📚 Mastering A-Level Physics Unit 1: Mechanics and Materials | A-Level 物理第一单元：力学与材料
Unit 1 builds the core problem-solving toolkit for A-level Physics. It covers motion, forces, energy, momentum, equilibrium and the mechanical behaviour of materials. A clear grasp of definitions, vector methods, conservation laws and stress-strain relationships is essential before moving to later units.
第一单元是 A-level 物理核心解题能力的基础。它涵盖运动、力、能量、动量、平衡以及材料的力学行为。在进入后续单元之前，清晰掌握定义、矢量方法、守恒定律以及应力-应变关系至关重要。
1. Scalar and Vector Quantities | 标量与矢量
A scalar quantity has magnitude only. Typical examples include distance, speed, mass, energy, time and density. A vector quantity has both magnitude and direction, such as displacement, velocity, acceleration, force and momentum.
标量只有大小。常见例子包括路程、速率、质量、能量、时间和密度。矢量既有大小又有方向，例如位移、速度、加速度、力和动量。
When two vectors act at right angles, the resultant magnitude is found using Pythagoras' theorem. The direction is given by trigonometry, usually with the tangent function.
当两个矢量互相垂直时，合力大小用勾股定理求出。方向由三角函数给出，通常使用正切函数。
R = √A² + B²
θ = tan⁻¹(B / A)
F₁² + F₂² = F²
For non-perpendicular vectors, resolve each vector into horizontal and vertical components before adding. This avoids incorrect scalar addition and is especially important in equilibrium problems.
对于不垂直的矢量，应先将各矢量分解为水平和竖直分量，再分别相加。这可以避免错误的标量加法，在平衡问题中尤为重要。
2. Equations of Motion (SUVAT) | 运动学方程（SUVAT）
The SUVAT equations apply only when acceleration is constant and motion is along a straight line. The symbols are s for displacement, u for initial velocity, v for final velocity, a for acceleration and t for time.
SUVAT 方程只适用于匀加速直线运动。符号 s 表示位移，u 表示初速度，v 表示末速度，a 表示加速度，t 表示时间。
v = u + at | s = ut + ½at² | v² = u² + 2as | s = ½(u + v)t
Always choose a positive direction and assign signs to all displacement, velocity and acceleration values consistently. If a vehicle is slowing down, acceleration and velocity will have opposite signs.
始终先规定正方向，并对所有位移、速度和加速度统一赋予符号。如果车辆正在减速，加速度与速度的符号应相反。
In questions involving free fall, the magnitude of acceleration is approximately 9.81 m s⁻² near the Earth's surface. Using g as a positive or negative quantity depends on the chosen direction convention.
在自由落体问题中，地球表面附近的加速度大小约为 9.81 m s⁻²。g 取正还是取负取决于所选择的方向规定。
3. Projectile Motion | 抛体运动
Projectile motion is analysed by treating horizontal and vertical components separately. The horizontal component of velocity remains constant because there is no horizontal acceleration when air resistance is ignored.
分析抛体运动时，应将水平与竖直分量分别处理。忽略空气阻力时，水平方向没有加速度，因此水平分速度保持恒定。
The vertical component has a constant downward acceleration g. The trajectory is a parabola, and the horizontal and vertical motions are independent of each other.
竖直分量具有恒定的向下加速度 g。轨迹为抛物线，水平运动与竖直运动彼此独立。
x = u cosθ × t | y = u sinθ × t − ½gt²
At the highest point of a projectile's path, the vertical velocity is momentarily zero, but the horizontal velocity is unchanged. Time of flight is found from the vertical motion alone.
在抛体轨迹的最高点，竖直速度瞬时为零，但水平速度不变。飞行时间只由竖直方向运动决定。
4. Newton's Laws and Free-Body Diagrams | 牛顿定律与受力分析
Newton's first law states that an object remains at rest or in uniform motion unless acted on by a resultant force. Newton's second law relates resultant force, mass and acceleration. Newton's third law states that forces occur in equal and opposite pairs acting on different bodies.
牛顿第一定律指出，物体在不受合力作用时保持静止或匀速直线运动。牛顿第二定律将合力、质量与加速度联系起来。牛顿第三定律指出，力成对出现，大小相等、方向相反，且作用在不同物体上。
F = ma
forces include weight W = mg, normal reaction N, tension T, friction F and applied forces.
受力分析图是画出作用在单个物体上所有力的示意图。常见的力包括重力 W = mg、法向反作用力 N、拉力 T、摩擦力 F 和外加力。
Newton's third-law pairs are often confused with equilibrium forces. Action-reaction pairs must act on two different objects and be of the same type; equilibrium forces act on the same object and may be of different types.
牛顿第三定律的作用力与反作用力常与平衡力混淆。作用力-反作用力对必须作用在两个不同物体上且属于同一类型；平衡力作用在同一物体上，且可以属于不同类型。
5. Work, Energy and Power | 功、能量与功率
Work is done when a force moves its point of application in the direction of the force. If the force is at an angle θ to the displacement, only the component of force parallel to displacement does work.
当力使其作用点沿力的方向移动时，力做功。如果力与位移成 θ 角，则只有平行于位移的力分量做功。
W = Fs cosθ
Kinetic energy is the energy of motion, and gravitational potential energy is energy stored due to position in a gravitational field. Power is the rate of energy transfer or work done per unit time.
动能是物体由于运动而具有的能量，重力势能是物体因在重力场中的位置而储存的能量。功率是能量转移的速率或单位时间内所做的功。
Eₖ = ½mv² | ΔEₚ = mgΔh | P = W / t = Fv
In many Unit 1 problems, energy conservation allows speed to be found without using SUVAT. Always include any work done against friction or other resistive forces when energy is transferred.
在许多第 1 单元问题中，利用能量守恒可以不使用 SUVAT 方程求解速度。若存在克服摩擦或其他阻力做功，能量转移时一定要计入。
6. Momentum and Impulse | 动量与冲量
Linear momentum is the product of mass and velocity. It is a vector quantity, so direction must be considered in calculations. Momentum is conserved in all collisions and explosions provided no external resultant force acts.
线动量是质量与速度的乘积。它是矢量，因此在计算中必须考虑方向。在无外部合力作用时，所有碰撞和爆炸过程中动量守恒。
p = mv
Impulse is the product of force and the time for which it acts. It equals the change in momentum. This is why airbags and crumple zones reduce injury by increasing contact time and reducing peak force.
冲量是力与力作用时间的乘积。它等于动量的变化量。这就是安全气囊和碰撞吸能区通过延长接触时间、降低峰值力来减少伤害的原因。
FΔt = Δp = mv − mu
For two objects that collide, total momentum before the collision equals total momentum after the collision. Write one equation with all velocities measured in the same direction convention.
对于两个碰撞物体，碰撞前的总动量等于碰撞后的总动量。列方程时所有速度必须采用同一方向规定。
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
7. Moments and Equilibrium | 力矩与平衡
The moment of a force about a point is defined as the product of the force and the perpendicular distance from the line of action of the force to the point. It measures the turning effect of a force.
力对某点的力矩定义为力与从力作用线到该点的垂直距离的乘积。它表示力产生的转动效应。
M = Fd
An object is in equilibrium when the resultant force on it is zero and the resultant moment about any point is zero. For a body in static equilibrium, both conditions must be satisfied simultaneously.
当物体所受合力为零，且对任意点的合力矩为零时，物体处于平衡状态。对于静力平衡的物体，必须同时满足这两个条件。
ΣF = 0 | ΣM = 0
When taking moments in bridge, beam or ladder problems, choose a pivot that eliminates unknown forces. The normal reaction or tension can then be found by resolving vertically and horizontally.
在桥梁、梁或梯子问题中取矩时，应选择能消去未知力的支点。然后通过竖直和水平方向的受力分解求法向反作用力或拉力。
8. Stress, Strain and Young Modulus | 应力、应变与杨氏模量
Stress is defined as the force applied per unit cross-sectional area. Strain is the extension produced per unit original length, so it has no units. Young modulus is the ratio of tensile stress to tensile strain within the linear elastic region.
应力定义为单位横截面积上所受的力。应变是单位原始长度上产生的伸长量，因此没有单位。杨氏模量是线弹性区域内拉应力与拉应变之比。
σ = F / A | ε = ΔL / L | E = σ / ε
The Young modulus describes the stiffness of a material. A large Young modulus means the material resists stretching strongly; it does not simply mean the material is strong or difficult to break.
杨氏模量描述材料的刚度。杨氏模量大意味着材料抗拉伸能力强，但并不等同于材料强度高或不易断裂。
On a stress-strain graph, the gradient of the initial straight-line region gives the Young modulus. The area under the curve gives the strain energy stored per unit volume.
在应力-应变图中，初始直线段的斜率给出杨氏模量。曲线下方的面积表示单位体积内储存的应变能。
| Property 性质 | Brittle 脆性材料 | Ductile 延性材料 |
|---|---|---|
| Elastic region 弹性区域 | Short, then sudden fracture 短，随后突然断裂 | Clearly defined 明确存在 |
| Plastic deformation 塑性变形 | Very little or none 很少或无 | Large before breaking 断裂前明显 |
| Example 例子 | Glass, cast iron 玻璃、铸铁 | Copper, mild steel 铜、低碳钢 |
9. Hooke's Law and Elastic Strain Energy | 胡克定律与弹性应变能
Hooke's law states that the extension of a spring or wire is directly proportional to the applied force, provided the limit of proportionality is not exceeded. The constant k is the stiffness constant.
胡克定律指出，只要不超过比例极限，弹簧或金属丝的伸长量与施加的力成正比。比例常数 k 为劲度系数。
F = kx
The elastic strain energy stored in a stretched spring or wire is equal to the area under the force-extension graph. For an ideal spring obeying Hooke's law, this gives a simple quadratic formula.
拉伸弹簧或金属丝时储存的弹性应变能等于力-伸长图下方的面积。对于遵守胡克定律的理想弹簧，该能量可由简单的二次公式求出。
Eₚ = ½kx² = ½Fx
Elastic deformation is reversible: the object returns to its original shape when the load is removed. Plastic deformation is permanent because the atoms or layers have moved to new positions and cannot return.
弹性形变是可逆的：卸去载荷后物体恢复原状。塑性形变是永久的，因为原子或分子层已经移动到新的位置，无法复原。
10. Common Exam Pitfalls and Tips | 常见考试失分点与建议
One of the most common errors is adding vector quantities as if they were scalars. Always resolve or use vector diagrams for forces, velocities and momenta, especially when directions differ.
最常见的错误之一是把矢量当作标量相加。对于力、速度和动量，尤其是方向不同时，一定要先分解或使用矢量图求解。
Another common mistake is confusing mass and weight. Mass is measured in kg and remains constant; weight is the gravitational force on that mass, measured in newtons, and depends on the gravitational field strength g.
另一个常见错误是混淆质量与重量。质量以 kg 为单位且保持不变；重量是该质量受到的重力，以牛顿为单位，并取决于重力场强度 g。
Always convert quantities into SI units before substituting them into equations. For example, use metres, seconds, kilograms, newtons and pascals unless the question asks otherwise.
代入公式前，务必把各物理量换算为国际单位制。例如，除非题目另有要求，应使用米、秒、千克、牛顿和帕斯卡。
Finally, show your working clearly and state the direction of vector answers. A numerical answer without a unit or direction may lose marks even if the calculation is correct.
最后，清楚展示计算过程，并说明矢量答案的方向。即使计算正确，缺少单位或方向的数字答案也可能丢分。
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