A potential energy function is given by U(x) = (x ^−8) *e^ (x ^2) . Let’s...
A potential energy function is given by U(x) = (x ^−8) *e^ (x ^2) . Let’s only focus on the region where x > 0.
a) Find the position where the potential energy is a minimum
b) For small oscillations around this minimum, what is the angular frequency ω?
c) At what distance (either to the left or right) from the equilibrium point is the exact value of the force (derived from the full potential) more than 10% different from the force corresponding to the second order expansion of the potential used in part b?
Homework Answers
Add Answer to:
A potential energy function is given by U(x) = (x ^−8) *e^ (x
^2) . Let’s...
A particle of mass 5 kg is subject to a conservative force whose potential energy (in...
A particle of mass 5 kg is subject to a conservative force whose potential energy (in joules) as a function of position (in meters) is given by the equation U(x) =-100x5e-1x [where x > 0] (a) Determine the position xo where the particle experiences stable equilibrium (b) Find the potential energy Uo of the particle at the position x 2106 The particle is displaced slightly from position x = xo and released (c) Determine the effective value of the spring...
The potential energy function for either one of the two atoms in a diatomic molecule is...
The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by U(x )- where x is the distance between the atoms. 12 istance of separation does the potential energy have a local minimum (not at x -co)? (Use the following as necessary: a and b.) (b) What is the force on an atom at this separation? (Use the following as necessary: a and b.) (o) How does the force vary with the...
h2 4. In a region of the x-axis, a particle has a wave function given by...
h2 4. In a region of the x-axis, a particle has a wave function given by y(x) = Ae-*4722° and energy where L is some length. (a) Find the potential energy as a function of x, and sketch V (x) versus x. (b) What is the classical potential (or corresponding force function) that has this dependence? (c) Find the kinetic energy as a function of x. (d) Show that x = L is the classical turning point (i.e. the place...
Given a potential energy function U(x), the corresponding force F is in the positive x direction...
Given a potential energy function U(x), the corresponding force F is in the positive x direction if:a) u is positiveb) u is negativec) u is an increasing function of xd) u is an decreasing function of x
The Lennard-Jones potential energy Ulj(x) is important in chemical bonding theory and is given by 1012...
The Lennard-Jones potential energy Ulj(x) is important in chemical bonding theory and is given by 1012 ool ULJ 1 1 1 ULJ = 4€ | (x12 26 I 0 E 012 where e and o are constants and ř=r/o. (a) Sketch a graph of this potential energy. (b) Use IDL to obtain a careful graph of ULJ(x)/€ versus x/0. (c) Locate any equilibrium points, (d) determine which ones are stable, and (e) find the frequency of small oscillations about about...
1) Consider a one dimensional potential given by U (x )=ax 8−bx6 . a) What are...
1) Consider a one dimensional potential given by U (x )=ax 8−bx6 . a) What are the units of the constants a and b? b) For positive values of s a and b, find the equilibrium points for this potential and determine if they are stable or not. c) What is the frequency of small oscillations about the stable equilibrium points?
12 R Consider the van der Waals potential U(r) used to model the potential energy function...
12 R Consider the van der Waals potential U(r) used to model the potential energy function of two molecules, where the minimum potential is at - 2 Ro. Find the force as a function of r. (Use any variable or symbol stated above as necessary.) r = F(r = n(n 1)(n 2)3 n(n 1) Consider a small displacement r R + r' and use the binomial theorem, (1 + x)" = 1 + nx + , to show that the...
A particle is introduced to a region with a potential described by U(x)--2x2 +x*+1 Joules. 3. a. ...
A particle is introduced to a region with a potential described by U(x)--2x2 +x*+1 Joules. 3. a. (2 pts) In software, plot the potential U) Set your axis ranges: -2 SxS2 and 0s b. (5 pts) Find the equilibrium positions and determine whether they are stable or c. (8 pts) Describe the motion of the particle for total energy values E-О.0.05. 1.0, 2.0 unstable. Explain how you arrived at your answers. (all in Joules). What I am looking for here...
Question 7 The figure shows a plot of potential energy U versus position x of a...
Question 7 The figure shows a plot of potential energy U versus position x of a 0.220 kg particle that can travel only along an x axis under the influence of a conservative force. The graph has these values: UA = 9.00 J, Uc = 20.0 J and UD-24.0 J. The particle is released at the point where U forms a "potential hiir of "height" UB-12.0J, with kinetic energy 5.00 J. What is the speed of the particle at (a)x...
The figure shows a plot of potential energy U versus position x of a 0.280 kg particle that can t...
The figure shows a plot of potential energy U versus
position x of a 0.280 kg particle that can travel only
along an x axis under the influence of a conservative
force. The graph has these values: UA
= 9.00 J, UC = 20.0 J and
UD = 24.0 J. The particle is released
at the point where U forms a “potential hill” of “height”
UB = 12.0 J, with kinetic energy 5.00
J. What is the speed of the...
A particle of mass 5 kg is subject to a conservative force whose potential energy (in joules) as a function of position (in meters) is given by the equation U(x) =-100x5e-1x [where x > 0] (a) Determine the position xo where the particle experiences stable equilibrium (b) Find the potential energy Uo of the particle at the position x 2106 The particle is displaced slightly from position x = xo and released (c) Determine the effective value of the spring...
The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by U(x )- where x is the distance between the atoms. 12 istance of separation does the potential energy have a local minimum (not at x -co)? (Use the following as necessary: a and b.) (b) What is the force on an atom at this separation? (Use the following as necessary: a and b.) (o) How does the force vary with the...
h2 4. In a region of the x-axis, a particle has a wave function given by y(x) = Ae-*4722° and energy where L is some length. (a) Find the potential energy as a function of x, and sketch V (x) versus x. (b) What is the classical potential (or corresponding force function) that has this dependence? (c) Find the kinetic energy as a function of x. (d) Show that x = L is the classical turning point (i.e. the place...
The Lennard-Jones potential energy Ulj(x) is important in chemical bonding theory and is given by 1012 ool ULJ 1 1 1 ULJ = 4€ | (x12 26 I 0 E 012 where e and o are constants and ř=r/o. (a) Sketch a graph of this potential energy. (b) Use IDL to obtain a careful graph of ULJ(x)/€ versus x/0. (c) Locate any equilibrium points, (d) determine which ones are stable, and (e) find the frequency of small oscillations about about...
12 R Consider the van der Waals potential U(r) used to model the potential energy function of two molecules, where the minimum potential is at - 2 Ro. Find the force as a function of r. (Use any variable or symbol stated above as necessary.) r = F(r = n(n 1)(n 2)3 n(n 1) Consider a small displacement r R + r' and use the binomial theorem, (1 + x)" = 1 + nx + , to show that the...
A particle is introduced to a region with a potential described by U(x)--2x2 +x*+1 Joules. 3. a. (2 pts) In software, plot the potential U) Set your axis ranges: -2 SxS2 and 0s b. (5 pts) Find the equilibrium positions and determine whether they are stable or c. (8 pts) Describe the motion of the particle for total energy values E-О.0.05. 1.0, 2.0 unstable. Explain how you arrived at your answers. (all in Joules). What I am looking for here...
Question 7 The figure shows a plot of potential energy U versus position x of a 0.220 kg particle that can travel only along an x axis under the influence of a conservative force. The graph has these values: UA = 9.00 J, Uc = 20.0 J and UD-24.0 J. The particle is released at the point where U forms a "potential hiir of "height" UB-12.0J, with kinetic energy 5.00 J. What is the speed of the particle at (a)x...
The figure shows a plot of potential energy U versus
position x of a 0.280 kg particle that can travel only
along an x axis under the influence of a conservative
force. The graph has these values: UA
= 9.00 J, UC = 20.0 J and
UD = 24.0 J. The particle is released
at the point where U forms a “potential hill” of “height”
UB = 12.0 J, with kinetic energy 5.00
J. What is the speed of the...
Most questions answered within 3 hours.
-
No matter how a company measures the benefits provided
by an online business implementation, it usually...
asked 1 minute ago -
A circular (0.8 m diameter) footing with q=50 kN/m^2 is placed
on the ground surface. Compute...
asked 21 minutes ago -
Suppose there are 1000 students in a business administration
program. 620 students are in an IT...
asked 4 minutes ago -
Let G be an undirected graph and let X be a subset of the
vertices of...
asked 5 minutes ago -
An empty truck traveling at 10 km/h has kinetic energy. How much
kinetic energy does it...
asked 2 minutes ago -
Physicians add a special dimension to a governing board. What
are the important things to consider...
asked 17 minutes ago -
Rank the following titrations in order of increasing pH at the
halfway point to equivalence (1...
asked 13 minutes ago -
Mr. Smalley, who had been diagnosed as manic-depressive and had
been in and out of mental...
asked 15 minutes ago -
Calculate the effective radiation dosage in rems for a 75 ‑kg
person who is exposed to...
asked 22 minutes ago -
Determine the heat of combustion (ΔH2) for propane
(C3H8) using the bond energy table. HINT: you’ll...
asked 33 minutes ago -
1 Give the host id in binary for the following IP addresses
(assuming classful):
a) 130.11.6.9...
asked 35 minutes ago -
A concert loudspeaker suspended high off the ground emits 32 W
of sound power. A small...
asked 38 minutes ago