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Work is said to be done by a force when the force produces a displacement in the body on which it acts in any direction except perpendicular to the direction of the force.
Work done by constant force
Consider an object undergoes a displacement S along a straight line while acted on a force F that makes an angle θ with S as shown.
The work done W by the agent is the product of the component of force in the direction of displacement and the magnitude of displacement.
i.e., W=FS Cosθ …..(1)
Work done is a scalar quantity and its S.I. unit is N-m or joule (J). We can also write work done as a scalar product of force and displacement.
Where S is the displacement of the point application of the force.
From this definition, we conclude the following points
Work done by a force is zero If displacement is perpendicular to the force (θ 90o)
Important points about work:
UNITS OF WORK:
In case system, the unit of work is erg. One erg of work is said to be done when a force of one dyne displaces a body through one centimetre in its own direction.
1 erg = 1 dyne × 1 cm = 1 g cm s–2 × 1 cm = 1 g cm2
Note: Another name for joule is newton metre
Relation between joule and erg
1 joule = 1 newton ×1 metre
1 joule = 105 dyne × 102 cm = 107 dyne cm
1 joule = 107 erg
1 erg = 10–7 joule
Dimensions of Work:
[Work] = [Force] [Distance] = [MLT–2] [L] = [ML2T–2]
Work has one dimension in mass, two dimensions in length and ‘–2’ dimensions in time, On the basis of dimensional formula, the unit of work is kg m2 s–2.
Note that 1 kg m2s–2 = (1 kg m s–2) m = 1 N m = 1 J.
Work done by multiple Forces:
If several forces act on a particle, then we can replace F in equation W=F.S by the force
The gives the work done by the net force during a displacement S of the particle.
We can rewrite equation (i) as:
So, the work done on the particle is the sum of the individual work done by all the forces acting on the particle.
W= Fs cos Φ =
F(x)= - ΔU /Δx
1 watt= 1 joule/second
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