Explain with graphs the difference between work done by a constant force and by a variable force.

Explain with graphs the difference between work done by a constant for

1.	Explain with graphs the difference between work done by a constant force and by a variable force.
Answer» Solution :Workdoneby aconstantforce: whena constantforceF acts on a body, thesmallworkdone(dW )by theforceinproducinga smalldisplacement drgivenbytherelation. ` dW= (fcos theta)dr ` The totalworkdonein producinga displacementfrominitialposition`r_i`to finalposition` r_f `is , `W=int_( r_i )^( r_f) dW` `W= int_(r_i )^(r_f)( F costheta )dr = ( f cos theta )int_(r_i )^(r_f)dr= (Fcos theta)( r_(f)- r_i)` Thegraphicalreprentationof hteworkdonebyaconstantforceis SHOWNIN FIGUREGIVEN belowtheareaunderthe graphshowsthe workdoneby theconstantforce. workdoneby avariableforce: whenthe componantof avariableforceF actson abodythe smallworkdone(dW )by theforcein producinga smalldisplacementdrisgivenbythe relation dW =`Fcos thetadr ` [ F cos` theta`is thecomponentof thevariableforceF ] whereFand ` theta`arevariables. thetotaldonefor adisplacementfrominitialposition`r_i`to finalposition`r_f `isgivenby therelation , ` W= int_( r_i )^(r_f)dW = int_(r_i)^(r_f)F costhetadr ` A graphicalrepresentationof theworkdoneby avariableforceis shownin figuregivenbelow, theareaunderthegraphis theworkdoneby thevariableforce.