University Physics I · Work, energy, and conservative systems
Turning points in an inverse-square-plus-quadratic potential
Problem
Work in an inertial laboratory frame, taking $+x$ right and $+y$ upward when components are needed. Treat the named body or bodies as the system, use SI units, and neglect only forces explicitly declared negligible. A particle moves on $x>0$ with $U(x)=4/x^2+x^2$ joules, where $x$ is numerically in metres. Find the potential minimum and the turning points when the total energy is $E=5\,\mathrm J$.
Hint
Differentiate $U$ to locate its minimum on $x>0$.
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