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...