📚 Cambridge Checkpoint Science Video: Gravity | 剑桥 Checkpoint 科学视频课：重力
Gravity is one of the first "big ideas" that Cambridge Checkpoint Science students meet, and it is also one of the ideas that video lessons explain best. A short animation can show a ball falling, a parachute opening and a satellite circling the Earth in ways that a static textbook diagram cannot. This guide follows the structure of a typical Checkpoint gravity video lesson and turns it into a written revision resource you can read, pause over and test yourself against.
重力是剑桥 Checkpoint 科学学生最早接触的"大概念"之一，也是最适合用视频讲解的内容之一。一段短动画可以直观呈现小球下落、降落伞张开、卫星绕地球运行的过程，这是静态课本插图做不到的。本文按照一堂典型 Checkpoint 重力视频课的结构展开，把视频内容转化为可以阅读、可以暂停思考、也可以自测的书面复习资料。
1. What Gravity Actually Is | 重力到底是什么
Gravity is a non-contact force of attraction between any two objects that have mass. It acts at a distance, so no touching is needed. In the classroom we usually talk about the Earth pulling objects towards its centre, but the same force exists between you and your pencil - it is simply far too small to notice.
重力是任何两个有质量的物体之间的非接触吸引力。它可以远距离作用，不需要接触。课堂上我们通常讨论地球把物体拉向地心，但你和铅笔之间也存在同样的力——只是小到无法察觉。
The strength of the gravitational attraction between two objects depends on two things only: the masses of the objects, and the distance between their centres. The bigger the masses, the stronger the pull; the greater the distance, the weaker the pull. This is why the Earth pulls you strongly while you pull the Earth only immeasurably.
两个物体之间引力的大小只取决于两件事：两个物体的质量，以及它们中心之间的距离。质量越大，引力越强；距离越大，引力越弱。这就是为什么地球对你的拉力很强，而你对地球的拉力微乎其微。
For a deeper (extension) view, Newton's law of universal gravitation is written as:
F = G × m₁ × m₂ ÷ r²
s the gravitational constant, about 6.67 × 10⁻¹¹ N m² kg⁻². At Checkpoint level you are not expected to calculate with G, but you should be able to describe the relationship in words.
其中 F 是引力，单位牛顿（N）；m₁ 和 m₂ 是两个物体的质量，单位千克（kg）；r 是两中心间的距离，单位米（m）；G 是引力常量，约为 6.67 × 10⁻¹¹ N m² kg⁻²。Checkpoint 阶段不需要用 G 计算，但你必须能用文字描述这层关系。
2. Mass vs Weight: The Most Tested Distinction | 质量与重量：最常考的区分
Mass is the amount of matter in an object. It is measured in kilograms (kg) and it does not change when you move the object to another planet, to the top of a mountain or into orbit. Mass is a scalar quantity - it has size but no direction.
质量是物体所含物质的多少，用千克（kg）测量，把物体移到别的行星、山顶或轨道上都不会改变。质量是标量——只有大小，没有方向。
Weight is the force of gravity acting on that mass. It is measured in newtons (N) with a newton meter, and it does change from place to place because the gravitational field strength changes. Weight is a force, so it is a vector quantity and always acts towards the centre of the planet.
重量是作用在该质量上的重力，用弹簧测力计测量，单位牛顿（N）。因为重力场强度会变化，所以重量在不同地方会改变。重量是一种力，因此是矢量，方向始终指向星球中心。
Gravitational field strength, g, is defined as the force per unit mass. That gives the key equation used in almost every Checkpoint gravity question:
W = m × g
ogram (N/kg). On Earth, g ≈ 9.8 N/kg, often rounded to 10 N/kg in Checkpoint calculations.
W 是重量（N），m 是质量（kg），g 是重力场强度，单位 N/kg。地球表面 g ≈ 9.8 N/kg，在 Checkpoint 计算中常取 10 N/kg。
- Mass: kg, balance, same everywhere. | 质量：千克，用天平测，处处相同。
- Weight: N, newton meter, changes with g. | 重量：牛顿，用弹簧测力计测，随 g 变化。
3. Measuring Gravity in the Lab | 在实验室里测量重力
A top-pan balance compares an unknown mass with standard masses, so it reads in grams or kilograms. A newton meter (spring balance) contains a spring that stretches when the weight pulls on it, and the scale is marked in newtons. If you hang the same 1 kg mass from a newton meter on Earth, it reads about 9.8 N; on the Moon it reads about 1.6 N.
托盘天平把未知质量与标准质量比较，读数单位是克或千克。弹簧测力计内部有一根弹簧，被重量拉伸后指针在刻度上显示牛顿值。把同一个 1 kg 的物体挂在地球的测力计上读数约为 9.8 N，在月球上约为 1.6 N。
Good practical technique matters for marks. Check the zero reading before you start, read the scale at eye level to avoid parallax error, and repeat each measurement to spot anomalies. Record results in a table with the quantity, the value and the correct unit in the column heading.
规范的实验操作也能得分。实验前检查零点，读数时视线与刻度齐平以避免视差，每个测量重复几次以发现异常值。数据填入表格，列标题要写清物理量、数值和正确单位。
| Object | 物体 | Mass / kg | 质量 | Weight on Earth / N (g = 10) | 地球上的重量 | Weight on Moon / N (g = 1.6) | 月球上的重量 |
| Pencil case | 笔袋 | 0.2 | 2.0 | 0.32 |
| Textbook | 课本 | 0.8 | 8.0 | 1.28 |
| Student | 学生 | 45 | 450 | 72 |
Notice that the mass column never changes. Only the weight column changes, and it changes in direct proportion to g.
注意质量一列始终不变，只有重量一列在变，而且与 g 成正比。
4. Free Fall and Falling Objects | 自由落体与下落物体
When the only force acting on an object is gravity, we say it is in free fall. Near the Earth's surface, all objects in free fall accelerate at the same rate, about 9.8 m/s², regardless of their mass. A hammer and a feather dropped in a vacuum tube hit the bottom together - the classic video demonstration.
当物体只受重力作用时，我们说它处于自由落体状态。在地球表面附近，所有自由落体物体的加速度相同，约为 9.8 m/s²，与质量无关。在真空管中同时释放锤子和羽毛，它们会同时落地——这是视频中最经典的演示。
In air, the feather loses the race because of air resistance, not because it is lighter. Air resistance is a frictional force that opposes motion through the air and increases with speed and with surface area.
在空气中羽毛落后，是因为空气阻力，而不是因为它更轻。空气阻力是阻碍物体穿过空气运动的摩擦力，会随速度和迎风面积的增大而增大。
The motion of a falling object can be described with the equations of uniform acceleration:
v = u + a × t
s = u × t + ½ × a × t²
where v is final velocity in m/s, u is initial velocity in m/s, a is acceleration in m/s², t is time in s and s is distance in m. These belong to the later IGCSE course, but seeing them early makes the transition easier.
其中 v 是末速度（m/s），u 是初速度（m/s），a 是加速度（m/s²），t 是时间（s），s 是位移（m）。这些公式属于后续 IGCSE 内容，但提前认识它们会让过渡更顺畅。
5. Gravity, Orbits and the Solar System | 重力、轨道与太阳系
Gravity keeps the planets moving around the Sun and keeps moons moving around planets. The force acts towards the centre of the larger body, and that inward pull is exactly what bends the planet's path into a curve. Without gravity, a planet would simply fly off in a straight line.
重力让行星绕太阳运行，也让卫星绕行星运行。这个力指向较大天体的中心，正是这个向内的拉力把行星的路径弯成曲线。如果没有重力，行星会沿直线飞出去。
The Sun contains almost all the mass of the solar system, so its gravitational pull dominates. The further a planet is from the Sun, the weaker the pull and the longer its year, which is why Neptune takes about 165 Earth years for one orbit while Mercury takes only 88 days.
太阳集中了太阳系几乎全部质量，因此它的引力占主导。行星离太阳越远，受到的引力越弱，公转周期越长——所以海王星绕一圈约需 165 个地球年，而水星只需约 88 天。
Astronauts on the International Space Station are not outside gravity. They are in continuous free fall, falling around the Earth rather than towards it, which is why they appear to float.
国际空间站上的宇航员并没有脱离重力，他们处于持续的自由落体状态——是"绕着地球掉落"，而不是"朝地球掉落"，所以看起来像漂浮。
6. Terminal Velocity and Parachutes | 终端速度与降落伞
As a falling object speeds up, air resistance grows. Eventually the upward air resistance equals the downward weight, the resultant force becomes zero, and the object stops accelerating. It then falls at a steady maximum speed called terminal velocity.
下落物体速度增大时，空气阻力也随之增大。当向上的空气阻力等于向下的重量时，合力为零，物体不再加速，此后以恒定的最大速度下落，这个速度叫终端速度。
A skydiver's video lesson usually shows three stages: acceleration in free fall, terminal velocity at roughly 50-60 m/s, and a sharp slowdown when the parachute opens because the canopy hugely increases surface area and therefore air resistance.
跳伞运动的视频通常展示三个阶段：自由落体加速、约 50-60 m/s 的终端速度、以及打开降落伞后速度骤降——伞盖极大增加了迎风面积，从而增大空气阻力。
- Small resultant force - slow acceleration. | 合力小——加速度小。
- Zero resultant force - constant speed (terminal velocity). | 合力为零——匀速（终端速度）。
- Upward force greater than weight - deceleration. | 向上的力大于重量——减速。
7. Comparing Gravity Across Planets | 比较不同行星的重力
Gravitational field strength depends on a planet's mass and radius. Jupiter, the most massive planet, has by far the strongest surface gravity among the planets, while the Moon and Mars have much weaker gravity than Earth.
重力场强度取决于行星的质量和半径。木星是质量最大的行星，表面重力远高于其他行星；月球和火星的重力则比地球弱得多。
| Body | 天体 | g / N kg⁻¹ | Weight of 60 kg student / N | 60 kg 学生的重量 |
| Moon | 月球 | 1.6 | 96 |
| Mars | 火星 | 3.7 | 222 |
| Earth | 地球 | 9.8 | 588 |
| Jupiter | 木星 | 23.1 | 1386 |
wer always links back to W = m × g: the mass is unchanged, so a smaller g gives a smaller weight.
常见题型是计算某物体在另一颗行星上的重量，或解释为什么宇航员在月球上能跳得更高。答案都要回到 W = m × g：质量不变，g 更小，重量就更小。
8. Balanced and Unbalanced Forces with Gravity | 重力与平衡、不平衡力
Weight is only one of several forces acting on an object. When an object rests on a table, the table pushes up with a normal contact force equal to the weight. The two forces are balanced, so the resultant force is zero and the object stays still.
重量只是作用在物体上的几种力之一。物体放在桌面上时，桌面向上的支持力等于重量。这两个力平衡，合力为零，物体保持静止。
If the upward force becomes smaller than the weight, the forces are unbalanced and the object accelerates downwards. Adding force arrows to a diagram, with the length of each arrow showing the size, is a standard Checkpoint skill.
如果向上的力小于重量，力就不平衡，物体向下方加速。在受力图上画出箭头，用箭头长度表示力的大小，这是 Checkpoint 的标准技能。
Friction acts parallel to surfaces and opposes sliding. Together with air resistance, friction converts kinetic energy into thermal energy, which is why a falling object does not keep accelerating forever.
摩擦力平行于接触面，阻碍滑动。摩擦力和空气阻力一起把动能转化为热能，这就是下落物体不会无限加速的原因。
9. How to Use a Gravity Video Effectively | 如何高效使用重力视频课
Watching a video is passive unless you make it active. Pause the video before the explanation and predict what will happen - for example, which of two balls will land first. Then play it and check whether your prediction was right.
如果只是看，视频学习是被动的。在讲解之前暂停视频并做出预测，比如两个球哪个先落地，然后再播放，验证自己的预测是否正确。
Keep a two-column note page: on the left, write the key statement or equation from the video; on the right, write your own example or a question you still have. At the end of the video, answer the questions without looking back.
准备一页双栏笔记：左边写视频中的关键结论或公式，右边写自己的例子或仍未解决的问题。视频结束后，先不看笔记回答问题。
- Watch once for the big picture. | 第一遍看整体思路。
- Watch again with a pen, pausing at every calculation. | 第二遍拿笔看，每个计算处暂停。
- Redraw every diagram from memory. | 凭记忆重画每一张图。
- Do three past-paper questions the same day. | 当天完成三道真题。
10. Practical Investigations into Gravity | 关于重力的实验探究
A classic Checkpoint investigation asks: does the time for a pendulum to swing depend on the mass of the bob? The independent variable is the mass, the dependent variable is the time for ten swings, and the control variables include the length of the string and the angle of release.
经典 Checkpoint 探究题是：单摆摆动的时间是否取决于摆锤质量？自变量是质量，因变量是摆动十次的时间，控制变量包括摆线长度和释放角度。
Another common investigation drops paper cones of different sizes from the same height to test whether air resistance affects fall time. Results are plotted as a line graph with the independent variable on the x-axis, and a conclusion must be justified with data, not just a general statement.
另一个常见探究是把不同大小的纸锥从同一高度释放，检验空气阻力是否影响下落时间。结果画成折线图，自变量放在 x 轴；结论必须用数据支持，不能只说一句笼统的话。
Safety and accuracy always earn marks: stand clear of falling masses, use a stopwatch with a reaction-time comment, and take an average of repeated readings to reduce random error.
安全与准确性总能得分：远离下落物，使用秒表时说明反应时间带来的误差，多次读数取平均值以减少随机误差。
11. Common Mistakes in Gravity Questions | 重力题目中的常见错误
The equation works in kilograms only, so 500 g must become 0.5 kg before multiplying by g.
最常见的错误是把克直接代入 W = m × g。公式只适用于千克，所以 500 g 必须先换成 0.5 kg 再乘以 g。
The second most frequent error is writing "weight in kg" or "mass in N". Check your unit every single time: mass in kg, weight in N, g in N/kg. A unit error usually loses the mark even when the arithmetic is right.
第二常见的错误是写出"重量 5 kg"或"质量 50 N"。每次都要检查单位：质量用 kg，重量用 N，g 用 N/kg。即使算对了，单位错误通常也不给分。
- Saying there is no gravity in space. | 说太空中没有重力。
- Forgetting g is different on the Moon. | 忘记月球上的 g 不同。
- Confusing mass with the amount of force. | 把质量当成力的大小。
- Not rounding or not showing working. | 不四舍五入、不写计算过程。
Show your working in three steps: write the equation, substitute the values with units, then state the answer with its unit. Examiners award marks for the method, not only the final number.
计算过程分三步写：写出公式，代入数值和单位，最后写出带单位的答案。评分看重方法，而不只是最终数字。
12. Revision Checklist and Next Steps | 复习清单与下一步计划
Use the checklist below before your Checkpoint test. Tick each item only when you can explain it out loud without looking at your notes, because that is the level of understanding the written papers require.
参加 Checkpoint 考试前使用下面的清单。只有在不看笔记也能口头解释清楚的情况下才打勾，因为笔试要求的正是这种理解水平。
- Define mass, weight and gravitational field strength. | 定义质量、重量和重力场强度。
- State the units: kg, N, N/kg, m/s². | 说出单位：kg、N、N/kg、m/s²。
- Use W = m × g in both directions. | 正反两个方向使用 W = m × g。
- Describe free fall and terminal velocity. | 描述自由落体和终端速度。
- Explain orbits and apparent weightlessness. | 解释轨道运动与失重现象。
- Explain the effect of g on other planets. | 解释其他行星上 g 的影响。
- Design an investigation with named variables. | 设计一个标明变量的实验。
The best next step is to combine video with writing. Watch one gravity video, then immediately attempt past-paper questions on mass, weight and forces. If you can only do one of those two things, do the questions - recall practice under timed conditions is what moves marks fastest.
最佳的下一步是"视频 + 动笔"结合：看完一段重力视频，立刻做质量、重量与力的真题。如果两者只能选一个，就做题——限时条件下的回忆练习是提分最快的方式。
Published by TutorHao | Cambridge Checkpoint Science Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图