Ever wondered why a cyclist can zip up a hill while you struggle with a grocery bag?
💡 In Simple Words: Work is what you do when you push or pull something and it moves. Energy is the ability to do work, like a battery storing power for a toy. Power tells you how fast the work gets finished, like finishing a race in less time.
What is Work?
In physics, work isn’t just any effort. It’s the product of a force (a push or pull) and the displacement (how far the object moves) in the direction of that force.
Think of water flowing through a pipe. The pressure that pushes the water is like the force, and the length of pipe the water travels is the displacement. If the pipe is straight, the water does the most work.
Mathematically, work (W) = Force (F) × Displacement (s) × cosθ, where θ is the angle between the force and the direction of motion. If you push straight ahead, θ = 0° and cosθ = 1, so the formula simplifies to W = F × s.
Worked Example 1
A student pushes a 5 kg box across the floor with a constant force of 20 N for 3 m. How much work is done?
- Force = 20 N, Displacement = 3 m, θ = 0° (force is along the motion).
- Work = 20 N × 3 m × 1 = 60 J (joules, the unit of work).
So the student does 60 J of work on the box.
Energy: The Ability to Do Work
Energy is the capacity to perform work. It comes in many forms, but the two you’ll meet most in class are kinetic energy (energy of motion) and potential energy** (stored energy due to position).
Imagine a roller‑coaster at the top of a hill. It has lots of potential energy because of its height. As it zooms down, that stored energy turns into kinetic energy, letting the coaster move fast.
Kinetic Energy Formula
Kinetic energy (KE) = ½ m v², where m is mass and v is speed. The faster something moves, the more kinetic energy it carries.
Potential Energy Formula
Gravitational potential energy (PE) = m g h, where g is the acceleration due to gravity (≈9.8 m/s²) and h is height above a reference level.
Worked Example 2
A 2 kg ball is dropped from a height of 5 m. Find its potential energy at the top and kinetic energy just before it hits the ground (ignore air resistance).
- PE = m g h = 2 kg × 9.8 m/s² × 5 m = 98 J.
- When the ball reaches the ground, all that PE becomes KE, so KE ≈ 98 J.
This shows how energy can change form but the total amount stays the same (the principle of conservation of energy).
Power: How Quickly Work Is Done
Power measures the rate at which work is performed or energy is transferred. It’s like checking how fast a water tap is flowing.
Power (P) = Work (W) ÷ Time (t). The SI unit is the watt (W), equal to one joule per second.
Worked Example 3
It takes 10 seconds for a person to lift a 30 kg weight 2 m high. What’s the power output?
- First find work: Work = m g h = 30 kg × 9.8 m/s² × 2 m = 588 J.
- Power = 588 J ÷ 10 s = 58.8 W.
The person’s average power is about 59 watts.
Quick Comparison Table
| Concept | What It Tells You | Formula | Unit |
|---|---|---|---|
| Work | Amount of force applied over a distance | W = F s cosθ | Joule (J) |
| Energy | Capacity to do work | KE = ½ m v², PE = m g h | Joule (J) |
| Power | How fast work or energy changes | P = W/t | Watt (W) |
Key Points to Remember
- Work only happens when a force moves an object in the force’s direction.
- Energy can change form but never disappears (conservation).
- Power is a rate – more power means the same work done in less time.
- All three share the same unit of energy (joule) except power, which adds “per second”.
📝 Likely Exam Questions
- Define work and state its SI unit.
Work is the product of the component of force in the direction of displacement and the displacement itself (W = F s cosθ). Its unit is the joule (J). - A 10 kg crate is pulled 4 m across a floor with a force of 15 N at 30° to the horizontal. Calculate the work done.
Component of force = 15 N cos30° = 13 N. Work = 13 N × 4 m = 52 J. - State the formula for kinetic energy and compute the KE of a 0.5 kg ball moving at 6 m/s.
KE = ½ m v² = 0.5 × 0.5 kg × (6 m/s)² = 9 J. - Explain the difference between power and energy with an everyday example.
Energy is the total amount of work possible (like the fuel in a car). Power tells how quickly that energy is used (like how fast the car accelerates). A 1000‑W heater uses the same energy as a 500‑W heater in half the time. - A motor does 200 J of work in 5 s. What is its power output?
Power = Work ÷ Time = 200 J ÷ 5 s = 40 W.