Edexcel物理 Forces 受力分析 F=ma 动量守恒
Edexcel IGCSE 物理（4PH1）的 Section 1 Forces and motion 是整门课的地基：速度、加速度、受力分析、胡克定律、动量全在这里。这篇按考试顺序把它们串成一条线，每个知识点配一道真题式的计算，并标明哪些内容只在 Paper 2P 出现。
This walkthrough follows Section 1 of the Pearson Edexcel International GCSE Physics (4PH1) specification, from identifying forces through to momentum, with a worked calculation for each idea. It marks clearly which content belongs to Paper 1P and which is examined only in Paper 2P, so revision time goes where the marks are.
力改变速度、形状或方向
力的作用只有三种结果：让物体加速或减速、让物体变形、让物体转向，Edexcel 大纲 Section 1 的原话就是 changes in speed, shape or direction。判断一个物体受哪些力，最稳的做法按接触关系来找：物体与地球之间有重力，与桌面或绳之间有接触力，运动时有摩擦力与阻力，浸在液体或气体里有浮力。力是矢量，大小和方向都要写；质量、时间、距离、速率是标量，只有大小。很多学生以为物体在运动就一定有力在推它，其实匀速直线运动的结果力是零。常见的错误是拿重力的反作用力去顶重力：书放在桌上，重力向下 19.6 N，桌面支持力向上 19.6 N，两个力结果为零，书才保持静止。
Forces do just three things: they change an object's speed, its shape, or its direction of travel, which is exactly how Section 1 of the Edexcel specification words it. Listing the forces on a body is easiest from what touches it and what pulls it from a distance; weight comes from the Earth, contact forces from desks and ropes, friction and drag appear whenever something moves, and upthrust acts in a fluid. A 2 kg book resting on a desk has 19.6 N of weight downwards balanced by 19.6 N of contact force upwards, giving a resultant of zero, so it stays still; students who write that nothing is moving so no forces act lose that mark.
速度时间图的斜率与面积
距离时间图的斜率读的是速率，速度时间图的信息更多：斜率是加速度，图线与时间轴围出的面积是位移。加速度按 a =（v 减 u）÷ t 计算，单位 m/s²；减速时加速度与速度方向相反，写成负数。题目没给时间却给了速度、距离和加速度时，用（末速度）² =（初速度）² + 2 × a × s，这几条公式都印在随试卷一起发的 Equation List 上，不必背但必须会挑。比如一辆车在 4 秒内由 20 m/s 匀减速到停止，加速度是（0 减 20）÷ 4 = -5 m/s²，位移等于三角形面积 20 × 4 ÷ 2 = 40 m，用 v² = u² + 2as 检验也能得到 40 m。阅卷时最常见的是把匀减速段的加速度写成正数，方向对了符号错了，两分的题只拿一分。
On a velocity-time graph the gradient gives the acceleration and the area between the line and the time axis gives the distance travelled, while a distance-time graph only ever gives you speed. Acceleration is (v - u) / t in m/s², and slowing down simply means the acceleration points opposite to the velocity so it carries a minus sign; when a question gives no time at all, the equation to reach for is (final speed)² = (initial speed)² + 2 × a × s, which is printed on the Equation List issued with the paper. A car braking uniformly from 20 m/s to rest in 4 s has an acceleration of -5 m/s² and covers 20 × 4 ÷ 2 = 40 m, a figure the same equation confirms.
再看一类常考的距离时间图：物体先以 6 m/s 匀速走 30 m，停下 2 秒，再以 4 m/s 返回 20 m。图上第一段是斜率为 6 的直线，中间是水平线，返程是斜率为负的直线；总位移是 30 减 20 = 10 m，总路程是 50 m，平均速率按路程除以总时间算，平均速度按位移除以总时间算，两个数并不相等。水平线的长度就是停留时间，读图时别把它当成匀速运动。
F = ma 里的 F 是结果力
F = m × a 中的 F 是结果力，不是随便挑某一个力。做法是先定正方向，同向的力相加、反向的力相减，再代入公式；结果力为零时物体保持静止或匀速直线运动，这也是牛顿第一定律的另一种说法。质量越大或结果力越小，加速度就越小，这是同一个公式的两种读法，改写题里常问。题目给出的每一个数都要落到具体物体上，受力对象不同，结果力完全不同，同一个 5 N 对甲是动力、对乙可能就是阻力。比如一辆 1200 kg 的汽车驱动力 3600 N、阻力 1200 N，结果力 2400 N，加速度 2400 ÷ 1200 = 2 m/s²；若阻力升到 3600 N，结果力为零，车就匀速行驶。很多学生会把 N 与 kg 相除后忘记写单位，或者在绳连接题里直接拿绳的拉力当结果力。
The F in F = m × a is the resultant force on one chosen object, never a single force picked at random. Add the forces acting one way, subtract those acting the other way, then substitute; when the resultant is zero the object either stays at rest or keeps a steady velocity, which is Newton's first law in its everyday form. A 1200 kg car with 3600 N of driving force and 1200 N of drag accelerates at 2400 ÷ 1200 = 2 m/s², and raising drag to 3600 N leaves it cruising at constant speed.
绳与滑轮的连接题有个固定套路：把每个物体单独画出来，各自的 F 都取自己受到的结果力，绳的拉力在两个物体身上方向相反。若 A 受 12 N 拉力与 4 N 摩擦，结果力是 8 N；B 质量 2 kg、只受绳的 8 N，加速度就是 4 m/s²，与 A 相同，因为绳不可伸长。
W = mg 与 g 的取值
质量是物体含物质的多少，单位 kg，换到月球上数值不变；重量是重力，单位 N，随当地的 g 变化。Edexcel 卷面上地球表面取 g = 9.8 N/kg，官方评分方案同时接受 9.8 与 10，因此代数前先看题目打印的数值。以 8 kg 的书包为例，地球上重量是 8 × 9.8 = 78.4 N，在 g 约为 1.6 N/kg 的月球上只有 12.8 N，质量仍是 8 kg。这一步最容易丢分：有学生写月球上质量变小。天平测质量、弹簧测力计测力，读数是否随地点变，取决于用哪种仪器。斜面题里还要把重力分成沿斜面与垂直斜面两个分量，别再拿 W = mg 直接当结果力出答案。
Mass is the amount of matter in an object and stays the same wherever it goes, while weight is a force that changes with the local gravitational field strength g; on Earth's surface Edexcel papers take g as 9.8 N/kg, and Pearson mark schemes also accept 10 N/kg, so read the value printed on the question before substituting. An 8 kg school bag weighs 78.4 N on Earth but only 12.8 N on the Moon, where g is about 1.6 N/kg, and its mass is still 8 kg. A top-pan balance measures mass whereas a newton meter measures force, which is precisely why only one of the two readings changes with location.
胡克定律与劲度系数 k
弹簧受力时在最初的线性区间内 F = k × x，x 是伸长量（新长度减原长，单位 m），k 是劲度系数，单位 N/m，数值就是力-伸长图直线的斜率。超过比例极限后图线弯曲，胡克定律不再适用；去掉外力后能回到原长的性质叫弹性，拉过头就留下永久变形。大纲要求的实验用铁架台、弹簧、标尺与砝码：先读弹簧原长，每次加等量砝码（100 g 对应约 0.98 N），记录新长度，逐个算出伸长量，再画力-伸长图取斜率。很多学生把弹簧总长当成 x 代入，整题数字全错。比如 k = 125 N/m 的弹簧挂 25 N 的力，伸长是 25 ÷ 125 = 0.20 m；换成 250 N/m 的硬弹簧，同样 25 N 只伸长 0.10 m。
Below its limit of proportionality a spring obeys F = k × x, where x is the extension rather than the total length and k is the spring constant in N/m taken from the gradient of a force-extension graph. Beyond that limit the line curves and Hooke's law fails, and a material that still returns to its original shape once the load is removed is showing elastic behaviour. A spring with k = 125 N/m stretches 0.20 m under a 25 N load, whereas a stiffer 250 N/m spring stretches only 0.10 m under the same force.
实验题还会问控制变量：同一根弹簧、每次增加相同的质量、等弹簧静止后再读数，这三条保证了力与伸长的对应关系可靠。换成橡皮筋，图线会出现回线，伸长与恢复时的读数不同，说明它偏离胡克定律更早。写实验结论时把范围写清：在 0 到 4 N 之间伸长与力成正比，超过 4 N 之后图线弯曲。
停止距离的两段构成
停止距离由两段相加：反应时间内车以原速行驶的思考距离，以及刹车起作用后行驶的制动距离。影响因素要分清归属，疲劳、酒精、药物、分心只拉长反应时间，只加长思考距离；车速、车重、路面湿滑、轮胎与刹车状态改变的是制动距离。Edexcel 的评分方案里，把酒精写成增加制动距离是典型的丢分点。车速影响最大，制动距离大致与速度的平方成正比，30 mph 升到 60 mph 会让制动距离变成约四倍。养熟一条思路：结果力为零时物体保持匀速，车匀速时驱动力与阻力大小相等。落体也可以照这套看，速度变大阻力变大，阻力与重力相等时物体就以恒定的收尾速度下落。
A vehicle's stopping distance is the thinking distance travelled at constant speed during the driver's reaction time plus the braking distance covered once the brakes bite. Tiredness, alcohol, drugs and distraction lengthen reaction time and therefore only change the thinking distance, whereas speed, mass, wet or icy roads and worn tyres or brakes change the braking distance, so blaming alcohol for a longer braking distance loses the mark in Pearson mark schemes. Speed matters most because kinetic energy rises with the square of velocity, which is why going from 30 mph to 60 mph roughly quadruples the braking distance; a falling object behaves in a similar way, reaching terminal velocity once drag grows to balance its weight.
用数字走一遍最清楚：司机反应时间 0.7 s，车速 20 m/s，思考距离就是 20 × 0.7 = 14 m；刹车让车以 5 m/s² 减速，制动距离是 20² ÷（2 × 5）= 40 m，停止距离 54 m。车速换成 30 m/s，思考距离升到 21 m，制动距离升到 90 m，总共 111 m，多出来的部分几乎全落在制动那一段。
Paper 2P 专属的动量与守恒
动量是质量乘速度，单位 kg m/s，方向与速度一致，所以它是矢量。没有外力作用的系统里，碰撞或爆炸前后的总动量相等，用法是把碰撞前各物体的 m × v 相加，让它等于碰撞后各物体的 m × v 相加。Edexcel 把动量、冲量与力矩放在 Paper 2P（1 小时 15 分钟，70 分，占 38.9%），Paper 1P（2 小时，110 分，占 61.1%）不考这部分；官方 Equation List 也把 p = m × v 与 F =（mv 减 mu）÷ t 列在第二部分。安全设计题要用冲量的思路：安全带、气囊、溃缩区都是把碰撞时间拉长，把作用在乘员身上的力压下去。比如 2 kg 的小车以 3 m/s 撞上静止的 1 kg 小车并粘在一起，碰撞前总动量 6 kg m/s，碰撞后共同速度 v 满足（2 + 1）× v = 6，得 v = 2 m/s。
Momentum is mass multiplied by velocity and points the same way as the velocity, which makes it a vector measured in kg m/s; in a system with no external force the total momentum before a collision or explosion equals the total momentum afterwards. Pearson examines momentum, force-time ideas and moments in Paper 2P (1 hour 15 minutes, 70 marks, 38.9% of the qualification) rather than Paper 1P (2 hours, 110 marks, 61.1%), and the official Equation List keeps p = m × v and F = (mv - mu) ÷ t in its second, Paper-2-only section. Safety design follows the same logic every time: a seat belt, an airbag or a crumple zone stretches the collision time in order to reduce the force on the occupants, so a 2 kg trolley moving at 3 m/s that sticks to a stationary 1 kg trolley leaves both moving at 2 m/s.
爆炸与后坐也归这条定律管：静止的物体炸开之后，各部分的动量矢量相加仍然是零，所以质量小的碎片速度大。计算时先写总动量为零，再把两件的 m × v 写成大小相等、方向相反，正负号交给方向去定。
哪些公式只在 Paper 2P 出现
复习 Section 1 时把公式分成两堆，安排时间就不会乱：两张卷都可能考的是平均速度、加速度、（末速度）² =（初速度）² + 2as、F = ma、W = mg 与 F = kx，只在 Paper 2P 考的是 p = mv、F =（mv 减 mu）÷ t 与力矩。答题顺序固定成写公式、代数、写单位三步，单位写全了，N 与 kg 的混淆会少很多。实验题的文字分靠细节：砝码等量递增、记录原长、用指针读数、重复测量取平均。动量题里方向比算术更容易出错，先把正方向写在草稿上再算；题目问平均作用力时，力的方向与速度方向相反就要带负号，只写大小会丢掉方向分。
Splitting the Section 1 equations into two piles keeps revision honest: average speed, acceleration, (final speed)² = (initial speed)² + 2 × a × s, F = m × a, W = m × g and F = k × x can appear on either paper, while p = m × v, F = (mv - mu) ÷ t and the moment equation are reserved for Paper 2P. Writing the equation, substituting and adding the unit as three fixed steps removes most careless errors, and in practical questions the marks sit in the details such as equal mass steps, the original length and repeat readings averaged. Momentum questions go wrong on direction more often than on arithmetic, so fix the positive direction in your working before you start calculating.
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