Work, Power And Energy
Definition Of Work : When a force is applied on an object to displace it from its initial position then it is said to be work is done. It is the Dot Product of Force and Displacement.
Types Of Work :
1 ) Positive Work : When the applied force and displacement of the objects take place in the same direction or at acute angle , then it is said to be positive work is done. That is the applied force and displacement are parallel to each other and angle between them is zero degree and the value of cos0 is 1 i.e
W = FS
W = FS cosθ
- Kicking of a football
- Moving a chair
- pushing and moving a table
- A car moving forward
- throwing a stone
2 ) Negative Work : When the applied force and displacement of the objects take place in the opposite direction, then it is said to be negative work is done. That is the applied force and displacement are antiparallel to each other and angle between them is 180 degree and the value of cos180 is ( – 1 ) i.e
W = -FS
- Two boys push each other
- In Tug of War when opponent team pulls hard.
- Trying to catch a heavy object, hands move down
3 ) Zero Work : When the applied force and displacement of the objects take place perpendicularly, then it is said to be zero work is done. That is the applied force and displacement are normal to each other and angle between them is 90 degree and the value of cos90 is 0 . when we apply a force on the object but it does not displace from its position, then there is zero work done .
W = 0
- Pushing a wall
- Walking on the road
- Motion of planet on its orbit
Summary of types of work
Unit Of Work :
1 ) SI – Unit —- Joule
2 ) CGS – Unit ——— erg
Dimension Of Work :
[ W ] = [ F ] [ S ] = [ MLT-2 ] [ L ] = [ ML2T-2 ]
Workdone By Variable Force :
In everyday life, most of the force are variable in nature.
Whenever we apply variable force on the object to displace it from its previous position, the workdone in this case may be termed as workdone by variable force.
Definition Of Power : The rate of doing work is called as Power.
Power = Work / time
P = dw / dt
where dw = small workdone
dt = time interval
It is the scalar product of Force and Velocity.
P = F . v
Unit Of Power :
1 ) SI – Unit : ( 1) Watt ( 2 ) J / Sec ( 3 ) N-m / sec
2 ) CGS unit : ( 1 ) gm – cm / sec ( 2 ) dyne – cm / sec
Dimension Of Power :
[ Power ] = [ Work ] / [ Time ] = [ ML2T-2 ] / [ T ] = [ ML2T-3 ]
Definition of energy :
The capacity of doing work is called energy.
Types Of Energy :
There are several types of energy which are given below:
- Mechanical Energy
- Chemical energy
- Atomic energy
- Light energy
- Sonic energy
- Wind energy
- Thermal energy
- Nuclear energy
- Electromagnetic energy
- Gravitational energy
- Ionization energy
- Electrical energy
- Heat energy
- Radiant energy
- Elastic energy
- Internal energy
These are not enough but in the syllabus of class – 11 physics, we will discuss only mechanical energy in detail.
Mechanical Energy :
The energy possessed by an object according to its structure, configuration, position and motion, is called as Mechanical energy .
There are two types of mechanical energy
- Kinetic energy
- potential energy
Kinetic energy :
The energy possessed by an object with respect to its motion, is termed as kinetic energy.
1 ) A moving car
2 ) Moving fan
3 ) The arrow flying through air when the string is released on the bow.
There are basically several types of kinetic energy
Rotational kinetic energy, Translational kinetic energy, Vibrational kinetic energy, Translational – rotational kinetic energy and etc.
Expression for kinetic energy :
u = initial velocity = 0 ( ∵ the object is initially at rest )
v = final velocity
a = acceleration
m = mass of the object
t = time
F = force applied on the object to displace it from its position
s = displacement
From Newton’s 2nd law of motion we have
F = ma —————————————— ( 1 )
From equation of motion we have
v2 = u2 + 2as
⇒ v2 = 2as
⇒ s = v2 / 2a
Now, workdone = force * displacement = ma * v2 / 2a = mv2 / 2
Potential energy :
The energy possessed by an object due to its configuration, structure and height is called as potential energy. This energy is associated with the objects at rest.
1 ) A stretched string
2 ) A coiled spring
3 ) A snow pack
4 ) A stretched rubber band
5 ) A rock sitting at the edge of cliff
6 ) A raised weight
7 ) stored water in a tank or dam
Expression Of The Potential Energy :
Let an object of mass ‘ m ‘ is raised to a height of ‘ h ‘. The work done in raising the object is stored in the form of potential energy.
∴ Potential energy = Force by which the object is raised * height = Weight * height = mgh
where g = acceleration due to gravity.
P.E = mgh