A-force-F-2xj-newton-acts-in-a-region-where-a-particle-moves-anticlockwise-in-a-square-loop-of-2-m-in-x-y-plane-Calculate-the-total-amount-of-work-done-Is-this-force-a-conservative-force-or-

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Question Number 22696 by Tinkutara last updated on 22/Oct/17

$$\mathrm{A}\mathrm{force}\overrightarrow{F}=2x\stackrel{\wedge }{j}\mathrm{newton}\mathrm{acts}\mathrm{in}\mathrm{a}\mathrm{region}$$$$\mathrm{where}\mathrm{a}\mathrm{particle}\mathrm{moves}\mathrm{anticlockwise}$$$$\mathrm{in}\mathrm{a}\mathrm{square}\mathrm{loop}\mathrm{of}2\mathrm{m}\mathrm{in}x-y\mathrm{plane}.$$$$\mathrm{Calculate}\mathrm{the}\mathrm{total}\mathrm{amount}\mathrm{of}\mathrm{work}$$$$\mathrm{done}.\mathrm{Is}\mathrm{this}\mathrm{force}\mathrm{a}\mathrm{conservative}\mathrm{force}$$$$\mathrm{or}\mathrm{a}\mathrm{non}-\mathrm{conservative}\mathrm{force}?$$

Commented by ajfour last updated on 22/Oct/17

$$whatifF=F_0(x\hat{i}+y\hat{j})?$$

Commented by Tinkutara last updated on 22/Oct/17

Commented by Sahib singh last updated on 22/Oct/17

$$\mathrm{then}\mathrm{it}\mathrm{would}\mathrm{be}\mathrm{a}\mathrm{conservative}$$$$\mathrm{force}\mathrm{and}\mathrm{work}\mathrm{done}\mathrm{would}$$$$\mathrm{be}\mathrm{zero}\mathrm{joules}\mathrm{from}\mathrm{A}\mathrm{to}\mathrm{A}$$$$$$

Commented by ajfour last updated on 22/Oct/17

$$W==\int F_0(x\hat{i}+y\hat{j}).(dx\overline{i}+dy\hat{j})$$$$W=\int \overline{F}.d\overline{s}=F_0\int (xdx+ydy)$$$$=\frac{F_0}{2}[(x^2-x_0^2)+(y^2-y_0^2)].$$$$whileifF=2x\hat{j},then$$$$W=\int \left(2x\hat{j}\right).d\overline{s}={\int }_{ABCDA}2xdy$$$$=(0+8+0+0)J=8\mathit{J}.$$$$$$

Commented by Tinkutara last updated on 22/Oct/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

Answered by Sahib singh last updated on 22/Oct/17

$$$$$$WorkdonefromAtoB:$$$$sincethedirectionofforce$$$$is\mathrm{\perp }tothedisplacement$$$$\Rightarrow W=0J$$$$WorkdonefromBtoC:$$$$F=2\times 2=4andisparallel$$$$todisplacement$$$$\Rightarrow W=\overrightarrow{F}\cdot \overrightarrow{d}=\left(4\times 2\right)\times Cos0°$$$$=8J$$$$FromCtoD:$$$$W=0asforceis\mathrm{\perp }to$$$$displacement$$$$FromDtoA:$$$$W=0asF=0.$$$$$$$$Totalwork{done}_{fromAtoA}=8J$$$$forceisnonconservative$$

Commented by Tinkutara last updated on 22/Oct/17

$$\mathrm{Work}\mathrm{done}\mathrm{from}\mathrm{B}\mathrm{to}\mathrm{C}\mathrm{is}\mathrm{why}\mathrm{not}0?$$$$\mathrm{Since}\mathrm{there}x\mathrm{does}\mathrm{not}\mathrm{change}.$$

Commented by Sahib singh last updated on 22/Oct/17

$$\mathrm{because}\mathrm{it}\mathrm{is}\mathrm{displacing}\mathrm{in}$$$$\mathrm{y}\mathrm{direction}.\mathrm{And}\mathrm{force}\mathrm{is}$$$$\mathrm{eing}\mathrm{constant}\mathrm{as}\mathrm{x}\mathrm{constant}.$$

Commented by Tinkutara last updated on 22/Oct/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

Commented by Sahib singh last updated on 22/Oct/17

$$\mathrm{you}\mathrm{are}\mathrm{welcome}.$$

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