Chapter Overview
Work, Energy, and Power provide an alternative approach to mechanics problems, often simpler than using Newton’s laws directly. This chapter introduces scalar quantities that help analyze motion through energy considerations rather than forces.
What You’ll Learn
By the end of this chapter, you’ll be able to:
- Calculate work done by constant and variable forces
- Apply the work-energy theorem to solve problems
- Distinguish between kinetic and potential energy
- Use conservation of mechanical energy
- Analyze motion in vertical circles
- Understand elastic and inelastic collisions
Prerequisites
Before starting this chapter, you should be comfortable with:
- Newton’s Laws of Motion
- Basic calculus (integration for variable forces)
- Vector dot product
Learning Path
Follow these topics in order for the best understanding:
- Work Done by Forces
- Kinetic Energy
- Work-Energy Theorem
- Potential Energy
- Conservation of Energy
- Vertical Circular Motion
- Power
- Collisions
Topics in This Chapter
Foundation
| Topic | Description | Time |
|---|---|---|
| Work Done by Forces | Work by constant and variable forces, sign convention | 4 min |
| Kinetic Energy | Energy of motion, relation with momentum | 3 min |
Core Concepts
| Topic | Description | Time |
|---|---|---|
| Work-Energy Theorem | Net work equals change in kinetic energy | 3 min |
| Potential Energy | Gravitational and spring potential energy | 4 min |
| Conservation of Energy | Conservative forces and energy conservation | 4 min |
Advanced Topics
| Topic | Description | Time |
|---|---|---|
| Vertical Circular Motion | Minimum speeds, tension in string | 4 min |
| Power | Rate of doing work, instantaneous and average power | 3 min |
| Collisions | Elastic, inelastic collisions, coefficient of restitution | 5 min |
Concept Map
graph TD
A[Work, Energy & Power] --> B[Work]
A --> C[Energy]
A --> D[Power]
A --> E[Collisions]
B --> B1[Constant Force]
B --> B2[Variable Force]
C --> C1[Kinetic Energy]
C --> C2[Potential Energy]
C --> C3[Conservation Laws]
E --> E1[Elastic]
E --> E2[Inelastic]Quick Reference
Key Formulas
| Concept | Formula |
|---|---|
| Work (constant force) | $W = \vec{F} \cdot \vec{s} = Fs\cos\theta$ |
| Work (variable force) | $W = \int \vec{F} \cdot d\vec{r}$ |
| Kinetic Energy | $KE = \frac{1}{2}mv^2 = \frac{p^2}{2m}$ |
| Work-Energy Theorem | $W_{net} = \Delta KE$ |
| Gravitational PE | $U = mgh$ |
| Spring PE | $U = \frac{1}{2}kx^2$ |
| Power | $P = \frac{dW}{dt} = \vec{F} \cdot \vec{v}$ |
| Coefficient of Restitution | $e = \frac{v_2 - v_1}{u_1 - u_2}$ |
Important Values
| Constant | Value |
|---|---|
| 1 horsepower | 746 W |
| 1 kWh | $3.6 \times 10^6$ J |
| Elastic collision | $e = 1$ |
| Perfectly inelastic | $e = 0$ |
JEE Weightage
Exam Focus
- JEE Main: 2-3 questions typically from this chapter
- High-yield topics: Work-energy theorem, conservation problems, collisions
- Common mistakes: Sign errors in work calculation, forgetting non-conservative forces
Start Learning
Ready to begin? Start with the first topic: → Work Done by Forces