potential energy of a system is given by u(x )is equal to (X + 1) (X + 2 )then we'll be at stable equilibrium at the position
Answers
Explanation:
Often, you can get a good deal of useful information about the dynamical behavior of a mechanical system just by interpreting a graph of its potential energy as a function of position, called a potential energy diagram. This is most easily accomplished for a one-dimensional system, whose potential energy can be plotted in one two-dimensional graph—for example, U(x) versus x—on a piece of paper or a computer program. For systems whose motion is in more than one dimension, the motion needs to be studied in three-dimensional space. We will simplify our procedure for one-dimensional motion only.
First, let’s look at an object, freely falling vertically, near the surface of Earth, in the absence of air resistance. The mechanical energy of the object is conserved,
E
=
K
+
U
,
and the potential energy, with respect to zero at ground level, is
U
(
y
)
=
m
g
y
,
which is a straight line through the origin with slope
m
g
. In the graph shown in (Figure), the x-axis is the height above the ground y and the y-axis is the object’s energy.
The energy, in units of Joules, is plotted as a function of height above the ground in meters. The graph of potential energy U is a straight red line through the origin, where y sub zero equals zero. The equation of the line is given as U of y equals m g y. The graph of the total energy E which is equal to K plus U is a constant, which appears as a black horizontal line. The height above the ground where the E and U graphs intersect is y sub max. The energy between the red U line and the horizontal axis us U sub A. The energy between the red U of y line and the black E line is K sub A.