question_answer

A force is acting on a body moving along x-axis in the direction of motion of the body. If this force produces a potential energy \[U=A{{x}^{4}}\], where \[A=1.2J{{m}^{-4}}\], then what is the force acting on the body when the body is at x = -0.8 m.

Answer:

                Here, \[U=A{{x}^{4}}\] \[{{F}_{x}}=-\frac{dU}{dx}=\frac{d}{dx}\left( A{{x}^{4}} \right)=-4A{{x}^{3}}\] When \[x=-0.8m\]then \[{{F}_{x}}=-4\times 1.2{{\left( -0.8 \right)}^{3}}=2.46N\]