A particle constrained to move along the -axis has a potential energy that varies…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power
Problem
A particle constrained to move along the x-axis has a potential energy that varies qualitatively with position as follows: the curve is symmetrical about x=0, attains a minimum value at x=0, and rises smoothly on either side, appearing parabolic for small ∣x∣ and steeper for larger ∣x∣.
(i) Identify the nature of equilibrium at x=0 and justify your answer with reference to the given shape of the potential energy curve.
(ii) Explain how the sign of the slope of the curve on either side of x=0 determines the direction of the force acting on the particle.
(iii) Suppose elsewhere on the x-axis the same potential energy curve possessed an isolated local maximum. State the type of equilibrium that would exist at such a point and give one reason for your choice.