Energy, work and power
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| kinetic energy/kɪˈnetɪk ˈenədʒi/ | động năng |
| gravitational potential energy/ˌɡrævɪˈteɪʃənl pəˈtenʃl ˈenədʒi/ | thế năng hấp dẫn |
| conservation of energy/ˌkɒnsəˈveɪʃn ɒv ˈenədʒi/ | bảo toàn năng lượng |
| Sankey diagram/ˈsæŋki ˈdaɪəɡræm/ | sơ đồ Sankey |
| work done/wɜːk dʌn/ | công thực hiện |
| joule/dʒuːl/ | gioule |
| power/ˈpaʊə/ | công suất |
| efficiency/ɪˈfɪʃənsi/ | hiệu suất |
| watt/wɒt/ | watt |
Energy never disappears
- At the top of a roller-coaster hill the car is slow but high; at the bottom it is fast but low.
- The energy did not vanish — it just moved from one store to another.
- This is the big idea of this lesson: energy is stored, transferred, and always conserved.
Energy stores and transfers
- Energy can be stored as: kinetic, gravitational potential, chemical, elastic (strain), nuclear, electrostatic, and internal (thermal).
- It is transferred between stores by: forces (mechanical work), electric currents, heating, and waves (such as light and sound).
- "Using energy" really means moving it from one store to another.
Wind turbines transfer energy from moving air to electricity
Energy flow & efficiency
Input energy splits into useful output and wasted energy; efficiency is the useful fraction, and the total is always conserved.
Energy, work & power
PE + KE = constant
As an object falls, potential energy becomes kinetic — total fixed.
Select all of these that are energy stores.
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
Kinetic, chemical and gravitational potential are energy stores. "Loud" and "fast" describe things, but they are not energy stores.
Kinetic and potential energy
- Kinetic energy 动能 is the energy of a moving object:
- Lifting a mass by a height $\Delta h$ changes its gravitational potential energy 重力势能:
- A falling object turns gravitational PE into kinetic energy.
A $2.0\ \text{kg}$ ball moves at $3.0\ \text{m/s}$. What is its kinetic energy, in J?
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
$E_k = \tfrac{1}{2}mv^2 = \tfrac{1}{2} \times 2.0 \times 3.0^2 = 9.0\ \text{J}$.
Conservation of energy 能量守恒
- The principle of conservation of energy: energy is never made or destroyed — it only moves between stores.
- Some energy is always wasted — usually spread out as heat to the surroundings.
- A Sankey diagram 桑基图 shows the input energy splitting into useful energy and wasted energy.
On a roller-coaster, stored energy at the top becomes kinetic energy lower down
When a machine wastes energy, where does the wasted energy usually go?
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
Energy is conserved — it is never destroyed. Wasted energy is usually spread out as heat, which is hard to use again.
Work
- Work done 做功 equals the energy transferred. When a force moves an object along its direction:
- The unit of work and energy is the joule 焦耳 (J).
- Lifting a heavier load, or moving it further, does more work.
A swinging pendulum trades gravitational potential energy for kinetic energy and back
A force of $50\ \text{N}$ pushes a box $4.0\ \text{m}$ along the floor. How much work is done, in J?
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
$W = Fd = 50 \times 4.0 = 200\ \text{J}$.
Power 功率 and efficiency 效率
- Power is the work done (energy transferred) each second:
- The unit is the watt 瓦特 (W); $1\ \text{W} = 1\ \text{J/s}$.
- Efficiency is how much of the input energy becomes useful:
- It is always less than $100\%$ because some energy is always wasted.
A Sankey diagram: the band widths are proportional to the energy, so the input splits into useful output and wasted heat
A motor does $200\ \text{J}$ of work in $10\ \text{s}$. What is its power, in W?
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
$P = \dfrac{W}{t} = \dfrac{200}{10} = 20\ \text{W}$.
A lamp takes in $50\ \text{J}$ of electrical energy and gives out $30\ \text{J}$ of useful light. What is its efficiency, in %?
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
efficiency $= \dfrac{\text{useful}}{\text{total}} \times 100\% = \dfrac{30}{50} \times 100\% = 60\%$.
Worked examples
1. A $2.0\ \text{kg}$ box is lifted $1.5\ \text{m}$ onto a shelf in $3.0\ \text{s}$. $\Delta E_p = mg\Delta h = 2.0 \times 9.8 \times 1.5 = 29.4\ \text{J}$, and the power is $P = \dfrac{\Delta E}{t} = \dfrac{29.4}{3.0} = 9.8\ \text{W}$.
2. A lamp takes in $60\ \text{J}$ of electrical energy and gives out $12\ \text{J}$ as light. Efficiency $= \dfrac{12}{60} \times 100\% = 20\%$; the other $48\ \text{J}$ heats the surroundings.
A 4 kg ball moves at 4 metres per second. What is its kinetic energy, and by what factor does that energy change if the speed doubles?
One half of 4 times 16 is 32 joules. The square of 2 is 4, so the energy becomes four times as large.
What is the kinetic energy?
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
One half times 4 times 16 is 32 joules.
You've got it
- $E_k = \tfrac{1}{2}mv^2$ · $\Delta E_p = mg\,\Delta h$
- energy is conserved — wasted energy usually ends up as heat
- work $W = Fd$ (joule); power $P = \dfrac{W}{t}$ (watt)
- efficiency $= \dfrac{\text{useful}}{\text{total}} \times 100\%$, always below $100\%$
Write from a kinetic energy of 32 joules
- A 4 kg ball moves at 4 metres per second.
- Find the kinetic energy. Say what happens to that energy if the speed doubles.