Why does a roller coaster speed up after a dip?
That feeling of a sudden push is the same idea behind work, energy and power – the invisible forces that make everything move.
💡 In Simple Words: Work is what you do when you push or pull something and make it move. Energy is the stored ability to do work, like a battery waiting to power a toy. Power tells you how quickly the work gets done.
What is Work?
In physics, work means a force (a push or pull) acting over a distance. Imagine you’re pushing a shopping cart. If you push with a steady force and the cart rolls 5 meters, you’ve done work.
Formula: Work (W) = Force (F) × Displacement (d) × cosθ
- Force: the push or pull, measured in newtons (N).
- Displacement: how far the object moves, in meters (m).
- θ (theta): the angle between the force direction and the movement direction. If you push straight forward, cosθ = 1.
If the force is perpendicular to the motion (like a person sliding a book sideways while it falls), the work is zero because cos90° = 0.
Understanding Energy
Energy is the ability to do work. Think of it as money in a bank – you can spend it later. There are many forms, but the two we meet most in class 10 are kinetic energy (energy of motion) and potential energy (stored energy).
Kinetic Energy (KE)
Kinetic energy is what an object has because it’s moving. The faster it goes, the more KE it carries.
Formula: KE = ½ m v²
- m = mass (kg)
- v = speed (m/s)
Imagine a rolling ball. Double its speed and its kinetic energy becomes four times bigger – because the speed is squared.
Potential Energy (PE)
Potential energy is stored because of position or condition. The most common type in class 10 is gravitational potential energy, which depends on height.
Formula: PE = m g h
- g = acceleration due to gravity (≈9.8 m/s² on Earth)
- h = height above a reference level (m)
Think of a book on a shelf. The higher the shelf, the more work you’d need to do to lift the book there, and the more PE the book has.
Power – How Fast Work Happens
Power measures the rate at which work is done or energy is transferred. If you finish your homework quickly, you’re being “more powerful” in the study sense!
Formula: Power (P) = Work (W) / Time (t) or P = Force × Velocity when the force and motion are in the same direction.
Unit: watt (W), where 1 W = 1 joule per second.
Key Formulas at a Glance
| Concept | Formula | Unit |
|---|---|---|
| Work | W = F d cosθ | joule (J) |
| Kinetic Energy | KE = ½ m v² | joule (J) |
| Potential Energy | PE = m g h | joule (J) |
| Power | P = W/t = F v | watt (W) |
Worked Example: From Rest to a Rolling Sled
Suppose a 30 kg sled starts from rest at the top of a 5‑m hill and slides down without friction. Find the speed at the bottom.
- Calculate the loss in gravitational potential energy:
PE_initial = m g h = 30 × 9.8 × 5 = 1470 J. - Since there’s no friction, all that PE turns into kinetic energy at the bottom: KE = 1470 J.
- Use KE formula to get speed:
1470 = ½ × 30 × v² → v² = (1470 × 2) / 30 = 98 → v ≈ 9.9 m/s.
The sled reaches about 10 m/s. Notice how the energy “conserved” – it just changed form.
Quick Comparison: Work, Energy, Power
- Work – a one‑time transfer (force × distance).
- Energy – the stored version of work; can be kinetic or potential.
- Power – how fast the transfer happens (work per second).
📝 Likely Exam Questions
- Define work and give its SI unit.
Answer: Work is the product of a force applied in the direction of displacement and the distance moved. Unit: joule (J). - A 2 kg ball is thrown vertically upward with a speed of 10 m/s. Calculate its kinetic energy at launch and its maximum height.
Answer: KE = ½ × 2 × 10² = 100 J. Using PE = m g h, set PE = KE → 100 = 2 × 9.8 × h → h ≈ 5.1 m. - State the relationship between power, work and time, and give the unit of power.
Answer: Power = Work ÷ Time. Unit: watt (W), where 1 W = 1 J/s. - Explain why no work is done when you carry a heavy box across a level floor at constant speed.
Answer: The force you exert (upward) is perpendicular to the displacement (horizontal), so the angle θ = 90°, cosθ = 0, making work zero. - Calculate the power developed by a motor that lifts a 50 kg load through 2 m in 4 seconds.
Answer: Work = m g h = 50 × 9.8 × 2 = 980 J. Power = 980 J / 4 s = 245 W.