Work, Energy and Power

What is Work?

• Work is a scalar product.
• It is defined as the scalar product of force and displacement.
• The formula for work is: Work = F • s = F cos(θ)
• The component of force in the direction of displacement when multiplied by the displacement is called work.

Unit and Dimension of Work

• Unit: Newton Metre (Joule)
• Dimension: [M L² T⁻²]

Work at Various Angles

• θ = 0°: Work = F • s (positive work)
• θ = 180°: Work = - F • s (negative work)
• θ = 90°: Work = 0 (no work)

Work Done for Constant Force

• If force and displacement are in the same direction, then Work = F × s
• Graphical Interpretation: The area under the graph represents work.

Work Done by Variable Force

• Using integration: Work = ∫ F(x) dx
• Work is the area under the force vs displacement curve.

Work Done by Different Forces

• Work of external force: F_ext • s
• Work of frictional force: F_friction • s (negative if opposite direction)
• Work by gravitational force and normal reaction: no work is done unless the force and displacement are in the same direction.

Numerical Example

• In problems, work is calculated according to the direction of force and displacement.
• The work formula varies for different forces.

Special Cases

• If the force is variable, work is derived by integrating.
• The area under the curve represents the work.

Case of Variable Force

• The area under the force vs displacement chart represents the total work done.

Points to Note

• Positive work: Giving energy
• Negative work: Taking energy

Understanding these concepts with practicals and examples is essential. In the following lectures, we will discuss the work-energy theorem, conservative and non-conservative forces.