Topics Covered
10 key topics in this chapter
Study Resources
Key Concepts
01. Scientific Definition of Work
Work is done when a force causes displacement. W = Fs cosθ, where θ is the angle between force and displacement. Work is zero if displacement is zero or if force is perpendicular to displacement (θ = 90°). SI unit: Joule (J = N·m).
02. Positive, Negative & Zero Work
Positive work: force and displacement in same direction (θ < 90°). Negative work: force opposes displacement (θ = 180°, e.g., friction while sliding). Zero work: θ = 90° (e.g., carrying a book horizontally).
03. Kinetic Energy
KE = ½mv² — energy possessed by a body due to its motion. Doubling mass doubles KE; doubling speed quadruples KE. KE is always positive. Units: Joule (J).
04. Work–Energy Theorem
Net work done on a body equals the change in its kinetic energy: W_net = ΔKE = ½mv² − ½mu². This connects kinematics with energy concepts.
05. Potential Energy & Conservation
Gravitational PE = mgh. At any point in free fall: Total Energy = KE + PE = constant. As object falls, PE decreases and KE increases by same amount. This is the law of conservation of mechanical energy.
06. Power
Power = work done / time = W/t = Fv. SI unit: Watt (W = J/s). Commercial unit: kilowatt-hour (kWh). 1 kWh = 3.6 × 10⁶ J. Used to calculate electricity bills.
Formulas at a Glance
| # | Name | Expression | Notes |
|---|---|---|---|
| 01 | Work | W = Fs cosθ |
Force × displacement × cosθ (J) |
| 02 | Kinetic Energy | KE = ½mv² |
Energy of motion (J) |
| 03 | Potential Energy | PE = mgh |
Gravitational potential energy (J) |
| 04 | Power | P = W/t = Fv |
Rate of doing work (W = J/s) |
| 05 | Work-Energy Thm | W_net = ½mv² − ½mu² |
Net work = ΔKE |
| 06 | Unit Conversion | 1 kWh = 3.6 × 10⁶ J |
Commercial energy unit |
Important Notes
Exam Tips & Common Mistakes
Always check the angle θ between force and displacement before applying W = Fs cosθ.
"Calculate the electricity bill" numericals: find energy in kWh = (power in kW) × (time in hours), then multiply by rate per kWh.
When asked for total mechanical energy at any point in free fall — always equal to mgh (the initial PE).
Work done by friction is always negative — friction acts opposite to displacement.
"A body is lifted at constant speed" → a = 0 → F_lift = mg, and W_lift = mgh (cos 0°). A standard 3-mark numerical.