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WORK:
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.
W=F.S …..(2)
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 90^{o})
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 cm_{2}
s_{–2}
Note: Another name for joule is newton metre
Relation between joule and erg
1 joule = 1 newton ×1 metre
1 joule = 10_{5} dyne × 10_{2} cm = 10_{7} dyne cm
1 joule = 10_{7} erg
1 erg = 10_{–7} joule
Dimensions of Work:
[Work] = [Force] [Distance] = [MLT_{–2}] [L] = [ML_{2}T_{–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 m_{2} s_{–2}.
Note that 1 kg m_{2}s_{–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.
Summary Points
W= Fs cos Φ =
F(x)= - ΔU /Δx
1 watt= 1 joule/second
Diagram
Energy Curve
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