Work is said to be done by a force on a body, if the body moves in
any direction except at 900 from force.
It is defines as the scalar product of force vector and displacement vector.
i.e.
W = FScos
Where
is anbgle between
It is scalar quantity. It's SI unit is
Joule (Kgm
2s-2) and cgs unit is (gcm
2s-2). It's dimensional formula is [ML
2T-2]
If
is anbgle between
< 900 then work done will be positive
i.e. w = Fscos
= positive works
For eg: When oject is falling freely under the action of gravity than work done by gravitational force an the
object is an example of positive work.
If
= 900 then work done wil
be zero
i.e. w = Fscos900 w = zero work
For eg: When a man carrying a load on his head and moving on a horizontalroad then work done by man on the load
is an example of zero workdone.
If
< 900 1800 then work
done wil be negative
i.e. w = Fscos1800 w = Negative work
For eg: When object is thrown verticaly upward against the gravity then workdone by gravitational force on
the object is an example of negative work.
Energy:
The capacity of doing work is called energy. It is scalar quantity and its unit in SI syste is joule and cgs is
erg. Dimensional formula is [ML
2T-2] 1 J = 107 erg.
Various Forms Of Energy are:
Heat Energy
Light Energy
Electrical Energy
Mechanical Energy(Kinetic Energy + Potential Energy)
Kinetic Energy:
The energy possess by an object due to it's motion is called
Kinetic Energy. Expression For K.E.
Consider an object mass "m " is initially at rest. Suppose
a constant force 'F' is applied on object to produce a displacement
Now, work
done by constant force, W =
.
W =
Fscosϴ (Where ϴ is angle between F and S vector) W = Fscos0 W = Fs W = mas ..........i)
F = ma
where a is the acceleration of object. If v be the final speed attained by an object then from equation of motion
v2 = u2 + 2as we ca write: v
2 = 02 + 2as (since u=0) v
2 = 2as v
2 / 2 = as ..........ii)
From eqn i) and ii), we get,
w = m × v2 / s w = 1/2 mv2
This work done is equal to kinetic energy
Kinetic energy = 1/2 mv2 .........iii)
Work Energy Theorem
The total work done by a force acting on a body is equal to total change in
it's kinetic energy. i.e, Total workdone = Total change in knetic energy
Proof:,
Consider an object mass 'm' is moving with constant speed 'u'. Suppose a constant force F vector is
applied on object is produce a displacement S vector. Now, workdone by constant force W =
.
W =
Fscosϴ (Where ϴ is angle between F and S vector) W = Fscos0 W = Fs W = mas .......i) (since f =
ma where
'a' is acceleration of a object)
If v be the final speed attained by an object then from equation of motion v
2 = u2 + 2as Now from eqn i) and ii)
W = 1/2 mv2 - 1/2
mu2
Total work done = final K.E - Initial K.E Therefore, Total work done = Total change in
kinetic energy which is work energy theorem.
Potential energy:
The energy possesses by an object due to its position or configuration is
called potential energy.
Gravitational Potential Energy = mgh Elastic Potential Energy = 1/2
kx2
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