An object moving in the xy-plane is acted on by a conservative force described by the potential energy function U(x,y)=α(1x2+1y2) where α is a positive constant. Derivative an expression for the force expressed terms of the unit vectors i→ and j→.

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Jeffery Romero · Accepted Answer

To find the force F→ associated with the given potential-energy function U(x,y)=a(1x2+1y2), we can use the relationship between force and potential energy. The force F→ can be expressed as the negative gradient of the potential energy function:F→=−∇U(x,y)Taking the partial derivatives of U(x,y) with respect to x and y, we obtain:∂U∂x=∂∂x(a(1x2+1y2))=−2ax3∂U∂y=∂∂y(a(1x2+1y2))=−2ay3The negative sign indicates that the force acts in the opposite direction of the gradient.Now, we can express the force F→ in terms of the unit vectors i^ and j^:F→=2ax3i^+2ay3j^Therefore, the expression for the force F→ in terms of the unit vectors i^ and j^ is:F→=2ax3i^+2ay3j^

An object moving in the xy-plane is acted on by a conservative force described b

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