题型概述：力学长题Question type: extended mechanics
BPhO Round 1 Section 2 的力学题通常以一个情境串联多个模型。本页三道完整长题均为 25 分，覆盖赛车、弹性系统与流体；常见失分点是没有交代受力方向、忽略模型切换，以及把瞬时静止误当成平衡。先拿稳每个小问的建模分，再处理微积分与近似。BPhO Round 1 Section 2 mechanics questions connect several models through a setting. These three complete 25-mark questions cover cars, elastic systems and fluids. Common losses come from unclear force directions, missed changes of model and confusing instantaneous rest with equilibrium. Secure the modelling steps before tackling calculus and approximations.
1先画系统，再选守恒量Draw the system before choosing a law
明确研究对象与参考系；外力改变总动量，变力做功改变动能。恒功率问题中牵引力随速率变化。Define the system and reference frame: external force changes total momentum, while work changes kinetic energy. Constant power gives speed-dependent thrust.
对应赛车的相对速度和功率模型。Used in the car velocity and power models.
2围绕平衡点求小振动Linearise about equilibrium
先求平衡点，再把净力展开成 −κx。弹性绳一旦松弛，原运动方程就不再适用，需要分段。Find equilibrium, then expand the net force as −κx. If an elastic string goes slack, its previous equation of motion no longer applies.
恢复力系数是净力的斜率，不一定等于单根弹簧的 k。The restoring constant is the slope of net force, not necessarily one spring’s k.
3浮力、力矩与能量各有用途Use buoyancy, moments and energy appropriately
排水体积决定浮力；铰链约束问题要取矩；物体下沉到最低点时通常仍有向上的加速度。Displaced volume determines buoyancy; hinge constraints call for moments; at the lowest point of a descent the acceleration is usually upward.
只有静态平衡才能同时令合力和合力矩为零。Only static equilibrium justifies zero net force and torque.
小交互：有效刚度与周期Small interactive: stiffness and period
固定质量 m = 1 kg，改变 κ，比较周期与恢复力。Fix m = 1 kg and change κ to compare period and restoring force.
子题型与真题Sub-types and past questions
| 子题型Sub-type | 识别特征Recognition | 核心步骤Core steps | 真题Question |
|---|---|---|---|
| 变力与功率Variable force and power | 恒功率、阻力随速率变Constant power, speed-dependent drag | 分量 → 牛顿定律 → 积分Components → Newton → integration | 2025 Q2 |
| 弹性系统与振动Elasticity and oscillations | 绳绷紧／松弛，小位移Taut/slack string, small displacement | 平衡 → 恢复力 → 分段运动Equilibrium → restoring force → stages | 2018 Q3 |
| 静水压与浮体Hydrostatics and flotation | 压强差、铰链、最低点Pressure difference, hinge, lowest point | 排水 → 力矩／能量Displacement → moments / energy | 2018 Q4 |
数值检验用于自动反馈，不替代原题推导。计分为练习进度，按答对输入框比例分配；查看解答后不再计入该题新得分。Numerical checks provide feedback and do not replace derivations. Practice marks are distributed across correct inputs; viewing a solution prevents new marks for that question.