Forces, Newton's laws and moments
Введено| English | Значение |
|---|---|
| force/fɔːs/ | сила |
| friction/ˈfrɪkʃn/ | трение |
| extension/ekˈstenʃn/ | удлинение |
| limit of proportionality/ˈlɪmɪt ɒv prəˌpɔːʃəˈnælɪti/ | предел пропорциональности |
| spring constant/sprɪŋ ˈkɒnstənt/ | жесткость пружины |
| resultant force/rɪˈzʌltənt fɔːs/ | равнодействующая сила |
| drag/dræɡ/ | сопротивление среды |
| moment/ˈməʊmənt/ | момент силы |
| pivot/ˈpɪvət/ | точка опоры |
| equilibrium/ˌiːkwɪˈlɪbrɪəm/ | равновесие |
| centre of gravity/ˈsentə ɒv ˈɡrævɪti/ | центр тяжести |
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.
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.
Forces & Newton's laws
F = ma (resultant)
The resultant force sets the acceleration; balanced forces ⇒ none.
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?
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
$k = \dfrac{F}{x} = \dfrac{8.0}{0.040} = 200\ \text{N/m}$.
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).
The resultant force on a moving car is zero. What does the car do?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Newton's first law: with zero resultant force, an object keeps moving at constant velocity (or stays at rest).
A resultant force of $6.0\ \text{N}$ acts on a $2.0\ \text{kg}$ trolley. What is its acceleration, in m/s²?
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
$F = ma$, so $a = \dfrac{F}{m} = \dfrac{6.0}{2.0} = 3.0\ \text{m/s}^2$.
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
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.
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?
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
moment = force × perpendicular distance = $20 \times 0.50 = 10\ \text{N m}$.
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?
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Balanced ⇒ clockwise = anticlockwise: $30 \times 0.20 = F \times 0.60$, so $F = \dfrac{6.0}{0.60} = 10\ \text{N}$.
Match each idea to what it says.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Each item links the term to its correct meaning.
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.
Which object is the most stable (hardest to tip over)?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
A low centre of gravity and a wide base make an object stable. The tall, thin shapes tip over easily.
Worked examples
1. A $1200\ \text{kg}$ car has a driving force of $3000\ \text{N}$ and friction of $600\ \text{N}$. Resultant force $= 3000 - 600 = 2400\ \text{N}$, so $a = \dfrac{F}{m} = \dfrac{2400}{1200} = 2.0\ \text{m/s}^2$.
2. A child of weight $400\ \text{N}$ sits $1.5\ \text{m}$ from the pivot of a see-saw. For balance, the clockwise and anticlockwise moments are equal: $400 \times 1.5 = F \times 2.0$, so a child $2.0\ \text{m}$ away must weigh $F = 300\ \text{N}$.
A force of 9.0 N stretches a spring by 0.030 m, within the straight-line region. What is the spring constant, and what motion follows from a zero resultant force?
9.0 divided by 0.030 is 300. Zero resultant force does not require the object to be stopped.
What is the spring constant?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
9.0 divided by 0.030 is 300 newtons per metre.
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
Write from a spring constant of 300 newtons per metre
- A force of 9.0 N stretches a spring by 0.030 m, inside the limit of proportionality.
- Find the spring constant. Say what a zero resultant force means.