Photoelasticity

The objective of the project is to visually observe the stress on a piece of plastic and measure the relative stress distribution when weight is added. This is accomplished by looking at the object through polarized light.

Our project was made by cutting a piece of polycarbonate into the shape of Notre Dame Cathedral. A laptop was used as the source of polarized light, and the effects of photoelasticity can be fully observed when looking at the model through a polarizer at the right angle.

 

As shown, the color of light represents the stress on the object, whether its internal or external. Adding weights can cause the colors to change, become more intense, and be distributed to other areas of the structure.

More information about photoelasticity can be found by the following link:

Photelasticty PowerPoint

Planck's Constant from an LED

The objective of the experiment to experimentally measure Planck's constant using an LED light up using a known voltage and measuring the wavelengths of the diffracted light.

Procedure:
See Physics 4C Lab Manual (Martin Sydney Mason), "Planck's Constant from an LED."

Data and Observations

 

Analysis

 

Using a curve fit for the data, the equation is y=1480*10^-6x-0.455. To get Planck's constant, h, it is necessary to multiply by e (the charge of an electron) and divide by c (the speed of light). Doing so, the experimental value of h is 7.938*10^-31. 

Conclusion and Error Analysis

Since the accepted value of h is 6.626*10^-34 J*s, the percent error is 119700%, which is extremely high. This is mostly likely due to the sensitivity of the experiment of small, precise values. As shown in the graph above, the shape of the curve does not fit the slope of 1480*10^-6 very well.

Color and Spectra

The objective of the experiment is to view of the spectrum of diffracted white light and calculate the wavelengths of several colors.

Procedure:

See Physics 4C Lab Manual (Martin Sydney Mason), "Color and Spectra."

 

 

Data and Analysis

 Hydrogen Gas Tube:

Conclusion

All of the experimental values fall within the uncertainty for the theoretical values. An interesting observation is the measured values for yellow light are non-sensical, and can be thrown out since they are probably caused by interference from the fluorescent light bulbs in the room.

Potential Energy Diagrams and Potential Wells

The objective of the activity is to simulate the quantum effects of a particle trapped in a high-energy potential. 

Procedure:
ActivPhysics: Part VI Modern Physics, Activities 20.1 and 20.3
http://wps.aw.com/aw_young_physics_11/13/3510/898597.cw/index.html

Analysis

Potential Energy Diagrams:

1. What will be the range of motion of the particle when subject to this potential energy function?   
Range of motion is between -5 and 5 cm.   
2. Clearly state why the particle can not travel more than 5 cm from the origin.  
The particle doesn’t have enough energy to surpass the potential barrier.
3. Assume we measure the position of the particle at several random times. Is there a higher probability of detecting the particle between -5 cm and 0 cm or between 0 cm and +5 cm?  
Probability of detection is higher between -5 and 0 because the particle spends more time there (less kinetic energy).
4. What will happen to the range of motion of the particle if its energy is doubled?
E=1/2kx^x, 2E>sqrt2x 
5. Clearly describe the shape of the graph of the particle's kinetic energy vs. position.

Kinetic energy vs potential is an upside down parabola with vertex at x=0 
6. Assume we measure the position of the particle at several random times. Where will the particle most likely be detected?

Most detected at extrema since kinetic energy is minimum 

Potential Wells: 

Question 1: Infinite Well
If the potential well was infinitely deep, determine the ground state energy. Is this also the ground state energy in the finite well?

1   The ground state energy in an infinite well in greater than a finite well

 

Question 2: First Excited State
If the potential well was infinitely deep, determine the energy of the first excited state (n = 2). Is this also the energy of the first excited state in the finite well?

     Energy of infinite=8.4 MeV. Not allowed in finite well.

 

Question 3: "Forbidden" Regions
Since the wavefunction can penetrate into the "forbidden" regions, will the energy of the first excited state in the finite well to be greater than or less than the energy of the first excited state in the infinite well? Why

     Energy infinite>energy finite; wavelength infinite<energy finite

 

Question 4: More Shallow Well
Will the energy of the n = 3 state increase or decrease if the depth of the potential well is decreased from 50 MeV to 25 MeV? Why?

     If U decreases, then wavelength decreases

 

Question 5: Penetration Depth
What will happen to the penetration depth as the mass of the particle is increased?

     If m increases, then penetration length decreases