Work, Energy and Power – Understanding How Energy Moves

Introduction

Whenever you lift a bag, climb stairs or ride a bicycle, you are doing work and using energy. In this lesson we connect work, energy and power in a gentle way so that you can solve problems with confidence.

Background / Prerequisites

You should be familiar with:

• Basic idea of force and displacement.
• Simple algebra (multiplication, division).

Core Concepts

• Work describes how a force causes displacement.
• Energy is the ability to do work.
• Power tells us how fast work is done.

Detailed Explanation

Work

For a constant force in the direction of motion:

\[ W = F \cdot s \]

Work is positive when force and displacement are in the same direction, and negative when they oppose each other.

Kinetic Energy

\[ K = \frac{1}{2} m v^2 \]

Potential Energy

\[ U = m g h \]

Work–Energy Theorem

\[ W_{\text{net}} = \Delta K \]

Power

\[ P = \frac{W}{t} \]

Measured in watts (W).

Examples / Applications

Example 1 – Lifting a Bag

You lift a 5 kg bag by 2 m at constant speed:

\[ W = m g h = 5 \times 9.8 \times 2 \approx 98,\text{J} \]

Example 2 – Stopping a Moving Bike

A 60 kg bike moving at 5 m/s:

\[ K_i = \frac{1}{2} \times 60 \times 25 = 750,\text{J} \]

Brakes do -750 J of work to stop it.

Common Mistakes & Tips

• Mixing up force and work.
• Ignoring direction of force relative to displacement.

Summary / Key Takeaways

• Work links force and displacement.
• Energy comes in different forms; mechanical energy often combines kinetic and potential.
• Power measures how quickly work is done.

Further Reading / Related Topics

• Conservation of mechanical energy.
• Power rating of appliances.
• Non-conservative forces.