The potential energy of a body of mass m is g | vedclass

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Question

(A) The force components are derived from the negative gradient of the potential energy: $F_x = -\frac{\partial U}{\partial x} = -a$ $F_y = -\frac{\pa

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$\frac{(a^2 + b^2)^{1/2}}{m}$

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(A) The force components are derived from the negative gradient of the potential energy: $F_x = -\frac{\partial U}{\partial x} = -a$ $F_y = -\frac{\partial U}{\partial y} = -b$ The magnitude of the net force $F$ is given by: $F = \sqrt{F_x^2 + F_y^2} = \sqrt{(-a)^2 + (-b)^2} = \sqrt{a^2 + b^2}$ Using Newton's second law,the acceleration $a_{acc}$ is: $a_{acc} = \frac{F}{m} = \frac{\sqrt{a^2 + b^2}}{m} = \frac{(a^2 + b^2)^{1/2}}{m}$

The potential energy of a body of mass $m$ is given by $U = ax + by$,where $x$ and $y$ are the position coordinates of the particle. The acceleration of the particle is:

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