Work
Real life applications :
. The main advantage of using Work and Energy methods is that it allows you to easily find the velocity of a body or system of bodies knowing how much "work" went into the system (provided energy is conserved, and there are no frictional losses)
. We can apply the work energy methods In our dialy life in order to convert one form of energy into another form.
. In the field of space, for a space shuttle heat proof tiles are needed to protect it from the heat resulting from doing work against the drag with a lot of KE so what must be the strength of
proof tile can be calculated by work energy methods.
. To produce the electricity the energy of wind movement performs work when it turns a Wind Turbine.
. In the field of mechanics,To run our vehicles the chemical energy in gasoline performs work on a piston, which in turn performs work on a vehicle to create kinetic energy.
. Work is performed on air as it enters a Jet Engine to speed up the air, which results in higher kinetic energy of the air particles, which pushes the airoplane.
Important Formulae :
1) \( W = \overline F .\overline S = FSCos\theta \)
2) \( W = mgh\left( {1 - \frac{{d_2 }} {{d_1 }}} \right) \)
3) \( W = mgl(1 - Cos\theta ) \)
4) \( \text{W} = \frac{{\text{mg}}} {\text{2}}\text{(1} - \text{Cos}\theta \text{)} \)
5) \( W = \frac{{mgl}} {4} \)
6) \( W = \frac{{mgl}} {{2n^2 }} \)
7) \( \text{W} = \text{(mg}\text{Sin}\theta \text{)S} \)
8) W = m(g+a) h
9) \( p = \sqrt {2mE} \)
10) P.E.=mgh
11) \( W = \frac{1} {2}mv^2 - \frac{1} {2}mu^2 \)
12) \( P = \frac{\text{w}} {\text{t}} \)
13) \( P = \mathop F\limits^ \to .\mathop V\limits^ \to \)
14) \( P = n\left( {\frac{1} {2}mv^2 } \right) \)
15) \( p = \frac{{mgh}} {t} \)
WORK
In ordinary language the word ‘’Work’’ means any physical or mental activity but in physics, Work is said to be done by a force if the point of application of force undergoes displacement either in the direction of force or in the direction of component of force.
Amount of work done is equal to the dot product of force and displacement. If \(\overline F\) is the force acting on a body and \(\overline S\) is displacement,
i.e. \( W = \overline F .\overline S = FSCos\theta \)
Since work is the dot product between force and displacement it is a scalar quantity.
Units of work : erg in CGS system, joule in S I system
Conversion: one joule = 107 erg