ from the bolt. What is the moment, in N m? · 一个扳手以 $20\ \text{N}$ 在离螺栓 $0.50\ \text{m}$ 的垂直距离被推。力矩是多少,以 N m 计?
moment = force × perpendicular distance = $20 \times 0.50 = 10\ \text{N m}$. · 力矩 = 力 × 垂直距离 = $20 \times 0.50 = 10\ \text{N m}$。
A see-saw balances. On the left, a $30\ \text{N}$ weight sits $0.20\ \text{m}$ from the pivot. On the right, a weight sits $0.60\ \text{m}$ from the pivot. What is the right-hand weight, in N? · 一个跷跷板平衡。在左边,一个 $30\ \text{N}$ 的重物坐在离支点 $0.20\ \text{m}$ 处。在右边,一个重物坐在离支点 $0.60\ \text{m}$ 处。右边的重物是多少,以 N 计?
Balanced ⇒ clockwise = anticlockwise: $30 \times 0.20 = F \times 0.60$, so $F = \dfrac{6.0}{0.60} = 10\ \text{N}$. · 平衡 ⇒ 顺时针 = 逆时针:$30 \times 0.20 = F \times 0.60$,所以 $F = \dfrac{6.0}{0.60} = 10\ \text{N}$。
Match each idea to what it says. · 把每个想法与它说的内容配对。
Each item links the term to its correct meaning. · 每一项把术语与它正确的含义联系。
Centre of gravity 重心 and stability
- The centre of gravity is the single point where all the weight seems to act.
- An object is more stable when its centre of gravity is low and its base is wide.
- It tips over when the centre of gravity passes outside the base.
重心与稳定性
- 重心(centre of gravity)是所有重量似乎作用的那个单一的点。
- 当一个物体的重心低且它的底座宽时,它更稳定。
- 当重心越过底座之外时,它翻倒。
Which object is the most stable (hardest to tip over)? · 哪个物体最稳定(最难翻倒)?
A low centre of gravity and a wide base make an object stable. The tall, thin shapes tip over easily. · 一个低的重心和一个宽的底座使一个物体稳定。高、瘦的形状容易翻倒。
You've got it
- spring constant $k = \dfrac{F}{x}$, straight up to the limit of proportionality
- resultant zero → constant velocity; resultant force $F = ma$
- moment = force × perpendicular distance; balanced ⇒ clockwise = anticlockwise moments
- stable = low centre of gravity + wide base
你掌握了
- 弹簧常数 $k = \dfrac{F}{x}$,直到比例极限都是直的
- 合力为零 → 恒定速度;合力 $F = ma$
- 力矩 = 力 × 垂直距离;平衡 ⇒ 顺时针 = 逆时针力矩
- 稳定 = 低重心 + 宽底座