Particle in a potential well Gre. 93

In summary, the concepts involved in this conversation are harmonic oscillator and ballistic motion. The period of motion for a particle with energy E in a potential with two different equations is given by the formula pi*Sqrt[m/k] + 2*Sqrt[2*E/(m*g^2)]. Ballistic motion is when a body moves in a field of constant gravity. The formula can be found in any basic mechanics resource.
  • #1
yxgao
123
0
What concepts are involved here?
93. A particle of mass m moves in the potential shown here. The period of the motion when the particle has energy E is
The potential is V = 1/2kx^2 for x <0 and V= mgx for x > 0.

A. Sqrt[k/m]
B. 2*pi*Sqrt[m/k]
c
. 2*Sqrt[2E/(mg^2)]
D. pi*Sqrt[m/k] + 2*Sqrt[2*E/(m*g^2)]
E. 2*pi*Sqrt[m/k] + 4*Sqrt[2*E/(mg^2)]



The answer is D.
 
Physics news on Phys.org
  • #2
Originally posted by yxgao
What concepts are involved here?

Harmonic oscillator and ballistic motion.
 
  • #3
What is ballistic motion?
How do you arrive at the answer?
 
  • #4
Ballistic motion is when a body moves in a field of constant gravity.

You can look up the formulae in any basic mechanics book (or basic mechanics website). Sorry, I'm really too lazy to type it all down here for you.
 

1. What is a particle in a potential well?

A particle in a potential well refers to a theoretical situation in which a particle is confined within a potential energy field. This can be visualized as a particle trapped in a valley surrounded by hills, where the valley represents the potential well and the hills represent the potential energy barriers.

2. What is the importance of studying particle in a potential well?

Studying particle in a potential well allows scientists to better understand the behavior of particles in confined spaces and how they interact with their surroundings. This has important implications in various fields such as quantum mechanics, material science, and chemistry.

3. What is the Schrödinger equation and how is it related to particle in a potential well?

The Schrödinger equation is a fundamental equation in quantum mechanics that describes the behavior of particles. It is used to calculate the wave function of a particle, which represents its probability of being found at a certain position. In the case of a particle in a potential well, the Schrödinger equation is used to determine the energy levels and wave functions of the particle within the potential well.

4. How does the depth of the potential well affect the behavior of the particle?

The depth of the potential well determines the energy levels that the particle can occupy. A deeper potential well will have higher energy levels, while a shallower potential well will have lower energy levels. This affects the behavior of the particle as it can only exist in discrete energy levels and must overcome the potential energy barriers to move to a higher energy level.

5. Can a particle in a potential well escape from the well?

Yes, a particle in a potential well can escape from the well if it has enough energy to overcome the potential energy barriers. This is known as quantum tunneling and is a crucial phenomenon in understanding the behavior of particles in confined spaces.

Similar threads

Need help with this question on Springs
    • Introductory Physics Homework Help
Replies
6
Views
288
Position and acceleration in simple harmonic motion given velocity
    • Introductory Physics Homework Help
Replies
16
Views
382
Time period of SHM & Energy conservation in pulley-spring-block system
    • Introductory Physics Homework Help
Replies
24
Views
1K
Potential difference between two points in an electric field
    • Introductory Physics Homework Help
Replies
1
Views
996
Difference between resonance in undamped vs damped mass-spring-dashpot
    • Introductory Physics Homework Help
Replies
17
Views
354
Calculation of Electrostatic Potential Given a Volume Charge Density
    • Introductory Physics Homework Help
Replies
6
Views
1K
Help Calculating probability between 2 limits for the ground state
    • Introductory Physics Homework Help
Replies
28
Views
347
MIT OCW, 8.02 Electromagnetism: Potential for an Electric Dipole
    • Introductory Physics Homework Help
Replies
1
Views
861
Solving for Electrical Potential Energy: Durcell's Example
    • Introductory Physics Homework Help
Replies
11
Views
1K
Potential of a square plate
    • Introductory Physics Homework Help
Replies
6
Views
906

Hot Threads

Recent Insights

Back
Top