HKDSE Physics – Work, Energy and Power

HKDSE Physics Core
Chapter 4: Work, Energy and Power | 作功、能量與功率

Billy Sir’s Smart Notes: Master Mechanical Energy, Work Done, Energy Conservation, and Power.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握動能、勢能、機械能守恆及功率。

1. Work Done | 作功

Work is done when a force moves an object through a displacement in the direction of the force. 當力使物體沿力的方向產生位移時，便作了功。

⚙️ Formula for Work Done | 作功公式

W = F s \cos \theta

Positive Work (+W): Force and displacement are in the same direction (e.g., pushing a car). Energy is transferred to the object. (正功：力與位移同向，物體獲得能量)
Negative Work (-W): Force and displacement are in opposite directions (e.g., friction). Energy is transferred away from the object. (負功：力與位移反向，如摩擦力，物體失去能量)
Zero Work: Force is perpendicular to displacement ($ \theta = 90^\circ $). (零功：力與位移垂直)

2. Mechanical Energy | 機械能

Energy Type (能量類型)	Definition (定義)	Formula (公式)
Kinetic Energy (KE) 動能	Energy possessed by an object due to its motion. (物體因運動而擁有的能量)	$$ KE = \frac{1}{2}mv^2 $$
Gravitational Potential Energy (GPE) 重力勢能	Energy stored due to an object’s height above the ground. (物體因高度而儲存的能量)	$$ GPE = mgh $$
Elastic Potential Energy 彈性勢能	Energy stored in a stretched or compressed elastic object (e.g., a spring). (儲存於被拉伸或壓縮的彈性物體中的能量)	$$ E = \frac{1}{2}kx^2 $$

3. Conservation of Mechanical Energy | 機械能守恆

In an isolated system with no external forces (like air resistance or friction) doing work, the total mechanical energy remains constant. 在沒有外力（如空氣阻力或摩擦力）作功的孤立系統中，總機械能保持不變。

🔄 Conservation Formula | 守恆公式

KE_{initial} + PE_{initial} = KE_{final} + PE_{final}

🎯 Example: The Simple Pendulum | 例子：單擺

A swinging pendulum is a perfect example of energy conversion: (擺動的單擺是能量轉換的完美例子：)

Highest Point (Maximum Height): The bob momentarily stops. $ v = 0 $, so $ KE = 0 $. The energy is 100% GPE. (最高點：速度為零，動能為零，全部為重力勢能)
Lowest Point (Equilibrium Position): The height is zero (reference level). $ h = 0 $, so $ GPE = 0 $. The speed is maximum, so energy is 100% KE. (最低點：高度為零，重力勢能為零，速度最大，全部為動能)
At any point in between, the total energy is the sum of KE and GPE. Energy continuously transforms between KE and GPE, but the total amount remains constant.

4. Mechanical Power | 機械功率

Power is the rate at which work is done or energy is transferred. 功率是作功或轉移能量的速率。

⚡ Power Formulas | 功率公式

General formula for power (Unit: Watt, W or J s$^{-1}$):

P = \frac{W}{t} = \frac{\Delta E}{t}

For an object moving at a constant velocity ($ v $) against a constant force ($ F $):

$$ P = F v $$

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