Question

(a) Sketch a graph of the potential energy function U(x) = kx2 /2 + Ae−αx2 ,...

(a) Sketch a graph of the potential energy function U(x) = kx2 /2 + Ae−αx2 , where k, A, and α are constants. (b) What is the force corresponding to this potential energy? (c) Suppose a particle of mass m moving with this potential energy has a velocity va when its position is x = a . Show that the particle does not pass through the origin unless A ≤ mva^ 2 + ka^2 / 2 ( 1 − e^ −αa^2)

Science   Advanced-Physics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A potential energy function is given by U(x) = x^(−8)e^x^2 . Let’s only focus on the...
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...
particle of mass m moves under a conservative force where the potential energy function is given...
particle of mass m moves under a conservative force where the potential energy function is given by V = (cx) / (x2 + a2 ), and where c and a are positive constants. Find the position of stable equilibrium and the period of small oscillations about it.
The electric potential in a region of space as a function of position x is given...
The electric potential in a region of space as a function of position x is given by the equation V(x) = αx2 + βx - γ, where α = 2V/m2, β = 7V/m, and γ = 15V. All nonelectrical forces are negligible. An electron starts at rest at x = 0 and travels to x = 20 m. Calculate the magnitude of the work done on the electron by the electric field during this process. Calculate the speed of the...
Force on a particle as a function of position is given as ??=?2−?−6. a. Find the...
Force on a particle as a function of position is given as ??=?2−?−6. a. Find the equilibrium points. b. Find the potential energy function V(x). c. Graph F(x) and V(x). d. Label the equilibrium points on the graphs.
7. A particle of mass m is described by the wave function ψ ( x) =...
7. A particle of mass m is described by the wave function ψ ( x) = 2a^(3/2)*xe^(−ax) when x ≥ 0 0 when x < 0 (a) (2 pts) Verify that the normalization constant is correct. (b) (3 pts) Sketch the wavefunction. Is it smooth at x = 0? (c) (2 pts) Find the particle’s most probable position. (d) (3 pts) What is the probability that the particle would be found in the region (0, 1/a)? 8. Refer to the...
A mass m is in a potential energy profile U(x). Determine the equilibrium positions in the...
A mass m is in a potential energy profile U(x). Determine the equilibrium positions in the following situations, as well as the frequency of oscillations around stable equilibria: 1. U(x) = U0 (λx^(-12) – µx^(-6) ) (This simulates the interatomic potential energy in a solid, U0 in Joules, λ is in m12 and µ is in m6 ) 2. U(x) = k.q.Q.x^(-1) + k.q.Q.(x-a)^(-1) (This would be the repulsive Coulomb potential of a charge q at position x, between two...
A mass m moves in a central potential U(r) = −A e^(−kr), where A and k...
A mass m moves in a central potential U(r) = −A e^(−kr), where A and k are positive constants. (a) Sketch the effective potential, and list the types of motion possible (bounded vs. unbounded, stable vs. unstable) and the energy ranges for each. (b) If the particle moves in a circular orbit of radius r0, find its angular momentum L in terms of m, k, A and r0. (c) Find the angular velocity of the circular orbit ωorb in terms...
Explain why this works: if one dimension, if we have a potential energy function U(x) along...
Explain why this works: if one dimension, if we have a potential energy function U(x) along with initial values for x and v, we can determine x and v for all subsequent times.
We wish to sketch the graph of the function f(x)=x^2−3x+1/ (x−1)^2 Find all the critical numbers...
We wish to sketch the graph of the function f(x)=x^2−3x+1/ (x−1)^2 Find all the critical numbers of ‌f and of ‌f'. There are two of them; enter their exact values, together with the value x=1 at which f is undefined, in the first column of the table below (in ascending order : ‌a<b<c). The second column consists of several drop-down menus. Do the following: for each of the intervals of ‌‌R defined by these points, select the phrase that best...
A force F= -F0 e(-x/λ ) (where F0 and λ are positive constants) acts on a...
A force F= -F0 e(-x/λ ) (where F0 and λ are positive constants) acts on a particle of mass m that is initially at x = x0 and moving with velocity v0 (> 0). Show that the velocity of the particle is given by, v(x) = ± ( v02 + (2F0λ/m)(e-x/λ - 1) ) 1/2 , where the upper (lower) sign corresponds to the motion in the positive (negative) x direction. Consider first the upper sign. For simplicity, define ve...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT