The discussion revolves around a vector field defined by F(x,y) = (x²y, xy²) and the determination of the line of force associated with it, as well as whether this vector field is conservative.
Some participants have provided interpretations of the problem and attempted to derive the line of force, while others have raised questions about the clarity of the problem statement and the definitions being used. There is a mix of interpretations regarding the function's classification as a vector field.
There appears to be confusion regarding the terminology used, with references to "function" versus "vector field." This may affect the understanding of the problem and the approaches taken.
The "problem statement" is a single function? What is F? Is it a vector force function? What are you asked to do? Please tell us what the question really is!MechanicalBrank said:Homework Statement
F(x,y) =(x2y,xy2)
Homework Equations
[/B]The Attempt at a Solution
I wrote the function as a differential equation dy/x2y = dx/xy2. After integration I got C+y2=x2. This gave me that the line of force is a hyperbolic paraboloid. The function is not conservative. ∂F1/∂y = x2 , ∂F2/∂x = y2 ⇒ ∂F1/∂y ≠ ∂F2/∂x
Silly me. Determine the line of force to the function F and if the function is conservative or not.HallsofIvy said:The "problem statement" is a single function? What is F? Is it a vector force function? What are you asked to do? Please tell us what the question really is!