A particle is moved along a path $$AB-BC-CD-DE-EF-FA$$, as shown in figure, in presence of a force F→$$=$$α$$yi^+2$$α$$xj^N$$, where x and y are in meter and α$$=$$−$$1Nm$$−$$1$$. The work done on the particle by this force F→ will be $$___$$ Joule.

Question

A particle is moved along a path $$AB-BC-CD-DE-EF-FA$$, as shown in figure, in presence of a force  F→$$=$$α$$yi^+2$$α$$xj^N$$, where x and y are in meter and  α$$=$$−$$1Nm$$−$$1$$. The work done on the particle by this force F→ will be $$___$$ Joule.

Infinity Learn · Accepted Answer

For AB:$$y=$$ const F→$$=$$−$$yi^$$−$$2xj^$$⇒F→$$=$$−$$i^$$−$$2xj^dr$$→$$=dxi^$$ So, $$WAB=$$∫$$x=01$$ F→⋅dr→$$=$$∫$$01$$ −$$dx=$$−$$1J$$ For BC:$$x=constF$$→$$=$$−$$yi^$$−$$2j^dr$$→$$=dyjWBC=$$∫$$y=10.5$$ −$$2dy$$⇒$$WBC=+1J$$ For CD:$$y=const$$ F→$$=$$−$$0.5i^$$−$$2xj$$ and dr→$$=dxi^WCD=$$∫$$10.5$$ −$$0.5dx=0.25J$$ For DE:$$x=$$ const F→$$=$$−$$yi^$$−$$j^dr$$→$$=dyj^WDE=$$∫$$y=0.50$$ −$$dy=+0.5J$$ For EF:$$y=0$$ F→$$=$$−$$2$$×$$j^dr$$→$$=dxi^$$⇒$$WEF=0$$ For FA:$$x=0$$ F→$$=$$−$$yi^dr$$→$$=dyj^$$⇒$$WFA=0WNet=$$−$$1+1+0.25+0.5=0.75J$$

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A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force $\vec{F} = (α y \hat{i} + 2 α x \hat{j}) N,$ where x and y are in meter and $α = - 1 N m^{- 1}$ . The work done on the particle by this force $\vec{F}$ will be ___ Joule.

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A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force F→=αyi^+2αxj^N, where x and y are in meter and α=−1Nm−1. The work done on the particle by this force F→ will be ___ Joule.

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free study material

A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force $\vec{F} = (α y \hat{i} + 2 α x \hat{j}) N,$ where x and y are in meter and $α = - 1 N m^{- 1}$ . The work done on the particle by this force $\vec{F}$ will be ___ Joule.