Question

A particle of mass $m$ moves in one dimension. Its potential energy is given by $U(x) = -U_0e^{-x^2/a^2}$ where $U_0$ and $a$ are constants. (a) Draw an energy diagram showing the potential energy $U(x)$. Choose some value for the total mechanical energy $E$ such that $-U_0 <$ $E < 0$. Mark the kinetic energy, the potential energy and the total energy for the particle at some point of your choosing. (b) Find the force on the particle as a function of position $x$. Express your answer in terms of some or all of the following: $x$, $a$, and $U_0$. (c) Find the speed at the origin $x = 0$ such that when the particle reaches $x = pm a$, it stops momentarily and reverses the direction of its motion. Express your answer in terms of some or all of the following: $x$, $a$, $m$ and $U_0$

          A particle of mass $m$ moves in one dimension. Its potential energy is given by
$U(x) = -U_0e^{-x^2/a^2}$
where $U_0$ and $a$ are constants. (a) Draw an energy diagram showing the potential
energy $U(x)$. Choose some value for the total mechanical energy $E$ such that $-U_0 <$
$E < 0$. Mark the kinetic energy, the potential energy and the total energy for the
particle at some point of your choosing. (b) Find the force on the particle as a
function of position $x$. Express your answer in terms of some or all of the following:
$x$, $a$, and $U_0$. (c) Find the speed at the origin $x = 0$ such that when the particle
reaches $x = pm a$, it stops momentarily and reverses the direction of its motion.
Express your answer in terms of some or all of the following: $x$, $a$, $m$ and $U_0$

A particle of mass m moves in one dimension. Its potential energy is given by
U(x) = -U0e^-x^2/a^2
where U0 and a are constants. (a) Draw an energy diagram showing the potential
energy U(x). Choose some value for the total mechanical energy E such that -U0 <
E < 0. Mark the kinetic energy, the potential energy and the total energy for the
particle at some point of your choosing. (b) Find the force on the particle as a
function of position x. Express your answer in terms of some or all of the following:
x, a, and U0. (c) Find the speed at the origin x = 0 such that when the particle
reaches x = pm a, it stops momentarily and reverses the direction of its motion.
Express your answer in terms of some or all of the following: x, a, m and U0

Added by James P.

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