Conservative force has the potential energy function, U(x) given by the graph. U

Question

Conservative force has the potential energy function, U(x) given by the graph. Use the graph to answer the following questions. A particle is moving in one dimension under the influence of this force. At position X_1 the particle has a kinetic energy, of 1.0 J. Consider the resulting motion of the particle. Is the motion bounded by turning points? If so, where are they? Explain how you know. Are there any locations where the force on the particle is zero? If so, where? Explain your answer. Which region of the graph shows a positive force? Explain. At position X_2, the particle has a kinetic energy of 1.0 J. Consider the resulting motion of the particle H the motion bounded by turning points? If so, where are they? Explain your answer.

Explanation / Answer

(a)

Turning points represents where the kinetic eenrgy is zero. The fixpoint of the motion represents where the potential enrgy is zero. Thererfore, x1 is not the turning point and it is mean (fixed) point.

(b)

The force on the particle is,

F= - (dU/dx), therefore, the force becomes zero if potential energy is zero. therefore, at x1 and x2 , the force beomes zero. The force is also zero if U is constant it occurs at x1.

(c)

The force is positive if U is negative. in the region x1 to x2, the force is positive.

(d)

Turning points represents where the kinetic eenrgy is zero. The fixpoint of the motion represents where the potential enrgy is zero. Thererfore, x2 is not the turning point and it is fixed point.

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