Work and Energy | IGCSE OCR 物理：功与能量考点精讲

📚 Work and Energy | IGCSE OCR 物理：功与能量考点精讲

Work and energy are foundational concepts in IGCSE OCR Physics, linking forces, motion, and the transfer of energy between different stores. Understanding how to calculate work done, kinetic energy, and gravitational potential energy is essential for solving real‑world problems and achieving top marks in the exam. This article covers all the key points you need, with clear definitions, equations, and practical examples.

功与能量是 IGCSE OCR 物理的基础概念，它把力、运动和能量在不同形式之间的传递联系在一起。理解如何计算做功、动能和重力势能，对于解决实际问题和在考试中取得高分至关重要。本文将涵盖你需要的所有关键知识点，包括清晰的定义、方程和实际例子。

1. Definition of Work | 功的定义

In physics, work is done when a force causes an object to move in the direction of the force. If there is no movement, no work is done, even if a force is applied. Work is a scalar quantity measured in joules (J).

在物理学中，当一个力使物体沿力的方向移动时，就做了功。如果没有移动，即使施加了力，也没有做功。功是一个标量，单位为焦耳 (J)。

The formula connects force, distance, and work: a force of one newton moving an object through one metre does one joule of work.

公式将力、距离与功联系起来：1 牛顿的力使物体移动 1 米，所做的功为 1 焦耳。

Work done (J) = Force (N) × distance moved in the direction of the force (m)
做功 (J) = 力 (N) × 物体沿力的方向移动的距离 (m)

2. Calculating Work Done | 计算做功

The equation W = F × d applies only when the force is constant and parallel to the direction of motion. If the force is at an angle, only the component of the force in the direction of motion contributes to the work done.

方程 W = F × d 仅当力恒定且与运动方向平行时适用。如果力存在角度，只有沿运动方向的分力才会对做功有贡献。

For example, lifting a 2 kg book vertically by 0.5 m: weight = 2 kg × 10 N/kg = 20 N, so work done = 20 N × 0.5 m = 10 J. The energy transferred to the book’s gravitational store is also 10 J.

例如，将一本 2 kg 的书竖直提升 0.5 m：重量 = 2 kg × 10 N/kg = 20 N，因此做功 = 20 N × 0.5 m = 10 J。转移到书的重力势能储存中的能量也是 10 J。

When a person pushes a wall but the wall does not move, no work is done on the wall, although chemical energy in the person’s muscles is still converted to heat.

当人推墙但墙没有移动时，人对墙没有做功，尽管肌肉中的化学能仍然转化为热能。

3. Energy – The Capacity to Do Work | 能量——做功的能力

Energy is defined as the ability to do work. It is a scalar quantity, measured in joules, and can exist in many forms: kinetic, gravitational potential, elastic potential, thermal, chemical, nuclear, etc. Energy can be transferred between stores, but it is never created or destroyed.

能量被定义为做功的能力。它是一个标量，单位为焦耳，可以多种形式存在：动能、重力势能、弹性势能、热能、化学能、核能等。能量可以在储存之间传递，但绝不会被创造或消灭。

In IGCSE problems, you will usually consider energy transfers between gravitational potential energy and kinetic energy, often ignoring friction to simplify calculations.

在 IGCSE 题目中，你通常会考虑重力势能和动能之间的能量转移，常常忽略摩擦以简化计算。

4. Gravitational Potential Energy | 重力势能

Gravitational potential energy (E_p or GPE) is the energy stored in an object because of its height above the ground. The higher the object, the greater its GPE.

重力势能 (E_p 或 GPE) 是由于物体离地高度而储存的能量。物体位置越高，它的重力势能越大。

The change in GPE when lifting an object is given by:

提升物体时重力势能的变化由下式给出：

ΔE_p = m × g × Δh

m = mass (kg)
g = gravitational field strength (N/kg, on Earth ~9.8 N/kg, often rounded to 10 N/kg in exams)
Δh = change in height (m)
m = 质量 (kg)
g = 重力场强度 (N/kg，地球表面约 9.8 N/kg，考试中常取 10 N/kg)
Δh = 高度变化 (m)

For a 5 kg mass raised by 3 m, the gain in GPE = 5 × 10 × 3 = 150 J. This equals the work done against gravity, assuming no other forces.

对于 5 kg 的物体被升高 3 m，重力势能的增加 = 5 × 10 × 3 = 150 J。这等于克服重力所做的功，假设没有其他力。

5. Kinetic Energy | 动能

Kinetic energy (E_k or KE) is the energy possessed by an object due to its motion. The faster an object moves, the more kinetic energy it has.

动能 (E_k 或 KE) 是物体由于运动而具有的能量。物体运动越快，它的动能就越大。

The kinetic energy of a moving object is:

运动物体的动能为：

E_k = ½ × m × v²

m = mass (kg)
v = speed (m/s)
m = 质量 (kg)
v = 速度 (m/s)

Notice that kinetic energy depends on the square of the speed. Doubling the speed quadruples the kinetic energy, which is why high‑speed collisions cause much more damage.

注意，动能与速度的平方成正比。速度加倍会使动能变为原来的四倍，这就是为什么高速碰撞会造成更大损坏的原因。

Example: a car of mass 800 kg moving at 15 m/s has E_k = ½ × 800 × (15)² = ½ × 800 × 225 = 90,000 J.

例子：一辆质量为 800 kg 的汽车以 15 m/s 的速度行驶，其动能 E_k = ½ × 800 × (15)² = ½ × 800 × 225 = 90,000 J。

6. Conservation of Energy | 能量守恒

The law of conservation of energy states that energy can be transferred usefully, stored, or dissipated, but it cannot be created or destroyed. In a closed system, the total energy remains constant.

能量守恒定律指出，能量可以被有用转移、储存或耗散，但不能被创造或消灭。在一个封闭系统中，总能量保持不变。

This principle allows you to relate changes in GPE to changes in KE, especially when an object falls or a pendulum swings (ignoring air resistance).

这个原理允许你将重力势能的变化与动能的变化联系起来，尤其是在物体下落或摆锤摆动时（忽略空气阻力）。

For a falling object: loss in GPE = gain in KE, so m g Δh = ½ m v². Mass cancels, giving v = √(2 g Δh).

对于下落的物体：减少的重力势能 = 增加的动能，因此 m g Δh = ½ m v²。质量可以消掉，得到 v = √(2 g Δh)。

Energy store	Change	Common transfers
GPE	Decreases	Converted to KE as object falls
KE	Increases	From loss in GPE or work done by a force
Thermal	Increases	Due to friction/air resistance dissipating energy

能量储存	变化	常见转移
重力势能	减少	物体下落时转化为动能
动能	增加	来自重力势能的损失或力做的功
热能	增加	因摩擦/空气阻力耗散能量

7. Work–Energy Principle | 功-能原理

The work–energy principle states that the work done on an object by a resultant force is equal to the change in its kinetic energy. This connects the concepts of work and energy directly.

功-能原理指出，合力对物体所做的功等于其动能的变化量。这直接将功与能量的概念联系了起来。

Mathematically: net work done = ΔE_k = E_k,final – E_k,initial. This is particularly useful when a force acts over a distance to change speed.

数学上：净做功 = ΔE_k = E_k,末 – E_k,初。当力作用一段距离改变速度时，这一点特别有用。

For a braking car, the work done by the friction force of the brakes reduces the kinetic energy, converting it to thermal energy in the brake pads and tyres. The braking distance can be estimated using: F × d = ½ m v², where F is the braking force.

对于制动的汽车，刹车摩擦力所做的功减少了动能，将其转化为刹车片和轮胎中的热能。制动距离可以用 F × d = ½ m v² 估算，其中 F 是制动力。

8. Power | 功率

Power is the rate at which work is done or energy is transferred. It measures how quickly energy is transformed from one form to another.

功率是做功或能量转移的速率。它衡量能量从一种形式转变为另一种形式的快慢。

The two main equations for power are:

功率的两个主要公式是：

P = W / t or P = E / t

P = power (W, watts)
W = work done (J)
E = energy transferred (J)
t = time taken (s)
P = 功率 (W，瓦特)
W = 所做的功 (J)
E = 转移的能量 (J)
t = 所用时间 (s)

For a motor lifting a 200 N weight through 5 m in 4 seconds, work done = 200 N × 5 m = 1000 J. Power = 1000 J / 4 s = 250 W.

对于一台在 4 秒内将 200 N 重物提升 5 m 的电动机，做功 = 200 N × 5 m = 1000 J。功率 = 1000 J / 4 s = 250 W。

Another useful form links power, force, and velocity: when a constant force moves an object at constant speed, P = F × v.

另一个有用的形式将功率、力和速度联系起来：当恒力以恒定速度移动物体时，P = F × v。

9. Efficiency | 效率

Efficiency describes how much of the input energy is converted to useful output energy. No device is 100% efficient because some energy is always dissipated as heat due to friction, air resistance, or electrical resistance.

效率描述了输入能量中有多少转化为有用的输出能量。没有任何设备是 100% 高效的，因为总有一些能量会因摩擦、空气阻力或电阻而以热的形式耗散。

Efficiency can be calculated using energy or power:

效率可以用能量或功率计算：

Efficiency = (useful output energy / total input energy) × 100%

Efficiency = (useful power output / total power input) × 100%

For an LED lamp, if 12 J of electrical energy is supplied and 8 J is transferred as light, the efficiency = (8 J / 12 J) × 100% ≈ 67%. The remaining 4 J is dissipated as heat.

对于一个 LED 灯，如果提供 12 J 的电能，其中 8 J 转化为光能，则效率 = (8 J / 12 J) × 100% ≈ 67%。剩下的 4 J 以热的形式耗散。

Sankey diagrams are a common way to represent energy transfers and efficiency visually. The width of the arrows is proportional to the amount of energy. In IGCSE, you may be asked to calculate efficiency from such diagrams.

桑基图是直观表示能量转移和效率的常用方法。箭头的宽度与能量大小成正比。在 IGCSE 考试中，你可能会被要求根据此图计算效率。

10. Real‑World Examples and Exam Tips | 实际例子与应试技巧

Apply the equations to everyday situations: a roller coaster (GPE to KE), a bouncing ball (energy lost to thermal/store), a person running up stairs (work done = gain in GPE, power = work/time), and a wind turbine (kinetic energy of wind → electrical energy).

将方程应用于日常情况：过山车（重力势能转为动能）、弹跳的球（能量损耗为热能）、人跑上楼梯（做功 = 增加的重力势能，功率 = 功/时间）以及风力发电机（风的动能 → 电能）。

Exam tip: always convert units to SI before substituting into formulas – mass in kg, distance in m, time in s. When using the KE equation, remember to square the speed before multiplying by half the mass.

应试技巧：在代入公式前始终将单位转换为国际单位制——质量用 kg，距离用 m，时间用 s。使用动能方程时，记住先将速度平方，再乘以质量的一半。

A common pitfall is confusing mass and weight, or forgetting that work depends on the distance moved in the direction of the force, not the total distance travelled. Practice past paper questions to become confident in selecting the correct equation and rearranging it.

常见的误区是混淆质量与重量，或者忘记功取决于沿力的方向移动的距离，而非总路程。通过练习历年真题，熟练选择正确的方程并进行变形。

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Work and Energy | IGCSE OCR 物理：功与能量 考点精讲