A particle moves along the -axis under the influence of a conservative force

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

0.20\,\text{kg}

particle moves along the

x

-axis under the influence of a conservative force. The potential energy

U(x)

of the system is given in the table below.

$x\,(\text{m})$	$-4$	$-2$	$0$	$2$	$4$
$U\,(\text{J})$	$20$	$5$	$8$	$5$	$20$

Between the tabulated points, the potential energy varies smoothly. Assume the particle is released from rest at

x=-4\,\text{m}

. (a) On appropriately labeled axes, sketch a smooth graph of

U

versus

x

that is consistent with the data in the table. Be sure your graph clearly shows any equilibrium points. (b) Identify the position(s) of stable equilibrium and unstable equilibrium, if any, and justify each classification using features of the graph. (c) The particle is released from rest at

x=-4\,\text{m}

. Determine its maximum speed during the subsequent motion and specify the

x

-position at which this maximum occurs. Use energy considerations and the graph to support your answer. (d) Explain whether the particle is bound (confined to a finite region of space) or unbound. Support your conclusion with reference to the graph of potential energy.

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