Ever wondered why you feel tired after climbing stairs but a roller‑coaster seems to zoom without anyone pulling it?
💡 In Simple Words: Work happens when you push or pull something and it moves. Energy is the ability to do work, like the fuel in a car. Power tells you how fast that work gets done.
What is Work?
Work (capital W) is the product of a force (a push or pull) and the distance over which that force acts, but only the part of the motion that’s in the same direction as the force counts.
Formula: W = F × d × cosθ
- F = magnitude of the force (newtons, N)
- d = distance moved (metres, m)
- θ = angle between force direction and displacement direction
Think of water flowing through a pipe. The pressure is like the force, the length of pipe is the distance, and the flow only does useful work when the water moves straight along the pipe (θ = 0°).
Worked Example 1
A student pushes a 10 kg box across a floor with a constant horizontal force of 30 N for 5 m. How much work is done?
Since the force and motion are in the same direction, θ = 0° and cosθ = 1.
W = 30 N × 5 m × 1 = 150 J (joules, the unit of work).
Energy – The Ability to Do Work
Energy is a broader idea: it’s the capacity to perform work. There are many forms, but two that appear a lot in Class 10 are kinetic energy (energy of motion) and potential energy (stored energy).
Kinetic Energy (KE)
When something moves, it has kinetic energy. The formula is KE = ½ mv², where m is mass (kg) and v is speed (m/s). Faster or heavier objects carry more KE.
Potential Energy (PE)
Potential energy depends on position. The most common type in school is gravitational PE, given by PE = m g h. Here g is the acceleration due to gravity (≈9.8 m/s²) and h is the height above a reference level.
Imagine lifting a book onto a shelf. You’re giving it gravitational PE; the higher the shelf, the more PE you store.
Worked Example 2
A 2 kg ball is dropped from a height of 3 m. Find its kinetic energy just before it hits the ground (ignore air resistance).
Initial PE = m g h = 2 kg × 9.8 m/s² × 3 m = 58.8 J.
Because energy is conserved (PE converts to KE), KE just before impact = 58.8 J.
Power – How Quickly Work Happens
Power measures the rate at which work is done or energy is transferred. The formula is P = W / t, where t is time in seconds. The SI unit is the watt (W), equal to one joule per second.
Think of a kitchen blender. Two blenders might have the same motor power, but one finishes chopping faster because it delivers the same work in less time.
Worked Example 3
A crane lifts a 500 kg load through a height of 10 m in 20 s. What is the average power output?
First find work done (which equals the gain in gravitational PE): W = m g h = 500 kg × 9.8 m/s² × 10 m = 49,000 J.
Power P = W / t = 49,000 J / 20 s = 2,450 W (or 2.45 kW).
Quick Comparison: Work, Energy & Power
| Aspect | What it tells you | Unit | Typical formula |
|---|---|---|---|
| Work | Amount of force‑displacement product | Joule (J) | W = F d cosθ |
| Energy | Capacity to do work | Joule (J) | KE = ½ mv², PE = m g h |
| Power | How fast work or energy is transferred | Watt (W) | P = W / t |
Common Mistakes to Avoid
- Forgetting the cosine factor when force isn’t along the displacement direction.
- Mixing up work (J) with power (W) – remember power adds “per second”.
- Assuming all forces do work; friction can do negative work, taking energy away.
📝 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 d cosθ). Its unit is the joule (J). - A 50 N force pulls a crate 8 m horizontally. Calculate the work done.
Since force and motion are parallel, θ = 0°, cosθ = 1. W = 50 N × 8 m = 400 J. - State the formula for kinetic energy and compute the KE of a 0.5 kg ball moving at 4 m/s.
KE = ½ mv² = 0.5 × 0.5 kg × (4 m/s)² = 4 J. - A motor lifts a 200 kg load 5 m in 10 s. Find the average power output.
Work = m g h = 200 kg × 9.8 m/s² × 5 m = 9,800 J. Power = 9,800 J / 10 s = 980 W. - Explain why a ball rolling on a rough surface loses kinetic energy.
The rough surface exerts a frictional force opposite to the motion, doing negative work. This converts kinetic energy into heat, reducing the ball’s KE.