A force field in the xy-plane has components Fₓ = 2xy + 3 and Fᵧ = x² + 4y. Which potential energy function is possible?
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A force field in the xy-plane has components Fₓ = 2xy + 3 and Fᵧ = x² + 4y. Which potential energy function is possible?

G1 Physics · Accepted Answer

Since F = −∇U, integrate −Fₓ with respect to x: U = −x²y − 3x + f(y). Then −∂U/∂y = x² − f′(y) = Fᵧ = x²+4y, giving f′(y)=−4y and f(y)=−2y²+C.