题型概述：浮力与流体静力学Question type: buoyancy & hydrostatics
Top Gold平均每年约 4 分。直接套阿基米德公式的题现在很少见，几乎都和受力分析绑在一起：绳子、弹簧、滑轮、测力计、天平、分层液体……做法永远是先还原场景（谁浸在哪种液体里、浸了多少体积），把浮力算出来，再对每个物体列力平衡。失分主要在：漏掉某个物体的浮力；忘了浮力的反作用力会压到天平上；"浸没体积"取错（整块 / 露出部分 / 分层）；g、cm³ 与 kg、m³ 的换算。About 4 marks a year. Plain "apply Archimedes" questions are now rare; buoyancy is almost always combined with force analysis: strings, springs, pulleys, newton-meters, balances, layered liquids. The method never changes: rebuild the scene (what is immersed in which liquid, and how much volume), find the buoyant force, then write force balance for each body. Marks are lost by: missing the buoyancy on one of the bodies; forgetting that the reaction to buoyancy pushes down on the balance; taking the wrong "submerged volume" (whole / exposed part / layers); and g, cm³ versus kg, m³ conversions.
本模块取Throughout this module g = 9.81 m s⁻², ρwater = 1.00 g cm⁻³ = 1000 kg m⁻³；用 9.8 得到的答案同样判对。; answers using 9.8 are also accepted.
1液体压强只看深度和密度Liquid pressure depends only on depth and density
静止液体中某点的压强来自它上方液柱的重量：深度每增加 h，压强增加 ρgh，与容器形状无关，并且同一深度向各个方向大小相同（所以侧壁也受压）。几层不相混合的液体叠在一起时，逐层累加。The pressure at a point in a still liquid comes from the weight of the column above it: going down by h adds ρgh, whatever the container's shape, and at a given depth it acts equally in every direction (so the side walls are pushed too). For several immiscible layers, add layer by layer.
p = p₀ + ρgh 分层layers: p = p₀ + ρ₁gh₁ + ρ₂gh₂ + …一面竖直墙上压强随深度线性变化，所以作用在一段墙上的平均压强就是这段墙中点处的压强，力 = 中点压强 × 面积。p₀（大气压）在求浮力时上下抵消，通常可以不写。On a vertical wall the pressure changes linearly with depth, so the average over a strip of wall is the pressure at its mid-height, and the force = mid-height pressure × area. The atmospheric p₀ cancels between top and bottom when finding buoyancy, so it is usually left out.
2浮力 = 上下表面的压力差（阿基米德原理）Buoyancy = the pressure difference (Archimedes' principle)
物体下表面比上表面深，受到向上的压强更大，合力向上，这就是浮力。算出来它恰好等于"被排开的那部分液体的重量"。注意：ρ 是液体的密度，V 是浸在液体里的体积，与物体本身的密度无关。The bottom face of a body is deeper than its top face, so it is pushed up harder; the net push is upward, and that is buoyancy. It works out to be exactly the weight of the liquid displaced. Note: ρ is the density of the liquid and V is the immersed volume; the body's own density does not enter.
Fb = ρliquid Vsub g 漂浮floating: Vsub/V = ρobj/ρliquid 恰好下沉just sinks: ρ̄ = mtotal/Vtotal = ρliquid拖动滑块把方块往下放：部分浸入时浮力随浸入深度增加；一旦完全浸没，上下压强都在增大但差值不变，所以浮力不再变化。Drag the slider to lower the block: while partly immersed the buoyancy grows with depth; once fully under, both face pressures keep rising but their difference stays the same, so the buoyancy is constant.
方块边长 0.10 m（面积 0.010 m²），水 ρ = 1000 kg m⁻³，压强为表压（不含大气压）。Cube of side 0.10 m (face area 0.010 m²), water ρ = 1000 kg m⁻³, gauge pressures (atmosphere excluded).
3受力分析 + 牛顿第三定律Force analysis + Newton's third law
对每个物体单独画受力图：重力向下，浮力向上，绳子/弹簧/测力计的拉力沿绳。轻绳绕过无摩擦滑轮时两端张力相等；弹簧串在绳里，伸长量 = T/k。液体推物体向上 Fb，物体就推液体向下 Fb，这个力经液体传到容器底，所以天平读数增加 Fb，测力计读数减少 Fb（"视重"）。Draw a separate force diagram for each body: weight down, buoyancy up, string/spring/newton-meter tension along the string. A light string over a frictionless pulley has the same tension at both ends; a spring in the string stretches by T/k. The liquid pushes the body up with Fb, so the body pushes the liquid down with Fb; this reaches the container floor, so a balance under the container reads more by Fb while a newton-meter holding the body reads less by Fb (the "apparent weight").
T = mg − Fb 天平balance: R = Mbeaker+waterg + Fb检查方法：把"物体 + 烧杯 + 水"看成一个整体，外力只有总重、测力计拉力和天平支持力，两个读数之和必须等于总重。Check: treat "body + beaker + water" as one system; its only external forces are the total weight, the newton-meter pull and the balance's push, so the two readings must add up to the total weight.
| 子题型Sub-type | 识别特征How to spot it | 核心步骤Core step | 真题Past paper |
|---|---|---|---|
| 融冰与液面 / 平均密度Melting ice, water level, mean density | "ice cube … melted", "just sank" | 漂浮时排水体积 = 总质量/ρw；恰好下沉 ⇔ 平均密度 = ρwFloating displaces total mass/ρw; just sinks ⇔ mean density = ρw | 2025 Q1(d) |
| 绳、滑轮、弹簧连接体Bodies joined by string, pulley, spring | "thread … over a pulley", "spring of constant k" | 同一张力 T；每个物体 T + Fb = mgOne tension T; each body T + Fb = mg | 2023 Q1(s) |
| 分层液体的压强与侧壁压力Layered liquids: pressure and wall force | "liquids which do not mix", "curved surface" | 逐层累加 ρighi；侧壁力 = 中点压强 × 面积Add ρighi layer by layer; wall force = mid-height pressure × area | 2022 Q1(g) |
| 测力计 + 天平读数Newton-meter + balance readings | "newton-meter", "mass balance", "without touching" | 测力计 −Fb，天平 +Fb（第三定律）Newton-meter −Fb, balance +Fb (third law) | 2021 Q1(n) |
| 漂浮在两层液体之间Floating across two liquid layers | "covered … by oil" | 浮力 = 两层各自排开液体的重量之和Buoyancy = sum of the weights displaced from each layer | 2018 Q1(l) |