Physics II Graphs: Velocity and Time Oscillator

Because Canvas is so bad at copying graphs, here is another quiz graph:

This is a graph for a mass on the end of a spring.

Physics II Graphs: Acceleration and Time Oscillator

Because Canvas is so bad at copying graphs, here is another quiz graph:

This is a graph for a mass on the end of a spring.

Physics II Graphs: Position and Time Oscillator

Because Canvas is so bad at copying graphs, here is another quiz graph:

This is a graph for a mass on the end of a spring.

Because Canvas is so bad at copying images/graphs/etc over, here is another image used in one of my quizzes:

This is an image showing the refractive index as a function of wavelength for several materials, considering visible wavelengths of light.


This image is taken from Douglas Giancoli's Physics for Scientists and Engineers, 4th Ed., Pearson Publishing (2014). I have modified it somewhat by removing some curves from it, and I am using it for educational purposes only.

Uncertainty in the Expected Value: A Ballistic Pendulum

In considering error analysis for an experiment, we often treat the "experimental" values--the measurements which we make--as having some uncertainty (e.g. a standard deviation) and the theoretical value as being certain. This is not, however, always the case. For example, the "nominal" value of a thing--resistor, mass, pull strength, etc--often has associated with it some error. The resistance in a resistor is specified by its colored bands, with an uncertainty value* explicitly specified by the fourth colored stripe. Thus, the "nominal" value is not without some uncertainty.

Furthermore, the "theoretical" value--calculated from some curve--may often have some uncertainty of its own. After all, the theoretical curve from which the theory value may be obtained is itself computed using a set of measured values. As an example, consider the maximum change in height for a ballistic pendulum as a function of the projectile's mass. If the pendulum is shot at using a spring loaded gun to launch the projectile, then this maximum height should be calculatable using the following parameters: effective mass of the pendulum, mass of the projectile, spring constant of the spring, initial and final compression of the spring, mass of the driver used to propel the ball, frictional forces within the system.

The maximum displacement height for a ballistic pendulum as a function of the mass of the projectile. This particular pendulum had an effective mass of 75 grams, a driver assembly mass of 42 grams, and a spring of spring constant 2730 N/m and a measured compression of about 2.3 cm (solid curve).This is plotted with data (averaged 10 shots, with error bars being standard deviations of the means) as well as two enveloping lines (dashed lines) representing 0.5 mm more (gray) or 0.5 mm less (black) for the spring compression.

Now consider a spring-loaded projectile gun with a very stiff spring and a very short compression distance. Any difference in the measured compression distance will easily result in a noticeable shifting of the theoretical curve computed using this distance (see the image above). An error of only 0.5 mm in measuring the spring's compression--and this is a decent guess as the the uncertainty of the measurement, which was made using a ruler--could result in the maximum displacement height's being "off" by 1 cm. Thus, the uncertainty in the "theoretical" curve may be great enough that the entire curve could overestimate or underestimate most values of the displacement. Instead, the curve is a sort of "theoretical envelope" within which the experimental values should fall.

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*Technically, this is the tolerance, and the uncertainty is much lower if the resistance is actually measured via an Ohmmeter.

Physics II Labs: Galvanometer and Voltmeter Diagram 1

Because Canvas is so bad at copying images/graphs/etc over, here is another image used in one of my quizzes:

This is a circuit diagram which shows a galvanometer which will be used to construct a simple voltmeter.

Sound in a Vacuum Chamber Pt. 2: Experiment

In the previous part to this, I briefly discussed the predicted relationship between ambient air pressure and sound intensity. I have in fact actually measured this relationship, and at a few different frequencies for sound.

Before I discuss the results, I should describe my setup. I have a small glass vacuum chamber, into which I place a handheld sound meter and a small bluetooth speaker. There is a simple analog pressure gauge on the vacuum chamber, and the bluetooth speaker is paired with my tablet. On my tablet, I run the app FREQUENCY SOUND GENERATOR ver. 2.30, which allows me to control frequency and volume output for the speaker.

The basic procedure is to turn on the vacuum pump, evacuate the chamber to the desired pressure level (air may be allowed back into the chamber as necessary). I then allow the chamber to stabilize its pressure, and I record the backround pressure as well as the sound level with the frequency generator turned "off." I turn on the speaker and play the sound at the pre-selected frequency and volume, and then record the detected sound intensity level from the sound meter. This value fluctuates a bit, so I estimate a rough average, which shows one area with room for improvement, I suppose.

Anyway, I have the data plotted below, for a set of three frequencies. The differences between the frequencies may give an approximation for the error involved--I don't expect frequency to make much difference, but I would need to repeat the experiment to confirm this.

Note that the fit is actually parabolic (quadratic, I ~ P^2), rather than linear (I~P) as predicted. I think that this may be a result of the detector's having some response to background pressure which is itself linear. The detector is, after all, basically just a condensor microphone, which detects intensity via variations of pressure which manifest in changes of the capacitor plate separation, hence capacitance, hence stored charge.