📚 IB Physics: Work, Energy and Power Exam Essentials | IB物理：功、能量与功率考点精讲
In IB Physics, work, energy and power form one of the most frequently tested topics in both Paper 1 and Paper 2. You need to be able to define work, calculate energy transfers, apply the work-energy theorem, use conservation of mechanical energy, and solve problems involving power and efficiency.
在 IB 物理中，功、能量与功率是 Paper 1 和 Paper 2 中考查最频繁的内容之一。你需要能够定义功、计算能量转移、应用动能定理、使用机械能守恒，并解决涉及功率与效率的问题。
1. Work: Definition and Units | 功的定义与单位
In physics, work is a measure of energy transferred by a force when it moves an object through a displacement. Work is a scalar quantity, even though it is calculated from force and displacement, which are vectors.
在物理学中，功是力使物体发生位移时转移能量的量度。尽管功由力与位移这两个矢量计算而来，但功本身是标量。
The SI unit of work is the joule (J). One joule is the work done when a force of one newton moves an object one metre in the direction of the force.
功的国际单位是焦耳（J）。1 焦耳等于 1 牛顿的力使物体沿力的方向移动 1 米所做的功。
1 J = 1 N m = 1 kg m² s⁻²
Energy and work have the same unit because work is a transfer of energy.
能量与功具有相同单位，因为做功本质上就是能量的转移。
2. Work Done by a Constant Force | 恒力做功
For a constant force F acting on an object while the object is displaced by a distance s, the work done is given by:
当恒力 F 作用在物体上，且物体发生位移 s 时，做功的表达式为：
W = F s cos θ
Here, θ is the angle between the force vector and the displacement vector. The term F cos θ is the component of the force along the direction of displacement.
其中 θ 是力矢量与位移矢量之间的夹角。F cos θ 是力在位移方向上的分量。
Key cases to remember:
需要牢记的关键情况：
If θ = 0°, then W = Fs. The force is parallel to the displacement and does positive work.
如果 θ = 0°，则 W = Fs。力与位移同向，做正功。
If θ = 90°, then W = 0. The force is perpendicular to the displacement and does no work.
如果 θ = 90°，则 W = 0。力与位移垂直，不做功。
θ = 180°, then W = -Fs. The force is opposite to the displacement and does negative work.
如果 θ = 180°，则 W = -Fs。力与位移反向，做负功。
Friction and air resistance usually do negative work because they act opposite to the direction of motion. A force can also do zero work, such as the normal reaction force on an object sliding along a horizontal surface.
摩擦力和空气阻力通常做负功，因为它们与运动方向相反。某些力也可以不做功，例如水平面上滑动物体受到的支持力就不做功。
3. Work Done by a Variable Force and F-x Graphs | 变力做功与F-x图像
ith a single value of F. Instead, the work done is the area under the force-displacement graph.
当力不是恒量时，不能用一个 F 值直接代入 W = Fs cos θ 计算。此时，功等于力-位移图像下方的面积。
W = ∫ F · d s = area under a force-displacement graph
This relationship is especially useful for springs. For an ideal spring obeying Hooke's law, the force needed to stretch or compress the spring is proportional to the extension x:
这个关系对弹簧尤其重要。对于服从胡克定律的理想弹簧，拉伸或压缩弹簧所需的力与伸长量 x 成正比：
F = k x
e to stretch the spring from x = 0 to x = x is the area of a triangle under the F-x graph:
将弹簧从 x = 0 拉伸到 x = x 所做的功是 F-x 图像下方三角形的面积：
W = ½ × x × kx = ½ k x²
This work becomes elastic potential energy stored in the spring. The same calculation applies when a spring is compressed.
这个功转化为弹簧储存的弹性势能。压缩弹簧时也有相同计算。
4. Kinetic Energy and the Work-Energy Theorem | 动能与动能定理
Kinetic energy is the energy an object has because of its motion. For an object of mass m moving with speed v:
动能是物体由于运动而具有的能量。质量为 m、速度为 v 的物体：
Eₖ = ½ m v²
Kinetic energy is always positive or zero, never negative, because v² cannot be negative.
动能永远为正或零，不可能为负，因为 v² 不可能为负。
The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy:
动能定理指出，物体所受合外力做的总功等于物体动能的变化量：
Wnet = ΔEₖ = ½ m v² - ½ m u²
Here u is the initial speed and v is the final speed. This theorem is very useful because it gives a direct link between force, displacement and speed.
其中 u 是初速度，v 是末速度。动能定理非常有用，因为它直接将力、位移与速度联系起来。
If the net work is positive, kinetic energy increases; if it is negative, kinetic energy decreases; if it is zero, the object continues at constant speed.
若总功为正，动能增加；
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