A material point of mass m interacts with a fixed center. Potential energy is U = a/r + br. At the initial moment, the point was at a distance r0 = 2 from the center and had zero speed. Find: 1) the minimum distance rmin at which the point can approach the center; 2) a stable equilibrium position of a material point; 3) the magnitude of the force acting on the material point at points r0 and rmin; 4) “first cosmic velocity” when a material point moves around the center.

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