الشغل والطاقة والقدرة

Holding a bag does no work

• Hold a heavy bag still and your arm aches — but in physics you do zero work.
• Work needs the force to move something along its own direction.
• No movement (or a sideways force) means no work done 功.

Work done by a force

• $W = F s \cos\theta$, where $\theta$ is the angle between force and displacement 位移.
• Only the part of the force along the motion does work. Unit: $\text{J} = \text{N}\cdot\text{m}$.

Positive, negative, zero

• Force along the motion → positive work (energy given to the object).
• Force opposite the motion → negative work (e.g. friction takes energy away).
• Force at right angles → zero work.

Only the component F cos(theta) along the displacement does work

Conservation of energy 能量守恒

• Energy is never made or destroyed — it only changes form or moves between objects.
• In a closed system the total energy stays constant.

Positive work (force along motion) and negative work (force opposite motion)

Efficiency 效率

• $\text{efficiency} = \dfrac{\text{useful output}}{\text{total input}} \times 100\%$.
• It is always below $100\%$ — some energy ends up as "useless" thermal energy 热能.

The same work done in less time means more power

Power 功率

• Power is the rate of doing work: $P = \dfrac{W}{t} = \dfrac{\Delta E}{\Delta t}$.
• Unit: $\text{W} = \dfrac{\text{J}}{\text{s}}$.

Power, force and velocity

• For a force $F$ along the motion at speed $v$: $P = Fv$.
• A car at steady speed needs $P = F_{\text{resist}} \times v$; lifting a weight at speed $v$ needs $P = mgv$.

Worked example: a car at steady speed

Marks that slip away

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