Work done and energy transfer
When a force moves an object, the force does work on the object. The energy transferred equals the work done.
Equation
$W = Fs$
- $W$ — work done, in joules (J).
- $F$ — force in newtons (N), parallel to motion.
- $s$ — distance moved in the direction of the force, in metres (m).
1 joule = 1 newton-metre.
If the force is at an angle $\theta$ to the motion, only the component along motion does work: $W = Fs\cos\theta$ (HT).
Where does the energy go?
- Lifting a weight against gravity → energy goes to its gravitational potential store.
- Pushing a box across a rough floor against friction → energy goes to thermal stores of the box and floor (warming them).
- Compressing a spring → energy goes to its elastic potential store.
✦Worked example— Worked example 1
You pull a 50 kg crate 8 m horizontally with a 200 N force. Work done?
- $W = Fs = 200 \times 8 = 1600$ J.
✦Worked example— Worked example 2
Lift a 5 kg book from floor to a 1.5 m shelf. Work done against gravity?
- Force needed = weight = mg = 5 × 9.8 = 49 N.
- W = Fs = 49 × 1.5 = 73.5 J.
This 73.5 J is now stored in the book's gravitational potential store.
Why work-against-friction warms surfaces
When you push a box at constant velocity, the applied force equals friction (zero net force, no KE gain). Yet you're still doing work — where does the energy go? Into thermal stores of the box and floor (the "heat of friction"). Useful for hand-warming, less useful in engines.
⚠Common mistakes
- Forgetting that distance must be in the direction of the force.
- Saying work is done when an object is held still — if it doesn't move, no work is done.
- Using mass instead of force (need to convert via mg first).
- Forgetting units: J = N × m.
AI-generated · claude-opus-4-7 · v3-deep-physics