Comprehensive notes for Chapter 4 Work, Energy and Power. Covers Work by Constant/Variable Forces, Power, Energy Types, Work-Energy Theorem, and Escape Velocity.
Definition: The dot product of force and displacement.
Formula: W = F . d = Fd cos θ.
Unit: Joule (J). 1 J = 1 N x 1 m.
Conditions:
Maximum Work: θ = 0° (cos 0° = 1).
Zero Work: θ = 90° (cos 90° = 0).
Negative Work: θ = 180° (cos 180° = -1).
When force magnitude or direction changes (e.g., rocket moving away from Earth, spring force).
Method: Divide path into small intervals (Δd) where force is approximately constant.
Formula: W = Σ (F cos θ Δd) = Limit(Δd→0) Σ F.Δd.
Graphically, it is the area under the Force-Displacement curve.
Conservative Field: Work done is independent of the path followed and work done in a closed path is zero. Example: Gravitational Field, Electric Field.
Non-Conservative Field: Work done depends on the path. Example: Frictional force, Air resistance.
The rate of doing work.
Formula: P = W / t = F . v.
Unit: Watt (W). 1 W = 1 J/s.
Commercial Unit: kWh (Kilowatt-hour). 1 kWh = 3.6 MJ.
Kinetic Energy (K.E): Energy due to motion. K.E = ½ mv².
Potential Energy (P.E): Energy due to position. P.E = mgh.
Work-Energy Theorem: Work done on a body equals the change in its kinetic energy. W = ΔK.E.
Work done in bringing a body from infinity to a point in the gravitational field.
Formula: U = - G Mm / r.
At Earth's surface (r=R): U = - G Mm / R.
The negative sign implies an attractive field.
The initial velocity required for an object to escape the Earth's gravitational field completely.
Formula: v_esc = √(2GM/R) = √(2gR).
Value for Earth: ~11.2 km/s.
For a falling body (ignoring friction): Loss in P.E = Gain in K.E.
With friction (f): Loss in P.E = Gain in K.E + Work done against friction (fh).