Why do we care about work, energy and power?
Ever wondered why a bike can zip uphill but a car needs fuel? That's work, energy and power in action.
💡 In Simple Words: Work is what you do when you move something, energy is the ability to do work, and power tells you how fast the work gets done. Think of work as the distance you push a shopping cart, energy as the battery inside it, and power as how quickly you reach the checkout.
What is Work?
Work (capital W) is a measure of how much force you apply to move something over a distance. Force is a push or pull, and distance is how far the object travels in the direction of the force. The formula is Work = Force × Distance × cosθ, where θ is the angle between the force and the direction of motion.
Imagine you’re pulling a sled across snow. If you pull with a steady force of 20 N for 5 m straight ahead, the work you do is 20 × 5 = 100 J (joules). A joule is just a tiny amount of work, like the energy needed to lift a small apple one meter.
What is Energy?
Energy is the ability to do work. It comes in many flavours – kinetic (energy of motion), potential (stored energy), thermal, chemical, etc. The key idea is that if something has energy, it can make something else move or change.
Think of a stretched rubber band. It holds potential energy because you can release it and it will snap back, doing work on anything it hits.
What is Power?
Power tells you how quickly work is done or energy is transferred. The formula is Power = Work ÷ Time or Power = Energy ÷ Time. The unit is the watt (W), where one watt equals one joule per second.
If you lift that same 20‑N box 5 m in 2 seconds, the power is 100 J ÷ 2 s = 50 W. A 100‑W light bulb uses energy faster than a 40‑W bulb, so it feels brighter.
How Work, Energy and Power Connect
All three are linked by simple equations:
- Work (J) = Force (N) × Distance (m)
- Energy (J) = Work (J) (they are numerically the same)
- Power (W) = Work (J) ÷ Time (s)
Remember the water‑pipe analogy: force is the water pressure, distance is the length of pipe, work is the total amount of water pushed through, and power is how fast the water flows.
Worked Example: Lifting a Box
Suppose you lift a 15‑kg textbook from the floor to a shelf 1.2 m high in 3 seconds. Find the work done, the gravitational potential energy gained, and the power required.
- Work done: The force you need equals the weight (mass × gravity). Gravity ≈ 10 m/s² for easy math, so weight = 15 kg × 10 = 150 N. Work = 150 N × 1.2 m = 180 J.
- Energy gained: The textbook’s potential energy increase is the same 180 J (energy stored because it’s higher).
- Power: Power = 180 J ÷ 3 s = 60 W.
So you did 180 joules of work, gave the book 180 joules of potential energy, and used 60 watts of power.
Quick Comparison Table
| Concept | What it Measures | Unit | Typical Example |
|---|---|---|---|
| Work | Force × distance (how much you move something) | Joule (J) | Pushing a crate 10 m |
| Energy | Ability to do work (stored or in motion) | Joule (J) | Battery powering a torch |
| Power | Rate of doing work (how fast) | Watt (W) | Running a 60‑W bulb |
Common Mistakes to Avoid
- Mixing up force and work – force alone isn’t work; you need distance too.
- Ignoring the angle θ – if you pull sideways, only the component along the motion counts.
- Using the wrong time unit – power needs seconds, not minutes.
📝 Likely Exam Questions
- Question: A student pulls a sled with a constant force of 30 N for 8 m. Calculate the work done.
- Answer: Work = 30 N × 8 m = 240 J.
- Question: A 2‑kg ball is dropped from 5 m height. Find its kinetic energy just before hitting the ground (take g = 10 m/s²).
- Answer: Potential energy lost = mgh = 2 × 10 × 5 = 100 J, which becomes kinetic energy = 100 J.
- Question: A motor lifts a 50 kg load 3 m in 5 seconds. Determine the power output.
- Answer: Force = mg = 50 × 10 = 500 N; Work = 500 × 3 = 1500 J; Power = 1500 J ÷ 5 s = 300 W.
- Question: Explain the difference between kinetic and potential energy with everyday examples.
- Answer: Kinetic energy is the energy of motion (a rolling ball). Potential energy is stored energy due to position or shape (a stretched spring).
- Question: A 100‑W bulb is switched on for 2 hours. How much energy does it consume?
- Answer: Energy = Power × time = 100 W × 2 h × 3600 s/h = 720 000 J (or 0.2 kWh).