The net force on a particle of mass m has the potential energy function graphed in Fig. 7.24a. If the total energy is E₁, graph the speed v of the particle versus its position x. At what value of x is the speed greatest? Sketch v versus x if the total energy is E₂.

Fig. 7.24a

A hypothetical potential-energy function U(x)

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Unstable equilibrium points are maxima in the potential-energy curve. A particle is initially at x = x1: If the total energy E > Ez, the particle can “escape" to x > x4*E, If E = E, the particle is trapped between x, and x E, If E = E1, the particle is trapped between xg and x" E, Minimum possible energy is Eg; the particle is at rest at x Stable equilibrium points are minima in the potential-energy curve. Eo X2 X3