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Work, Energy & Power - 1 Compiled by: Udit Gupta Alumnus MNNIT Allahabad Ex-Manager at Reliance Industries Limited Ex-VidyaMan Cofounder and HOD Physics-Elements Azamgarh dir Facuity of Physics

Content . Work done by a force . Work done by a constant force Work done by a variable force

Work done by a force There are two types of force for which we define the work done individually. A force can be constant in nature or it can be variable in nature.

For a constant force Let F be a constant force acting on a particle. If the displacement of the particle is S, then the work done by the force F is given by W = F.S-1F1151 cos where is the angle between F and S The SI unit of work is joule (J) F be

For a constant force If is acute, w is positive. If is obtuse, w is negative. If is 90 , w = 0 and the force is perpendicular to the displacement. We can safely say that: if F and S are in the same direction, W-F |S F be And if F and Sare in the opposite direction, W =-FIST

For a variable force If the force is a function of position, we need calculus to our rescue to find the work done due to this force. In this case we can consider that when a small displacement is occurring, the force would increase or decrease by an infinitesimal amount and can be assumed constant for that interval of displacement. Then on we know how to calculate the work done by a constant force as the area under the curve of F-x. F(x) ol F(x) O A *B

For a variable force The total work done can be said to be: F(x) And since we said that it was an infinitesimal displacement, in calculus form it can be written as: ol F(x) WRF.dx This represents the work done by force F (x) from an initial point A to final point B. *B