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Work-Power-Energy
Work-Power-Energy
LEARNING OBJECTIVES:
¨ Work and it’s nature.
¨ Expressions for workdone in different cases.
¨ Energy and it’s forms.
¨ Relation betwen K.E and linear momentum.
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 heat 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) \( W = mgh/4 \)
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
¶¶ POSITIVE WORK:
Workdone is said to be positive if applied force or one of it’s components is in the direction of displacement.
therefore W=FScos0°=positive.
If the force is in the same direction as the displacement, then the angle is 0 degrees
EXAMPLES:
1.Workdone by the gravitational force on a freely falling body is positive.
2.When a spring is stretched ,both the stretching force and displacement act in the same direction so workdone is positive.
3.When a block is lifted from the ground the workdone by lifting force is positive.
4.When a horse pulls a cart the applied force and displacement are in the same direction so work done by horse is positive.
¶¶ NEGATIVE WORK:
Workdone by a force is said to be negative if the applied force has a component in a direction opposite to that of the displacement.
EXAMPLES:
1.When a body is dragged on rough surface,workdone by frictional force is negative.
2.Workdone by the gravitational force on a vertically projected up body is negative.
¶¶ ZERO WORK:
If a body displaces perpendicular to the direction of force then the workdone is zero.
If there is no displacement then workdone is zero.
EXAMPLES:
1.A person carriyng a load and moving horizontally on a platform does no work against gravity.
2.When abody moves in a circle the workdone by the centripetal force is zero.
3.The tension in the string of a simple pendulum is always perpendicular to it’s displacement so,workdone by tension is zero.
4.A person carrying a load on his head and standing at a given place is zero.
EXPRESSIONS FOR WORKDONE IN DIFFERENT CASES
1) The work done in lifting a body of mass m having density d1 inside a liquid of density d2 through a height h is (a=0) \( W = mgh\left( {1 - \frac{{d_2 }} {{d_1 }}} \right) \)
2) A point sized sphere of mass m is suspended vertically using a string of length l . If the bob is pulled to a side till the string makes an angle \(\theta\) with the vertical, work done against gravity is \( W = mgl(1 - Cos\theta ) \)
3) A uniform rod of mass m and length l is suspended vertically. If it is lifted to a side till it makes an angle \(\theta\) to the vertical , work done against gravity is \( \text{W} = \frac{{\text{mg}}} {\text{2}}\text{(1} - \text{Cos}\theta \text{)} \)
4) A uniform chain of mass m and length is suspended vertically. If the lower point of the chain is lifted to the point of suspension, work done against gravity is \( W = mgl/4 \)
5) A uniform chain of mass m and length ‘l’ is kept on a table such that \( 1/n^{^{th} } \) of its length is hanging down vertically from the edge of the table. The work done against gravity to pull the hanging part on to the table is \( W = \frac{{mgl}} {{2n^2 }} \)
6) A bucket full of water of total mass M is pulled up using a uniform rope of mass m and length l , work done is \( W = Mgl + mg1/2 = \left( {M + m/2} \right)gl \) (Bucket is treated as point mass)
7) If a body of mass m slides down distance S, work done by gravity is \( \text{W} = \text{(mg}\text{Sin}\theta \text{)S} \) ( \(\theta\)is inclination to the horizontal)
8) A block of mass m is suspended vertically using a rope of negligible mass. If the rope is used to lift the block vertically up with uniform acceleration a, work done by the tension in the rope is W = m(g+a) h (h is distance through which it is lifted up)
In the above case if the block is lowered with acceleration a W = m (a-g)