Work, Energy & Power
CLASS 11 PHYSICS • COMPREHENSIVE REVISION NOTES
1. WORK
Work is done when a force applied to an object causes a displacement in the direction of the force.
Mathematical Definition
For a constant force F causing a displacement d:
W = F · d = F d cos θ
• θ is the angle between the force and displacement vectors.
• SI Unit: Joule (J) or kg·m²/s² (1 J = 1 N·m).
• Dimensions: [M1 L2 T-2]
• Nature: Scalar quantity.
Types of Work
• Positive Work (θ < 90°): Force and displacement act in the same general direction (e.g., pulling a cart).
• Negative Work (90° < θ ≤ 180°): Force opposes displacement (e.g., work done by friction).
• Zero Work (θ = 90° or d = 0): Force acts perpendicular to displacement or no movement occurs (e.g., carrying a
load horizontally on your head).
Work Done by a Variable Force
When force varies with position x:
W = ∫x xf F(x) dx
i
Key Rule: On a Force–Displacement (F–x) graph, the area under the curve represents the total work done.
2. ENERGY
Energy is the capacity of a body to do work. It is a scalar quantity measured in Joules (J).
Kinetic Energy (K)
The energy possessed by a body due to its motion:
K = ½ m v²
Relation Between Kinetic Energy and Linear Momentum (p):
K = p² / (2m) ⟹ p = √(2mK)
Class 11 Physics • Work, Energy & Power Page 1 of 3
CLASS 11 PHYSICS • COMPREHENSIVE REVISION NOTES
1. WORK
Work is done when a force applied to an object causes a displacement in the direction of the force.
Mathematical Definition
For a constant force F causing a displacement d:
W = F · d = F d cos θ
• θ is the angle between the force and displacement vectors.
• SI Unit: Joule (J) or kg·m²/s² (1 J = 1 N·m).
• Dimensions: [M1 L2 T-2]
• Nature: Scalar quantity.
Types of Work
• Positive Work (θ < 90°): Force and displacement act in the same general direction (e.g., pulling a cart).
• Negative Work (90° < θ ≤ 180°): Force opposes displacement (e.g., work done by friction).
• Zero Work (θ = 90° or d = 0): Force acts perpendicular to displacement or no movement occurs (e.g., carrying a
load horizontally on your head).
Work Done by a Variable Force
When force varies with position x:
W = ∫x xf F(x) dx
i
Key Rule: On a Force–Displacement (F–x) graph, the area under the curve represents the total work done.
2. ENERGY
Energy is the capacity of a body to do work. It is a scalar quantity measured in Joules (J).
Kinetic Energy (K)
The energy possessed by a body due to its motion:
K = ½ m v²
Relation Between Kinetic Energy and Linear Momentum (p):
K = p² / (2m) ⟹ p = √(2mK)
Class 11 Physics • Work, Energy & Power Page 1 of 3
