Work
Introduced| English |
|---|
| work/wɜːk/ |
| joule/dʒuːl/ |
Sweat to carry a box — yet transfer nothing to it?
- Hold a heavy box and walk across a flat floor. Tiring, yes — but in physics you do no work on the box.
- Work needs a force and movement in the force's direction.
- Your upward hold is perpendicular to your sideways walk, so it transfers no energy to the box.
- Getting this right is the key to the whole energy story.
The definition of work
- Work 功 is force times the distance moved along the force: $W = F d \cos\theta$.
- $\theta$ is the angle between the force and the displacement.
- It is a scalar, measured in joules 焦耳 ($1\ \text{J} = 1\ \text{N}\cdot\text{m}$).
- Work is how energy is transferred to or from an object.
A rope pulls a sled $5\ \text{m}$ with $20\ \text{N}$ at $60^\circ$ ($\cos 60^\circ = 0.5$). How much work is done, in joules?
$W = Fd\cos\theta = 20 \times 5 \times 0.5 = 50\ \text{J}$.
Work is measured in ____ (the same unit as energy).
$1\ \text{J} = 1\ \text{N·m}$ — work and energy share the joule.
Only the aligned part counts
- Split the force into a part along the motion and a part perpendicular to it.
- Only the along-the-motion part, $F\cos\theta$, does work.
- A force at $90^\circ$ to the motion ($\cos 90^\circ = 0$) does zero work.
- That is why carrying the box level, or a satellite's circular orbit, involves no work.
Work on a slope
Change the slope and mass to see how much work must be done to move the block along it.
A force acts at $90^\circ$ to an object's motion. How much work does it do?
$\cos 90^\circ = 0$, so $W = Fd\cos 90^\circ = 0$. A perpendicular force does no work.
Positive, negative, and zero work
- Positive work: force has a component along the motion (a push that speeds you up).
- Negative work: force opposes the motion (friction, or catching a falling ball).
- Zero work: force is perpendicular, or there is no movement at all.
- Negative work removes energy; positive work adds it.
Which situation involves negative work being done on a moving box?
Friction points opposite the motion ($\theta = 180^\circ$, $\cos = -1$), so it does negative work — removing energy.
Select all cases where a force does zero work on an object.
Zero work needs $\cos\theta = 0$ (perpendicular) or $d = 0$ (no motion). A force along the motion does positive work.
No movement means no work, however hard you strain. Pushing on an immovable wall does zero work in physics. And a force perpendicular to the motion — like the tension in a whirling string — also does zero work.
Pushing hard on a wall that does not move still does a lot of work in the physics sense.
No displacement means $W = 0$, no matter how hard you push.
A rope pulls a sled $5\ \text{m}$ with a force of $20\ \text{N}$ at $60^\circ$ above the ground ($\cos 60^\circ = 0.5$).
- $W = Fd\cos\theta = 20 \times 5 \times 0.5 = 50\ \text{J}$.
Only the horizontal part of the pull, $20\cos 60^\circ = 10\ \text{N}$, does the work over the $5\ \text{m}$.
Work transfers energy: $W = Fd\cos\theta$ (a scalar, in joules). Only the force component along the motion does work, so a perpendicular force does zero work. Work is positive when it adds energy, negative when it removes it.