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Work-less force: When a force is applied vertically in the direction of displacement of the body. Then that force does not perform any work. That is known as work-less force.
We know, W = PCosθ ✕ S
Where,
W = Work
P = Force
θ = angle of applied force with displacement of body
S = Displacement
Now, if the value of θ = 90° (i.e. the force is applied vertically in the direction of displacement of the body)
Then, W = P Cos90° ✕ S = 0. Therefore here P is a work-less force.
Example 1
If a coolie carries loads on his head and walks horizontally then no works is done against the force of gravity. Here the displacement of the load is normal to the direction of the force of gravity (which is applied vertically downwards).
Note: The coolie does not work against the force of friction when he moves with the load.
Example 2
When a body moves in a circular path in a horizontal plane, no work is done since the centre of force on the body is directed towards the centre of circular path and the displacement at all instance is along the tangent to the circular path, i.e., normal to the direction of force on the body. It is for this reason that in a circular path, the speed of the body does not change although a force acts on the body. Further in one complete rotation, the total displacement of the body is zero, so the work done in one complete rotation is zero.
Different conditions for the work done by a
force to be zero:
Then W = PCos180° ✕ S = (-ve).(thus, Cos180° = -1).
This is usually the case when the force opposes the motion or it tries to stop a moving body.
Let a body of mass m be moved down through a vertical height h. The force of the gravity acting vertically downwards on the body is F = mg. The displacement in the direction of force is S = h. therefore the work done by the gravity is
W = FS = mgh
S.I unit : The S.I. Unit of work is joule.
C.G.S unit : The C.G.S Unit of work is erg.
1 joule = 107 erg
