[Physics Class Notes] on Unit of Work Pdf for Exam

Whenever a force acting on a body displaces it, work is said to be done. If a force F acting on the body displaces it by a displacement s in the direction of force then the work done is given by 

W = F.s or W = |F||s|cos[Phi ] 

where [Phi ] is the angle between the direction of force applied and the direction of displacement, W is the work done and is a vector quantity, therefore, work done can be positive or negative and it does not depend on the path followed and time taken.

The SI unit of work is the joule (J) and in the CGS system, the unit of work is erg. 

1 joule = [10^{7}] erg

The SI unit of force is newton(N) and displacement is meter (m), therefore, J is also written as N.m. The MKS unit is kg [m^{2} s^{-2}] and in the CGS system, it is dyne-cm or erg.

Positive Work

If [Phi ] is acute (<90°), work done is positive as cos [Phi ] will be positive. For example, when a body free falls under gravity, [Phi ]=0, work done is positive.

Negative Work

If [Phi ]> 90°, work done is negative since cos[Phi ] will be negative. For example, when a ball is thrown up, its motion is opposed by gravity, [Phi ] between F and s is 180°. 

Zero Work

When [Phi ]=90°, the work done is zero since cos 90° is 0. For example, when a coolie carries a bag, the force applied is in the upwards direction but the displacement is towards the forward direction making the angle between force and displacement be 90°. Therefore, even though energy is expended in exerting the force but work done W is zero.

Work done by Force

When [Phi ] is 0° then the direction of force and displacement are in the same direction and work done is simply given by

W = |F||s|

As stated already, when the direction of force is perpendicular to the direction of displacement, [Phi ] is 90° which makes work done W to be equal to 0. 

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