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.
W = FScos
is anbgle between
It is scalar quantity. It's SI unit is
2s-2) and cgs unit is (gcm
2s-2). It's dimensional formula is [ML
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.
= 900 then work done wil
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.
< 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.
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:
Mechanical Energy(Kinetic Energy + Potential 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
done by constant force, 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
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 =
Fscosϴ (Where ϴ is angle between F and S vector) W = Fscos0 W = Fs W = mas .......i) (since f =
'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
Total work done = final K.E - Initial K.E Therefore, Total work done = Total change in
kinetic energy which is work energy theorem.
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
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