OCR GCSE物理 Forces 合力 牛顿定律 胡克定律
P2 Forces 是 OCR GCSE Physics A（Gateway Science，J249）的第二个教学主题，内容分成运动、牛顿定律、力的作用三块。考试局把它放进 Paper 1 和 Paper 3，也就是基础卷与高阶卷的第一场，和 P1 到 P4 加上实践技能主题 P9 一起考。很多学生以为力与运动就是背几条公式，实际题目更常问图线斜率的含义、单位要不要换算、结论为什么成立。下面按知识点把公式、图线、实验和扣分点串一遍，公式写法以 OCR 官方 Equation Sheet 为准。
P2 Forces is the second of the eight teaching topics in OCR GCSE Physics A (Gateway Science, J249), and it divides into motion, Newton's laws and forces in action. The exam board examines it in Paper 1 and Paper 3, the first paper of each tier, alongside P1 to P4 and the practical skills topic P9. The equations below are printed exactly as the official OCR equation sheet gives them, followed by the places where marks quietly disappear.
标量 矢量 与平均速度的方向
距离、速率、质量、时间只有大小，属于标量。位移、速度、力、加速度带方向，属于矢量。速率用路程除以时间，速度用位移除以时间。绕操场跑完一圈回到起点，平均速度为零，平均速率不是零。很多学生以为这两个词只是叫法不同，写答案时就漏掉方向这一半。题目里出现「向北 4 m/s」这类描述，方向本身就是得分点。矢量相加要看夹角，同向直接相加，反向相减，垂直时用勾股定理算大小。阅卷时算式正确、方向写错的卷面很常见，这一分丢得最不值。
Distance, speed, mass and time are scalars, so a size alone describes them completely. Displacement, velocity, force and acceleration are vectors, which means the direction belongs in the answer as much as the number does, and a missing arrow costs the mark even when the arithmetic is perfect. Run one full lap of a track and your average velocity comes out as zero while your average speed does not, which is why OCR wording keeps insisting on the word average instead of plain speed.
距离时间图与速度时间图的斜率
距离时间图的斜率是速率，越陡越快，水平段表示静止。速度时间图的斜率是加速度，图线落到时间轴下方表示速度为负、方向相反。速度时间图下方的面积是位移，算面积时上方与下方要相减。很多学生以为两条图长得像就可以互换，结果把加速度当成速度读。题目给分段图线时，先标出每一段的起止时刻，再逐段算斜率。曲线段的斜率要用切线，不要用连接两点的弦。这一步最容易在曲线段失分，读图前先确认题目问的是平均量还是瞬时量。
A distance-time graph gives speed as its gradient, so a steep line means fast and a flat line means stationary. A velocity-time graph gives acceleration as its gradient, and the area underneath gives displacement, which has to be subtracted rather than added once the line drops below the time axis. When the graph is piecewise, mark the time at every corner before touching the numbers; the gradient of a curve needs a tangent, never a chord drawn between two convenient points.
加速度与匀加速公式 v²-u²=2as
加速度是速度变化量除以所用时间，单位是 m/s²。减速时加速度与速度方向相反，代入公式要带符号，否则结果会翻倍。OCR 的 Equation Sheet 印的是 v²-u²=2as，这条只适用于匀加速。题目不给时间时优先用这条公式，比先求加速度再求位移省一步。常见的错误是把末速度与初速度的位置写反，导致 v²-u² 出现负值。单位要先统一成米和秒，km/h 直接代入会全错。算完看一眼数量级，汽车刹车的加速度通常在 5 到 10 m/s² 之间，写出 200 这种数就说明单位没换。
Acceleration is change in velocity divided by time, measured in metres per second squared. The equation sheet prints v squared minus u squared equals two a s, and it only holds when the acceleration is uniform, which is exactly the case in questions that give no stopwatch reading. Convert kilometres per hour into metres per second before substituting, because a braking car should land between five and ten metres per second squared, and a result in the hundreds simply means the units were never changed.
牛顿第一定律 合力与受力图
牛顿第一定律说，物体不受合力时保持静止或匀速直线运动。关键词是合力与匀速，速度大小不变但方向改变也算受力。受力图只画作用在该物体上的力，箭头长度表示大小，起点画在物体中心。很多学生以为画了重力就一定平衡，实际要看有没有支持力和摩擦力。题目问为什么匀速前进，答案要落到合力为零，不能只写受力平衡四个字。空气阻力随速度增大，速度稳定时阻力正好等于驱动力。阅卷时只写平衡不给分的卷面不少，缺的是哪一个力与哪一个力抵消。
Newton's first law says an object stays at rest or keeps moving in a straight line at constant velocity unless a resultant force acts on it. The two words that carry the marks are resultant and constant velocity, because a change of direction counts as acceleration even when the speed itself never changes. A free body diagram shows only the forces on that one object, drawn from its centre, and whenever a question asks why the speed is steady the answer is that the driving force equals the drag.
F=ma 与惯性质量
F=ma 里的 F 是合力，不是某一个力，先把同方向的力相加、反方向的力相减。质量用千克，加速度用 m/s²，算出来的力单位才是牛顿。惯性质量的定义是力除以加速度，质量越大越难改变运动状态。例题：1500 kg 的汽车受 3000 N 合力，加速度是 2 m/s²。同一个力作用在 500 kg 的小车上，加速度变成 6 m/s²。常见的错误是忘了减摩擦力，把驱动力直接当成合力。题目给两个力时，先在草稿上画一条坐标轴，标出正方向再做代数运算。
In F equals m a, the F is the resultant force, so add the forces pointing one way and subtract the ones pointing back before dividing by mass. Keep mass in kilograms and acceleration in metres per second squared, and the answer arrives in newtons without any further conversion. Inertial mass is simply force divided by acceleration, which is why a loaded trolley feels harder to start than an empty one, and why forgetting friction makes every answer too large by exactly the size of the friction force.
牛顿第三定律 与成对力
牛顿第三定律说，两个物体相互作用时，彼此施加的力大小相等、方向相反、作用在同一条直线上。这对力分别作用在两个物体上，所以不能相互抵消。很多学生以为这对力平衡，其实平衡力必须作用在同一个物体上。人推墙，墙也推人；火箭向下喷气，气体也就把火箭向上推。判断成对力要看同性质、同时出现、作用在两个物体上这三条。题目问人为什么能站住，答案要写支持力与重力作用在同一人身上，属于平衡力而不是作用力与反作用力。阅卷时把两对力写混的答案扣分最狠，动笔前先圈出研究对象是谁。
Newton's third law pairs two forces that are equal in size, opposite in direction and act along the same line, yet each one acts on a different object. That is precisely why the pair never cancels out: balanced forces share a single object, while action and reaction forces never do. Push a wall and the wall pushes back, fire a rocket and the exhaust pushes the rocket forward, and a student standing still is held up by a normal force from the floor that balances weight on the same body.
重量与质量 W=mg
质量是物质的多少，单位千克，去哪儿都不变。重量是重力的大小，单位牛顿，随引力场强度改变。OCR 的 Specification 写明地球表面附近的 g 取 10 N/kg，考试就按 10 算，不要用 9.8。例题：60 kg 的学生在地球上重量是 600 N。同一个人到了月球，质量还是 60 kg，重量只剩约 100 N。常见的错误是把 kg 当成重量单位写进答案，单位错整题不给分。测重量用弹簧测力计，测质量用天平，题目问仪器时要分清。场强越大，同样质量的物体重量越大，这就是不同行星上体重不同的原因。
Mass is the amount of matter in kilograms and stays the same wherever you go, while weight is a force in newtons that depends on the gravitational field strength. The OCR specification fixes g at ten newtons per kilogram near the Earth's surface, so use ten rather than 9.8 in the exam and quote the specification if a question asks you to justify the value. A sixty kilogram student weighs six hundred newtons on Earth and roughly one hundred on the Moon, with the mass unchanged, and a spring balance rather than a balance beam is what measures the force.
自由落体 空气阻力与终端速度
没有空气阻力时，所有物体下落的加速度相同，约 10 m/s²。真实下落时阻力随速度增大，合力逐渐变小，加速度随之减小。速度增大到阻力等于重力，合力为零，速度不再增加，这个速度叫终端速度。很多学生以为到达终端速度后物体停止运动，其实它仍在匀速下落。跳伞员开伞后面积变大，阻力增大，终端速度明显下降。题目问为什么加速度减小但速度还在增大，要点是合力仍然向下。答这类题要写出阻力随速度增大、合力减小这两步，只写阻力变大通常只给一半分。
Without air resistance every falling object accelerates at the same rate, about ten metres per second squared, which is why a coin and a feather agree in a vacuum. In real air the drag grows with speed, so the resultant force shrinks and the acceleration shrinks with it while the velocity keeps climbing. Once drag equals weight the resultant force is zero and the object falls at terminal velocity, and a parachute works by increasing area, which raises drag at the very same speed.
功与功率 W=Fs 与 P=W/t
功等于力乘以物体沿力的方向移动的距离，单位焦耳。力与位移垂直时不做功，提着箱子水平走路就是这种情形。例题：40 N 的力把小车推了 6 m，做功 240 J。功率是功除以时间，单位瓦特，表示做功的快慢。一焦耳的定义是一牛的力让物体沿力的方向移动一米。常见的错误是把位移写成斜边长度，实际只取沿力方向的分量。两人搬同样的箱子上楼，做功相同但功率不同，快的那位功率大。题目问电动机提升物体的功率，要先把重力当作需要的力，再乘提升高度。
Work done equals force multiplied by the distance moved along the line of that force, measured in joules, and a force at right angles to the motion transfers no energy at all. Pushing a trolley with forty newtons across six metres therefore does two hundred and forty joules of work. Power is work divided by time in watts, so two people carrying identical boxes upstairs do exactly the same work while the faster one delivers the greater power.
胡克定律 F=kx 与弹簧实验
弹簧受到的拉力与伸长量成正比，前提是不超过比例极限，写成 F=kx。k 是劲度系数，单位 N/m，k 越大弹簧越硬。伸长量是现在的长度减去原长，不是整根弹簧的长度。OCR 的实践技能主题里有测力与伸长的必做实验，用弹簧、钩码和尺子做，图像是过原点的直线，斜率就是 k。超过比例极限后图线开始弯曲，再拉下去弹簧不能恢复原长。常见的错误是把总长当伸长量代入，算出的 k 会偏小。读数时眼睛要与尺子平视，每加一个钩码都要等静止再读，否则振动会让数值偏大。
Hooke's law says the force a spring exerts is proportional to its extension, written F equals k x, and it holds only below the limit of proportionality. The extension is the new length minus the original length, never the total length, which is the single mistake that quietly ruins the value of k. In the OCR practical you hang masses on a spring, plot force against extension, and take the gradient of the straight section as the spring constant.
拉伸储存的弹性势能 ½kx²
拉伸弹簧做的功以弹性势能形式储存，公式是 E=½kx²。系数二分之一来自力从零线性增大到 F，平均力只有一半。例题：k 为 200 N/m 的弹簧伸长 0.1 m，储存能量 1 J。伸长量翻倍时能量变成四倍，因为公式里伸长量是平方。常见的错误是把 F=kx 的结果直接当成能量，算出 20 J，整整大了一倍。弹簧被压缩时公式同样适用，x 取压缩量。题目给的是总长时，先算出伸长量再代入，否则平方项会把误差放大很多。
The work done in stretching a spring is stored as elastic potential energy and equals one half k x squared. The factor of a half appears because the force rises steadily from zero to its final value, so the average force is half the maximum. Double the extension and the stored energy quadruples, and treating F equals k x as if it were the energy overstates the answer by exactly a factor of two.
力矩 M=Fd 与杠杆齿轮
力矩等于力乘以力到支点的垂直距离，单位牛米。距离必须垂直于力的方向，斜着拉时只算垂直分量。例题：在离支点 0.5 m 处用 20 N 的力，力矩是 10 Nm。杠杆平衡的条件是顺时针力矩等于逆时针力矩。大齿轮带小齿轮时转速变快、力矩变小，反过来转速变慢、力矩变大。常见的错误是把力的作用点到支点的斜线长度当成距离。题目给角度时，先画出力的作用线，再从支点作垂线，最后才量长度。
A moment is force multiplied by the perpendicular distance from the pivot, measured in newton metres. Use only the component of the force at right angles to the lever, because pulling at an angle wastes part of the effort along the lever instead of turning it. Gears trade speed for turning effect in the same way, and a lever balances the moment the clockwise turning effect equals the anticlockwise one.
压强 p=F/A 与液体压强浮力
压强等于垂直作用在表面上的力除以受力面积，单位帕斯卡，1 Pa 等于 1 N/m²。同样重的箱子，底面积小的那只对地面压强大。图钉尖端面积小，用很小的力就能产生很大的压强。液体内部压强随深度和密度增大，公式是 p=hρg。物体浸在液体中受到向上的浮力，浮力等于排开液体的重量。物体密度小于液体密度时上浮，浮力与重力相等时悬浮或漂浮。常见的错误是把压强与压力混用，压力是力、单位牛顿，压强是单位面积上的力、单位帕斯卡。
Pressure is the force acting at right angles to a surface divided by the area of that surface, in pascals, where one pascal is one newton per square metre. A drawing pin concentrates a small force onto a tiny area, which is why the same push produces a far larger pressure than a flat thumb would. In a liquid the pressure rises with depth and density, and an object floats when the upthrust equals its weight, which happens whenever its density is lower than the liquid's.
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