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Object moving in the xy-plane is acted on by a conservative force described by the potential-energy function u(x,y)=α(1/x2+1/y2), where α is a positive constant

Answer :

shinmin

It seems like the problem is asking for us to derive an expression for the force F⃗ stated in terms of the unit vectors i^ and j^.

The solution for this is:


U(x,y) = α (x^-2 + y^-2) 


F = - dU(x,y) 


F = - (dU/dx + dU/dy) 


F = - (-2αx^-3 - 2αy^-3) 


F = 2α (x^-3 + y^-3)


F = 2α (1/x^3 i + 1/y^3 j) 

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