Skip to content
04 - Work & Energy

Work & Energy

Work

  • If a force displaces or stops a moving body through a certain distance, the work is said to be done by the force on the body.
  • Dot product of force and displacement is called work.
\[ W=\bar{F}.\bar{d} \]
\[ W=Fd\cos\theta \]
  • SI unit of work is joule (\(J\)).
  • In particle physics, work is measured in electron volt (\(eV\)).
  • Dimensionally work is equivalent to \([ML^2T^2]\).

Positive Work

  • For \(0<90^o\), work done is positive.
  • Maximum positive work is done if \(\theta=0^o\)

Example

when an engine pulls a train.

Zero work

Work will be zero 1. When \(\theta=90^o\), (eg centripetal force and tension in pendulum string does not do any work) 2. When \(F=0\) 3. When \(d=0\), (eg car is not moving while its engine is running.)

Negative Work

  • For \(\theta>90^o\), work done is negative.
  • Maximum negative work when \(\theta=180^o\)

Example

Work done by frictional forces

Work from Graph

Graphically work can be obtained from force displacement graph The area under this graph is work done. Work is a scalar quantity.

  • Work done by constant force $$ \text{Area}=Fd=\text{work done} $$

To be completed...

Comments