Answer
(a) +x-axis
(b) (-x)-axis
(c) x = 0.75
(d) zero
(e) x = 2.2
(f) x = 0.75 and x= 1.8
(g) x = 1.4
Work Step by Step
(a) Since the slope of the potential energy function is negative, the force on the particle is positive. The force is directed toward the +x-axis.
(b) Since the slope of the potential energy function is positive, the force on the particle is negative. The force is directed toward the (-x)-axis.
(c) The kinetic energy of the particle is a maximum when the potential energy graph is a minimum. This point occurs at approximately x = 0.75.
(d) Since the slope of the potential energy function is zero, the force on the particle is zero.
(e) The largest value of x reached by the particle is x = 2.2 where the potential energy is equal to the potential energy at point A.
(f) The points x = 0.75 and x = 1.8 are points of stable equilibrium.
(g) When x = 1.4 (point C), this is a point of unstable equilibrium.
