Recall and use the equation for mechanical working W = F d = ΔE

1.7.2 Work

Work is the energy transferred when a force moves an object over a distance. Think of it like the effort you put into moving a heavy backpack up a flight of stairs – the more force you apply and the farther you move, the more work you do.

Key Formula

For a constant force acting along the direction of motion, the work done is:

$W = F \, d = \Delta E$

• $F$ = force applied (in newtons, N)
• $d$ = displacement in the direction of the force (in metres, m)
• $\Delta E$ = change in mechanical energy (in joules, J)

Units Cheat‑Sheet

Analogy: The Push‑and‑Carry Game 🎮

Imagine you’re playing a game where you have to push a heavy box across a hallway. The harder you push (larger $F$) and the farther you move it (larger $d$), the more “points” (work) you earn. If you push with a force of 30 N for 4 m, you earn $30 \times 4 = 120$ J of points.

Step‑by‑Step Example

1. Identify the force: A worker pushes a 12 kg crate with a horizontal force of 60 N.
2. Measure the displacement: The crate slides 3.5 m along the floor.
3. Calculate work: $W = 60 \, \text{N} \times 3.5 \, \text{m} = 210 \, \text{J}$.
4. Interpretation: The worker has transferred 210 J of mechanical energy to the crate.

Quick Check Quiz

• What is the work done if a force of 25 N moves an object 8 m? $200$ J
• True or False: Work can be negative if the force opposes the displacement. True
• Which unit is used for work? Joule (J)

Remember!

• Work is a scalar quantity – it has magnitude but no direction.
• Work is only done when the force has a component along the direction of motion.
• Positive work increases the system’s energy; negative work decreases it.