3.2 · Energy

牛津国际 AQA · International GCSE · 物理 · 知识点 2

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Energy: the accountant of physics

Nothing destroys energy — it is only moved between stores and partly dissipated into less useful forms. OxfordAQA's second topic builds the accounting: work and power, the three energy-store equations, conservation with Sankey diagrams, and the choices behind national energy resources.

OxfordAQA International GCSE Physics 9203, topic 3.2 (Version 5.1). Statements marked (P) are Paper-2-only.

Forces and energy

$$W = F \times d \qquad E_e = \tfrac{1}{2}ke^2 \qquad E_p = mgh \qquad E_k = \tfrac{1}{2}mv^2 \qquad P = \frac{E}{t}$$

Work 功 is done when a force moves its point of application through a distance; work against friction transfers energy by heating (shuttle re-entry, meteorites, brakes). A stretched spring stores elastic potential energy $\frac{1}{2}ke^2$; a raised mass stores gravitational potential energy mgh; a moving mass carries kinetic energy ½mv² — doubling mass doubles it, doubling speed quadruples it (the road-safety link). Power 功率 is the rate of energy transfer.

Worked check. A 1500 kg car at 20 m/s brakes to rest: KE removed $= \frac{1}{2} \times 1500 \times 400 = 300\,000$ J — all transferred to heating the brakes. Lifting it 2 m at g = 10 N/kg stores $1500 \times 10 \times 2 = 30\,000$ J.

Energy transfers and dissipation

Energy stores on top, transfer pathways below; a system change moves energy between stores.

When a system changes, energy is transferred — usefully, stored, or dissipated 耗散 ("wasted") into less useful stores; it is never created or destroyed. Friction and air resistance dissipate energy by heating. (P) A pendulum swaps kinetic and gravitational potential energy each swing.

A pendulum: all GPE at the top of each swing, all KE at the bottom.

$$\text{efficiency} = \frac{\text{useful energy out}}{\text{total energy in}} \times 100\% \ (=\frac{\text{useful power out}}{\text{total power in}})$$

Sankey diagrams show the redistribution: arrows split in proportion to the energy flows (draw them to scale — width ∝ energy).

Worked check. A 60 W lamp gives 6 W of light: efficiency 效率 $= 6/60 \times 100 = 10\%$.

Energy resources

Fuels are chosen for ease of storage, energy content and safety; some transfer more of their energy usefully than others. National generation trades renewability against cost, reliability and the environmental cost of extraction, use and disposal.

Four renewable technologies with one advantage and one drawback each.

Check yourself

Calculate the work done by a 50 N force moving 4 m.
Calculate the elastic energy in a spring (k = 200 N/m) stretched 0.15 m.
A 2 kg book is lifted 3 m at g = 10 N/kg. Calculate the GPE gained.
What happens to the kinetic energy of a car when it brakes?
A motor transfers 800 J in 20 s. Calculate its power.
State the efficiency equation in energy and power forms.
A lamp gives out 12 J of light for every 100 J in. Calculate the efficiency.
What does a Sankey diagram's arrow width show?
Give one advantage and one drawback of wind power.
What does "dissipated" mean?

Answers: 1 $W = 50 \times 4 = 200$ J; 2 $E_e = \frac{1}{2} \times 200 \times 0.0225 = 2.25$ J; 3 $E_p = 2 \times 10 \times 3 = 60$ J; 4 it is transferred to thermal energy of the brakes and surroundings by the friction force (the brakes heat up); 5 $P = 800/20 = 40$ W; 6 useful energy out ÷ total energy in (×100 %); equally useful power out ÷ total power in; 7 $12/100 \times 100 = 12\%$; 8 the energy flowing in that direction — width is proportional to energy; 9 renewable with no fuel or emissions; unreliable output with visual impact; 10 transferred to less useful stores (often waste heat), so it cannot readily do what we want.

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