One of the reasons my interest in physics took off was the labs. They presented me with an opportunity to utilize my previous coding skills - specifically data processing and visualization with numpy and matplotlib - in a different way. Besides learning how one approaches the scientific process, articulating and exploring the experiment numerically has taught me new methods of viewing data from new angles.
In AP Physics I worked in google docs, but for the PHYS 505 labs I was introduced and began using LaTeX. Below you can find some of the reports from these classes.
Full Lab Reports
The objective of this lab was separated into two parts. First, the emission lines of a known element, mercury, were observed. The results were compared with the known spectral lines recorded in the National Institute of Standards and Technology (NIST) Database to measure accuracy. Second, the emission spectrum for an unknown element was observed in a similar manner and compared to spectral lines of common elements in an attempt to identify the element. The lines matched the Balmer series for hydrogen with high levels of accuracy. The spectral lines for mercury in the NIST database matched the observed colors recorded during the experiment; however, the calculated wavelengths did not correlate very well.
The wave nature of light is indirectly verified by matching collected data to an equation describing wave behavior. These wave properties are then used to find the width of a CD track. The first experiment has a small percent error but the second had a large amount, possibly hinting that the process is difficult to implement in practice.
This lab was done with two other people. I am responsible for the results, footnotes, and the first half of the discussion.
The graphics on the following page are spectrograms, each representing a spectrum of frequencies over time. The spectrograms were created using recordings of trials 1,4 and 5. The frequency spectrum was decompressed from the recordings using the Fast Fourier Transform (FFT) algorithm along with the amplitudes, then plotted against time. The resonant frequencies from each recording can be seen in the dark red horizontal lines present in each graphic. The amplitude scale (supposed to be in dB) is inaccurate but is still scaled proportionally. If the dB measurements were accurate, we would all be in trouble, but high school physics labs usually don’t involve things with pressure waves on the scale of 30,000 tons of TNT (unfortunately). In all three spectrograms, there is a lot of low-frequency noise.
To explore the photo-electric effect the value of Plank’s constant was found along with the work function (Φ) of a photo-cathode in an attempt to identify the metal. The value of Plank’s constant was accurately determined to within 5% of the currently accepted value; however, the work function of the photo-cathode was unrealistically low.
This lab report was done with two other people. I am responsible for the results and the second half of the discussion.
In addition to deriving the deceleration during the drop, the average deceleration after the drop was found. This deceleration was likely due to friction and air resistance. This measurement was after the drop, so the mass of the cart would be combined with the mass of the dropped object. The force of friction is μmg, and changes with the mass. If you compare the work done by friction to kinetic energy (mv2 /2), you find that the masses cancel. The same thing happens if you convert the force of friction into acceleration, the masses cancel. This means that no matter the object if the coefficient of friction is the same, the objects will decelerate at the same rate. This isn’t what the data states, as ignoring the 1kg trial, each deceleration rate seems to get larger as the mass increases.
This experiment was performed to better understand the interactions between springs, friction, and marshmallows while using this understanding to shoot marshmallows into cardboard boxes quickly and accurately. To reach this goal, everything that interacted with the marshmallow during its journey from launch to landing had to be understood, which is what was attempted in this lab, with varying levels of success. The marshmallow begins its journey with springs (seen top-center in Figure 1.1), which is where it gets its kinetic energy. The amount of kinetic energy the marshmallow received is about Hooke’s Law (Elasticity, n.d). Now airborne, the marshmallow’s trajectory could be understood and predicted using Newton's Laws of Motion (Description of Motion in One Dimension, n.d.). Unfortunately, this mortar exists in the real world, meaning everything is under friction’s rein. Friction occurring in the barrel of the mortar could be accounted for by looking at the actual and expected muzzle velocities of the marshmallow. Friction in the air, or drag, on the other hand, is more complicated. The drag equation, which takes into account the fluid density, cross-sectional area of the projectile, and the velocity of the object, allows the calculation of the opposing frictional force on any object passing through a fluid. (The Drag Equation, n.d.) This equation was applied with limited success in the lab, as it requires a drag constant, which is found through experimentation usually performed in a wind tunnel. The mortar was built so that the effect of adjusting the angle of the barrel, as well as the length of pullback, on the projectile length could be tested.
This report was done with two other people. I am responsible for the results, the additional 3d-printed part of the experiment, the end of the discussion, and the equations
An additional interpretation of the results observed in this experiment can be attributed to the Heisenberg uncertainty principle, which states that the known position and momentum of a particle cannot both be known. The more you know about one of these two measurements, the less you know about the other. Normally this relation has no noticeable effect on our everyday lives because the constant they are related to is tiny. However when light passes through the tiny slits in this experiment, it’s position is “known” to a high enough degree that its momentum must be variable, resulting in the spreading out of the photons as they pass through the slits. More research should be done on the subject, but it is likely that the predictions due to Heisenberg's uncertainty principle go hand in hand with Young’s equation.