# A force =2xj N acts in a region where a particle moves counterclockwise in a square loop of 2m in XY plane .Calculate the total amount of work done.Is this force conserved

1
by Anurup12

2014-10-15T03:54:01+05:30

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See diagram.

Force = 2j   or 2xj ?        is there x (eks) in the formula for force ?

W = Force · displacement

Work done by the Force on the particle when the particle moves from : A to B:
W_AB = 2 j · 2 i = 0                W_BC = 2j · 2j = 4 N-m or Joules
W_CD = 2 j · (-2i) = 0              W_DA = 2 j · (-2j) = - 4 N-m

Total work done W_AA = 0    F = 2j is conservative.

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If F = 2 x j , it depends on the x position.

WA_B = 2x j · 2i = 0             W_BC = 2 X₂ j · 2j = 4 X₂
W_CD = 0                       W_DA = 2 X₁ j · (-2j)  = - 4 X₁

So total work done =  4 (X2 - X1).

This force F = 2x j is not conservative.