题型概述：牛顿第二定律与受力分析Question type: Newton's second law & force analysis
Top GoldSection 1 每年都有 1–2 道，合计约 8 分，通常出现在前几小题，是必须拿满的基础分。物理只有一条 ΣF = ma，失分几乎都出在四个地方：受力图漏画或多画了力；摩擦方向判断错；连接体里整体和隔离体混用；电梯、加速车厢里 g 与 a 的正负号搞反。Every Section 1 paper has one or two of these, about 8 marks in total, usually among the early parts. They are marks you must bank. The physics is a single law, ΣF = ma; marks are lost in four places: a missing or extra force on the diagram, friction pointing the wrong way, mixing up the whole-system and single-body equations in connected problems, and the sign of a relative to g in lifts and accelerating vehicles.
1受力图 + ΣF = ma：先隔离，再分解Free-body diagram + ΣF = ma: isolate, then resolve
选定一个物体，把"碰到它的东西"施加的力逐一画出（绳 → 拉力，接触面 → 法向力 + 摩擦力），再加上重力。然后沿加速度方向取坐标轴：沿该方向合力 = ma，垂直方向合力 = 0。斜面上沿斜面、垂直斜面分解最省事。Pick one body. Draw a force for everything that touches it (string → tension, surface → normal force + friction), then add its weight. Take one axis along the acceleration: the net force along it is ma, and the net force perpendicular to it is zero. On an incline, resolve along and perpendicular to the slope.
ΣF∥ = ma, ΣF⊥ = 0 斜面：incline: mg sin θ 沿斜面向下down the slope, N = mg cos θ检验技巧：θ = 0 时下滑分力应为 0（sin 0 = 0），θ = 90° 时法向力应为 0（cos 90° = 0）。Check with special values: at θ = 0 the down-slope component must vanish (sin 0 = 0); at θ = 90° the normal force must vanish (cos 90° = 0).
m = 2.0 kg。箭头长度按真实力的大小成比例。当 mg sinθ ≤ μN 时木块静止，静摩擦只取所需的大小（= mg sinθ），不是 μN。m = 2.0 kg. Arrow lengths are proportional to the real forces. While mg sinθ ≤ μN the block stays still and static friction takes only the value needed (= mg sinθ), not μN.
2连接体：整体求 a，隔离求内力Connected bodies: whole system for a, one body for internal forces
绳、拖杆、滑轮连在一起的物体加速度大小相同。把它们看成一个整体时，绳子张力是内力、成对抵消，方程里只剩外力，一步求出 a；要求张力，就把最简单的那一个物体隔离出来单独列式（通常是只受张力和一个阻力的那个）。光滑滑轮只改变绳的方向，不改变张力大小。Bodies joined by strings, tow bars or pulleys share the same size of acceleration. Treat them as one system and the tensions are internal pairs that cancel, so a comes straight from the external forces. To find a tension, isolate the simplest single body (usually the one with just the tension and one resistive force). A smooth pulley changes the direction of a string, not its tension.
a = (Fdrive − Fresist) / (m1 + m2 + …), T − Rrear = mreara"重量 w"不是质量：质量 = w/g。斜面上的物体被拉上去时，阻碍系统的只是它的下滑分力 w sinθ，不是整个 w。A weight w is not a mass: the mass is w/g. When a body is pulled up an incline, only its down-slope component w sinθ opposes the system, not all of w.
3摩擦、电梯与加速车厢Friction, lifts and accelerating vehicles
动摩擦 f = μN 总是与相对运动方向相反，物体掉头时摩擦也掉头。在竖直加速的电梯里，支持力（或弹簧力、秤的读数）= m(g + a)，a 向上为正。水平加速的车厢里，液面、悬挂的摆线都与"等效重力" g − a 垂直或平行，所以倾角满足 tanθ = a/g。Kinetic friction f = μN always opposes the relative motion: when the body turns round, friction turns round too. In a vertically accelerating lift the support force (spring force, scale reading) is m(g + a), with a positive upwards. In a horizontally accelerating vehicle a liquid surface or a hanging pendulum lines up with the "effective gravity" g − a, so the tilt obeys tanθ = a/g.
f = μN, N = m(g + a), tan θ = a/g速度不影响受力，加速度才影响：匀速上升的电梯里，秤的读数和静止时一样。Forces depend on acceleration, not velocity: in a lift rising at constant speed the scale reads the same as at rest.
| 子题型Sub-type | 识别特征How to spot it | 核心步骤Core step | 真题Past paper |
|---|---|---|---|
| 斜面 + 滑轮连接体Incline + pulley pair | 一个在斜面、一个悬挂；"interchanged"one on the plane, one hanging; "interchanged" | 驱动力 = 悬挂重 − w sinθ，除以总质量drive = hanging weight − w sinθ, divide by total mass | 2025 Q1(m) 2020(c) |
| 电梯 / 视重Lift / apparent weight | lift、spring、scale、"apparent weight"lift, spring, scale, "apparent weight" | 对物体：N − mg = maon the body: N − mg = ma | 2024 Q1(c) 2022(h) |
| 车 + 拖车 / 列车Car + caravan / train | tows、tow bar、carriagestows, tow bar, carriages | 整体求 F，隔离后车求 T，P = Fvsystem for F, rear body for T, P = Fv | 2023 Q1(b) |
| 粗糙斜面上下往返Up and back down a rough incline | projected up the plane … returnsprojected up the plane … returns | 上行 g(sin + μcos)，下行 g(sin − μcos)，v² = 2as 相除up g(sin + μcos), down g(sin − μcos); divide the two v² = 2as | 2022 Q1(f) 2023(a) |
| 加速参考系Accelerating vehicle | 车厢里的液面 / 摆线倾斜tilted liquid surface / pendulum in a vehicle | tan θ = a/g | 2021 Q1(d) |