Work and Energy for GCSE WJEC Physics | GCSE WJEC 物理：功与能量考点精讲

📚 Work and Energy for GCSE WJEC Physics | GCSE WJEC 物理：功与能量考点精讲

Work and energy are central ideas in GCSE WJEC Physics. They describe how forces cause changes and how energy is stored, transferred, and conserved. Mastering these concepts, their equations, and the ability to apply them to real-world situations is essential for exam success.

功与能量是 GCSE WJEC 物理的核心内容。它们描述力如何引起变化，以及能量如何储存、转移和守恒。掌握这些概念、相关公式以及在实际情况中应用它们的能力是考试成功的关键。

1. What is Work? | 什么是功？

Work is done whenever a force makes something move. The displacement must happen in the same direction as the force for work to be counted.

只要力使物体移动，就做了功。必须是在力的方向上发生了位移，才能算做功。

If you push a wall and it does not move, no work is done on the wall, no matter how tired you feel. In physics, work requires movement.

如果你推一面墙，它没有移动，那么无论你感到多累，都没有对墙做功。在物理学中，做功必须要有移动。

Lifting a book from the floor onto a table means you do work against gravity. The upward force moves through an upward distance.

把一本书从地上拿到桌子上，意味着你克服重力做了功。向上的力移动了向上的距离。

2. Work Done Formula and Units | 做功公式与单位

Work done is calculated as the force applied multiplied by the distance moved along the line of action of the force.

做功的计算方法是：施加的力乘以物体沿力的作用线移动的距离。

Work Done = Force × distance (W = F × d)

Force is measured in newtons (N) and distance in metres (m), so work done is measured in newton metres (N m). This unit is also called the joule (J).

力的单位是牛顿 (N)，距离的单位是米 (m)，因此功的单位是牛顿米 (N m)。这个单位也叫焦耳 (J)。

One joule is the work done when a force of 1 N moves an object 1 m in the direction of the force.

1 焦耳是当一个 1 N 的力使物体沿力的方向移动 1 米时所做的功。

3. Work and Energy Transfer | 功与能量转移

Doing work always transfers energy from one store to another. For example, when you lift a box, chemical energy in your muscles is transferred to gravitational potential energy in the box.

做功总是把能量从一个储存库转移到另一个储存库。例如，当你提起一个箱子时，肌肉中的化学能就转移为箱子的重力势能。

If a force does work against friction, energy is dissipated as thermal energy, heating up the surfaces.

如果力克服摩擦力做功，能量会以热能的形式消散，使接触面温度升高。

The amount of work done is equal to the amount of energy transferred. This is why joules are used for both work and energy.

做功的量等于转移的能量。这就是焦耳同时用于功和能量的原因。

4. Kinetic Energy | 动能

Any moving object possesses kinetic energy. The faster it moves and the greater its mass, the more kinetic energy it has.

任何运动的物体都具有动能。它运动得越快、质量越大，具有的动能就越多。

Kinetic Energy (Eₖ) = ½ m v²

where m is mass in kilograms (kg) and v is speed in metres per second (m/s). The unit of kinetic energy is the joule (J).

其中 m 是物体质量，单位为千克 (kg)；v 是速度，单位为米每秒 (m/s)。动能单位是焦耳 (J)。

Work done to accelerate an object is equal to the gain in its kinetic energy, assuming no energy losses.

在没有能量损失的情况下，使物体加速所做的功等于它增加的动能。

5. Gravitational Potential Energy | 重力势能

An object lifted against gravity stores energy called gravitational potential energy (GPE). The higher it is, the more GPE it gains.

被提起克服重力做功的物体储存的能量叫做重力势能 (GPE)。它升得越高，获得的 GPE 就越多。

Change in GPE (ΔEₚ) = m × g × Δh

m is mass (kg), g is gravitational field strength (9.8 N/kg on Earth, often rounded to 10 N/kg for GCSE), and Δh is the change in height in metres (m).

m 是质量 (kg)，g 是重力场强度（地球上取 9.8 N/kg，GCSE 考试中常四舍五入为 10 N/kg），Δh 是高度的变化 (m)。

When an object falls freely, its GPE is converted into kinetic energy. The work done by gravity equals the loss of GPE.

物体自由下落时，重力势能转化为动能。重力做的功等于重力势能的减少量。

6. Conservation of Energy and Work | 能量守恒与功

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another.

能量守恒定律指出，能量不能被创造或消灭，只能被转移或从一种形式转化为另一种形式。

In a swinging pendulum, GPE at the highest point is converted to kinetic energy at the lowest point. Work done by tension and gravity facilitates these transfers.

在摆动的单摆中，最高点的重力势能转化为最低点的动能。绳的张力和重力所做的功促成了这些转移。

In real systems, some work is always done against friction or air resistance, meaning total useful energy output is less than energy input.

在真实的系统中，总有一部分功用于克服摩擦或空气阻力，这意味着有用的总能量输出小于能量输入。

7. Power: Rate of Doing Work | 功率：做功的速率

Power is defined as the rate at which work is done or the rate at which energy is transferred.

功率定义为做功的速率，或能量转移的速率。

Power (P) = Work Done (W) ÷ time (t)

This can also be written as P = E / t where E is energy transferred. The unit of power is the watt (W), equivalent to joules per second (J/s).

这也可以写成 P = E / t，其中 E 是转移的能量。功率的单位是瓦特 (W)，等同于焦耳每秒 (J/s)。

A more powerful motor can do the same amount of work in less time, or more work in the same time.

功率更大的马达可以在更短的时间内做同样的功，或在同样的时间内做更多的功。

8. Efficiency in Energy Transfers | 能量转移中的效率

Efficiency describes how much of the input energy is converted into useful output energy. No device is 100% efficient because some energy is always lost, typically as heat.

效率描述输入能量中有多少转化为有用的输出能量。没有设备是 100% 高效的，因为总是有一部分能量损失，通常以热量形式散失。

Efficiency = (Useful energy output ÷ Total energy input) × 100%

You can also use power instead of energy: Efficiency = (Useful power output ÷ Total power input) × 100%.

你也可以用功率代替能量：效率 = (有用输出功率 ÷ 总输入功率) × 100%。

Improving efficiency reduces wasted energy and can involve lubrication to reduce friction or streamlining to reduce drag.

提高效率可以减少浪费的能量，这可以通过润滑来减少摩擦，或通过流线型设计来减少空气阻力。

9. Sankey Diagrams | 桑基图

A Sankey diagram is a visual representation of energy transfers. The width of each arrow represents the amount of energy.

桑基图是能量转移的可视化表示。每条箭头的宽度代表能量的多少。

Input energy is shown by an arrow entering from the left. This splits into useful energy (arrow continuing straight) and wasted energy (arrow branching downwards or sideways).

输入能量用左侧进入的箭头表示。它分叉为有用能量（箭头继续直行）和浪费能量（箭头向下或向侧边分支）。

The total width before the split equals the total width after the split, reflecting the conservation of energy.

分叉前箭头的总宽度等于分叉后箭头的总宽度，这反映了能量守恒。

Exam questions often ask you to interpret a Sankey diagram or to calculate efficiency from the widths given in mm or as proportions.

考试题目常要求你解读桑基图，或根据给出的宽度（以毫米或比例表示）计算出效率。

10. Practical: Investigating Work Done | 实验：研究做功

A common practical involves pulling a wooden block or trolley along a horizontal surface using a forcemeter (newton meter).

常见的实验包括使用弹簧测力计（牛顿计）水平拉动木块或小车。

Measure the steady force needed to pull the object at a constant speed. Record the distance the object moves while this force is applied.

测量使物体匀速运动时所需的恒定拉力。记录施加这个拉力时物体移动的距离。

Calculate work done using W = F × d. Repeat for different surfaces or masses to see how work changes with friction or weight.

使用公式 W = F × d 计算做功。在不同表面或不同质量下重复实验，观察功如何随摩擦力或重量变化。

You can also investigate work done against gravity by lifting masses vertically and calculating the gain in gravitational potential energy.

你也可以通过垂直提起重物并计算增加的重力势能，来研究克服重力所做的功。

11. Common Mistakes and Exam Tips | 常见错误与考试技巧

Do not confuse force, work, and power. Force is a push or pull, work is force × distance, and power is work ÷ time.

不要混淆力、功和功率。力是推或拉，功是力乘以距离，功率是功除以时间。

When using W = F d, the distance must be along the same line as the force. If a trolley is pushed at an angle, use only the horizontal component of the force.

使用 W = F d 时，距离必须与力沿同一直线。如果以一个角度推小车，只应使用力的水平分量。

Always convert units to SI: mass in kg, distance in m, speed in m/s, time in s. Resulting energies and work will be in joules.

始终将单位转换为国际单位：质量用 kg，距离用 m，速度用 m/s，时间用 s。得出的能量和功将是焦耳。

When using g = 10 N/kg, check the question. WJEC often states whether to use 9.8 or 10; if in doubt, use 10 and show your working clearly.

当使用 g = 10 N/kg 时，要看清题目要求。WJEC 通常会指明使用 9.8 还是 10；如果不确定，使用 10 并清晰地展示计算过程。

Efficiency has no unit and is either a decimal (0.2) or a percentage (20%). Do not mix the two.

效率没有单位，可以是小数（0.2）或百分比（20%）。不要将两者混用。

12. Summary of Key Equations | 关键公式总结

Quantity \| 物理量	Equation \| 公式	Units \| 单位
Work done (W) 功	W = F × d	joule (J)
Kinetic energy (Eₖ) 动能	Eₖ = ½ m v²	joule (J)
Change in GPE (ΔEₚ) 重力势能变化量	ΔEₚ = m g Δh	joule (J)
Power (P) 功率	P = W / t or P = E / t	watt (W)
Efficiency 效率	(Useful output ÷ Total input) × 100%	no unit / 无单位

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Work and Energy for GCSE WJEC Physics | GCSE WJEC 物理：功与能量 考点精讲