Lab 15: Activ Physics on Lasers

Lab Purpose:
     Solve some problems on activ physics on emission, absorption, and stimulation in relation to
     Lasers.

Part 1: Answer Questions

Question 1:

 Question 2:

 Question 3:

 
Question 4:

 The Answers:

     The answer to number 3 is confusing without context. The question was if the time atoms spent
     in their excited states was constant, however due to this being spontaneous emission of photons
     their can not be any set amount of time an atom spends in an excited state.

Lab 14: Color and Spectra

Lab Purpose:
     Examine the Spectrum of white light. More importantly compare between white light and the
     spectrum of single elements and explain why they are so radically different.

Part 1: White Light

     As can be seen in the picture, white light produces the full spectrum as a single line with multiple
     transitions.

     In our calculations, we obtained a range of 390 to 743 nanometers of wavelength which is very
     close to the 390 to 750 nanometer expected from white light.

Part 2: Mystery Element X

     This picture should strike people as odd, because the light given off by the mystery element
     does not produce a single line, but many distinctly colored "clones" of itself. However, being
     a student of physics, I have already learned that this is due to photon emission from elements
     being quantized, meaning only certain colors can be shown. Hooray education.

     In the picture above, the upright calculations show the different wavelengths that we have found
     compared to the expected wavelengths of Helium. There is a deviation of 18.2 nanometers.

Part 3: Hydrogen
     Sadly, a picture for the hydrogen spectrum could not be obtained, as the spectra was too dim to be
     seen. However, data was collected on 3 of the spectra lines that could be seen out of the 4 we
     expected.

     Correcting for error we get the equation lambda = 1.07 lambda_o - 8
     This error is quite large with a slope increase of 7%, however is could easily be attributed to
     the hydrogen tube being contaminated by other particles.

Lab 13: Activ Physics on Modern Physics

Lab Purpose:
     Do problems on time dilation to assist in complete understanding of the concept.

Part 1: Time Dilation

    
     These problems (work done manually by Austin Ku) were based on time dilation and asked some
     simple questions about the concepts of the dilation.

Part 2: Length Contraction

     These problems dealt with length contraction and many questions were similar in idea to those of
     the time dilation ones. The only interesting one was question 3, equivalent "length" objects must
     have equivalent relative velocities, but we can tell this is not true because one clock is moving
     where as the other is not.

Lab 12: CD Diffraction

Lab Purpose:
     Determine the size of the holes that are burned into the disc by examining the diffraction pattern
     that appears when a laser is shone on the recording side.

Part 1: Experiment

     This is a picture of our setup, the laser strikes the cd and bounces back slightly at an angle
     towards the laser. We then have a whiteboard placed right next to the point of emission and we
     measure the distance from the center and use that as our maxima distance.

     Calculations are quite trivial as it's mostly simple algebra. The value we obtained is
     1.5645 ± .0035 micrometer. The standard value is 1.6 micrometers, which means our value has
     an error of 2.2%.

Lab 11: Measuring a Human Hair

Lab Purpose:
     Using a human hair as a double slit, we attempt to find the width of the hair based upon the
     diffraction pattern that is shown.

Part 1: Experiment
     A hair was taped onto a card that had a hole punched into it.  This hole allows the laser to pass
     through while also interacting with the hair to cause a diffraction pattern as shown below.

    As we expected, the laser does cause a diffraction pattern.  We can use the difference between the
    maxima to determine the width of the hair.

     Our calculations produce a value of 97 ± 63 micrometers, putting it well within the expected
     values.  A significant portion of the error is due to the assumption that error in L is 2 cm.

Lab 10: Lenses

Lab Purpose:
     Observe changes in a real image when varying distance and amount of lens being covered.

Part 1: Focal Length
     To determine focal length, we went outside and used the sun as a source of parallel rays and then
     varied the distance until we found a distance that created the smallest spot.
     f = 18.3  ± .5 cm

     
     As you can see in the graph, we get obtain a slope of .928 and an x intercept of 5.067. The slope
     should be one, however we have an error of 7.2%. The inverse of the intercept should also be
     our focal length which is 19.7 cm. This is not within the bounds of uncertainty and is an error of
     7.8%.

Lab 9: Concave and Convex Mirrors

Lab Purpose:
      Examine and analyze the image that is formed by a convex and concave mirror.

Part 1: Convex Mirrors

      Images appear smaller and upright. The image appears to be further to the mirror than the actual
      object.  Moving the object closer increases the height of the image non linearly and for moving
      objects further from the mirror the image decreases in height non linearly.

Part 2: Concave Mirrors

      

     Images appear larger then object. Image is upright after coming close to the mirror and inverted

     from before that point.Compared to the object, the image seems to be closer to the mirror.  When

     you move the object closer to the mirror the image appears to slightly decrease in size. If you

     move the object significantly far away from the mirror, the image inverts.

Lab 8: Microwaves and Marshmallows

Lab Purpose:
     Determine the power of a microwave based upon information determined from examining
     marshmallows after 30 seconds in it.

 Part 1: Observe and Record data

     Change in temperature = 37 degrees c
     Change in time = 30 s
     Mass = .1 kg
     Wavelength = .24 m

     The picture shows all the calculations determining total energy, power, and energy per photon
     Total Energy = 15481 J
     Power = 516 W
     Energy per Photon = 8.29e-25 J/photon
     Total Photons = 1.87e28
     Total Pressure >= 1.33e-5 Pa (It is greater than or equal because some amount of photons may be
                                                      reflected while others are absorbed)

Lab 7: Standing Waves in a Tube

Lab Purpose:
     Determine the length of a tube based upon standing waves being created as it is spun around in a
     circle.

Part 1: Record Data

Open tube gives us the equation f = n*v/(2*L)
Unknowns are: L, N1, N2
We however say that N2 = N1 + 1, due to N2 being the next harmonic that was heard.

Going through the calculations we obtain the length of the tube to be .837 m

Lab 6: Introduction to Sound

Lab Purpose:
     Become acquainted with sound waves through the use of a LabPro and a microphone.

Part 1: Experiment

     We merely took a LabPro connected it to a microphone and said AAAAAAA for a couple of
     seconds.

Questions:
     a. The wave is periodic as it can be seen repeating after a certain amount of time
     b. 5 waves are shown, we determined this by counting the number of peaks
     c. The time for a single frame in most movies.
     d. The period of the wave is .006 s
     e. Frequency is 166 Hz
     f. Wavelength is 2.04 m.
     g. Amplitude was not determined, though it might be possible to find the amplitude through
     determining the low to high value and dividing by two.
     h. The graph should not be much different, as because it maintains a consistent periodicity
     the overall graph should still be similar albeit much more densely packed.

     When a different person voiced over the microphone, the only real change was a difference in
      amplitude.

Here is a graph of the sound wave produced by a tuning fork, done by Prof. Mason. As can be noted, the graph is much smoother and more consistent than the one produced by our voice.

Graphs for a second sample where the sound is not as loud was not taken, but it can easily be extrapolated that the amplitude would decrease as it directly determines the power.

Lab 5: Standing Waves

Lab Purpose:
     Analyze a wave that is affected by an external force, which in this case is a function generator
     combined with a frequency generator.

Part 1: Experiment
     We setup a function generator attached to a wave driver which is then attached to a length of string.
     We then vary the frequency until we get standing waves and note the frequencies obtained.

     Equations necessary:
     2L/λ = n
     v = fλ
     v = sqrt(T/μ)

 

Harmonic #	M =.2 kg	M =.05 kg
1	13 Hz	6 Hz
2	26 Hz	12 Hz
3	39 Hz	18 Hz
4	51.5 Hz	24 Hz
5	64 Hz	32 Hz
6	77.2 Hz	39.2 Hz
7	90.1 Hz	46 Hz

The average ratio is 2.08, which is close to the expected ratio which is the square root of the ratio of masses or in this case the square root of 4.  The wave velocity as determined by the graph is 62.73 m/s, which deviates significantly from the expected 40.4 m/s.
The error is a notable 55%.

Lab 4: Wavelength vs Frequency

Lab Purpose:
     Determine the relationship between the wavelength and frequency of a wave.

Step 1: Experiment
      As shown below, we attempted to create standing waves on the ground using a long spring.

     The time for ten peaks to pass was recorded.

Wavelength	2 m	1 m	3 m
Time	4.9	4.7	5.33
Frequency	2.041 Hz	2.128 Hz	1.887 Hz

Should you graph the values of wavelength versus the frequency, the slope of that graph would be the wave velocity.

Lab 3: Fluid Dynamics

Lab Purpose:
     Determine the rate at which water depletes from a filled bucket through the use of the Bernoulli
     Equation.

Part 1: Experiment
     

Trial	Time
1	17.55 s
2	17.08 s
3	17.54 s
4	17.50 s
5	17.50 s
6	17.46

     Average time is 17.44 seconds.
     Diameter = .62 cm
     Radius = .31 cm

     Volume of water = .473 L
     Height = 8.7 cm

Part 2: Calculation
    
     Volume emptied = .016 ft^3
     Area of drain hole = .06 in^2
     g = 32 ft/s^2
     Height = .25 ft
     Theoretical time to empty = 12.4 s

Part 3: Analyze
    
      Error is measured at 33% making it outside the bounds of uncertainty.
     If we assume the diameter is measured inaccurately, the actual diameter should be .548 cm
     This corresponds to a 13% error in diameter.

Lab 2: Fluid Statics

Lab Purpose:
     Measure buoyant forces experimentally through three different methods and compare measurements.

Part 1: Underwater Weighing Method
     Use Archimede's principle to determine the weight of an object through displacement of water.

     Mass in air = 1.101 N
     Mass in water = .73 N
     In the free body diagram, there are three forces acting upon the metal cylinder: tension, gravity, and
     buoyant force.

Part 2: Displaced Fluid Method
     Find the weight of water that is displaced.

     B = mg - T = .371 N
     Mass of beaker = .1282 kg
     Mass of beaker + water = .1672 kg
     Mass of water = .039 kg
     Mass of displaced water = .3822 N

Part 3: Volume of Object Method
     Use volume of a cylinder to find the volume of displaced water and then obtain the weight of that
     displaced water.

     Volume of Cylinder = h*πr^2
     Height = .076 m
     Diameter = .0255 m
     Volume = 3.88e-5 m^3
     Weight of water = ρgV = .38 N

Part 4: Summary
     1. The three values are respectively: .371 N, .3822 N, .38 N
     2. Force probe is likely most accurate due to it not relying on human accuracy.
     3. Buoyant force would be lower because the bottom of the cylinder would apply a normal force.

Lab 1: Pressure Due to Depth

Lab Purpose:
     Show that pressure changes with depth.

As can be obviously ascertained from the picture, the water pouring out the upper hole has less horizontal velocity than the water pouring out of the lower hole.  This is due to the fact that pressure increases as the depth of water increases such that P = Po + ρgh.

No calculations are done due to this being a lab to show that the concept is true.

We're Sorry.

It seems I made a fatal error and decided to put all the engineering labs onto my physics blog. I know you're out there Mason... laughing at me.