A particle experiences a force given by F(x)= α - βx³.Find the potential field U(x)the particle is in.(Assume that the zero of potential energy is located at x = 0.) A)U(x)= -αx + x⁴ B)U(x)= αx - x⁴ C)U(x)= 3βx² D)U(x)= -3βx²

Question

Quizplus · Accepted Answer

To find the potential field U(x), we need to integrate the force F(x) with respect to x. U(x) = - ∫ F(x) dx U(x) = - ∫ (α - βx)³ dx U(x) = - αx⁴ + (β/2)x^2² + C, where C is the constant of integration. Since the zero of potential energy is located at x = 0, we can set C = 0. Thus, U(x) = - αx⁴ + (β/2)x^2² U(x) = αx³ - (β/2)x^2² U(x) = -αx + 11eab929_29f3_74fe_99e6_7d933c1b63ff_TB4470_11 x⁴ Therefore, the correct choice is A.

A Particle Experiences a Force Given by F(x)= α -