Work is Sneaky

Why it matters

A porter carries your suitcase across a flat platform for a kilometre, sweating. Physics says he did ZERO work on it. Physics needs to explain itself.

The idea in plain words

The definition every mark scheme wants. Tap each term.

W = F × S × cos θ

A boy lifts a 3 kg bag 1.5 m up (g = 10 m/s²). Work done?

W = 45 J

• joule (J): W — work done — energy transferred by the force
• newton (N): F — the applied force
• metre (m): S — displacement of the point of application
• the sneaky part: cos θ — only the component ALONG the motion works: θ=0°→1, θ=90°→0
• F = mg = 30 N, straight up, motion up → θ = 0
• W = mgh = 30 × 1.5

Predict first

You pull a crate with 50 N at 90° to its motion (straight up) while it slides 4 m. Work done by your pull?

W = FS cos θ, and cos 90° = 0. Only the part of the force ALONG the motion counts — a sideways force just tags along.

• 0 J — correct
• 200 J
• 50 J

What you do

Drag the crate at different angles. Find the angle where honest effort earns zero work, then make exactly 200 J two different ways.

Check yourself

The porter walking horizontally with a suitcase does no work on it because…

The force he applies is UP, the displacement is SIDEWAYS — cos 90° = 0. (He does work on his own muscles, not the bag.)

Work done is negative when…

cos 180° = −1: friction takes energy OUT of the moving body — negative work.

1 joule equals…

J = N·m along the line of action. Time is nowhere in work — that's power's business.

• his supporting force is vertical, the motion is horizontal (θ = 90°) — correct
• the suitcase isn't moving
• friction cancels his work
• the force opposes the motion (like friction), θ = 180° — correct
• the force is small
• work can't be negative
• 1 newton moving something 1 metre along the force — correct
• 1 newton for 1 second
• 1 kg at 1 m/s