Carteret County Shore Protection Office Logo
Mark Jensen
Tanks Lined Up on the Port of Morehead City
From the Jerry Schumacher Photograph Collection.
Jan Matejko has done a fine job of capturing the essence of the change in science kicked off by Copernicus.
Matejko, Jan. 1872. Astronomer Copernicus, Conversation with God. Oil on canvas. Jan Matejko-Astronomer Copernicus-Conversation with God.jpg. Jagiellonian University Museum, Krakow. http://bit.ly/2gtUjZ8.
Emax, Eugene Zelenko, Palladinus, and Gnesener1900. 2004. Astronomer Copernicus, Conversation with God. Image/jpeg. Jan Matejko-Astronomer Copernicus-Conversation with God.jpg. Wikimedia Commons, the Free Media Repository. http://bit.ly/2gtUjZ8.
Sine and Cosine Animation
Animated diagram illustrating the definitions of the cosine and sine functions as the x-coordinate and y-coordinate of a point on the unit circle making an angle θ with the x axis.
Courtesy of Chetvorno. 2014. Sine and Cosine Animation. Image/gif. Wikimedia Commons, the Free Media Repository. http://bit.ly/2ubpr74.
Traveling Waves
What are the wave parameters for the above animation:
• Amplitude, A
• Frequency, f
• Period, T
• Phase Constant, φ0
• Velocity, angular, ω
• Velocity, phase, v
• Wavelength, λ
• Wave number, k
Describe the motion of the particle (red) located at x = 30 m.
Courtesy of Cooper, Ian. 2017. “Travelling Waves.” Education. Visual Physics Online. September 18, 2017. http://bit.ly/2u7E3UD.
Superposition
This basic animation is an illustration of how 2 travelling waves, i.e., the blue and black waves, moving in opposite directions, create the superposition or resultant waves shown in red as they pass each other. While the underlying travelling waves may be generated in a number of ways, we shall assume a process that best helps visualise the process we are trying to describe. To do this, we shall assume that the [B] node in diagram above is firmly fixed to a brick wall, while the [A] node is free to vibrate at a given rate to induce one of the observed standing waves. Vibrating the [A] node causes a travelling wave to move from [A] to [B], but when it reaches [B], the incoming travelling wave is inverted and reflected back towards [A]. Now assume that, at the point of reflection at [B], a second wave is generated at [A] such that we now have 2 travelling waves moving towards each other. For simplicity, just visualise the travelling waves as sine waves with the usual positive (+) and a negative (-) cycles, so that as the 2 travelling wave ‘pass` each other, the various combinations of the (+/-) wave amplitudes are added together to created the standing wave superposition.
Courtesy of MySearch Website. 2016. “Superposition of Waves.” Education. MySearch Website. November 11, 2016. http://bit.ly/2lU42LD.
Electric Field and Potential of a Parallel Plate Capacitor
The Electric Field and Potential of a Parallel Plate Capacitor.
Courtesy of Nave, C.R. 2009. Electric Field and Potential of a Parallel Plate Capacitor. Image/gif. HyperPhysics Concepts. http://bit.ly/2u8mm7p.
Water or Electric Circuit
Courtesy of Cenis. (N/D). Water or Electric Circuit. Image/gif. GIFER. http://bit.ly/2lYet11.
Regular Polygon Characteristics with Hexagon Example
A regular polynomial has n sides, a circumradius r, and side length s. You can decompose a regular polynomial into n isosceles triangles, each with leg length r, side s, and a vertex angle of θ=360°/n. The side length is s=2rsin(θ/2). The perimeter, p, of the polynomial is simply p=ns. The area of our triangle is T=1/2 r² sin(θ). Again, the area of the hexagon is A=nT. Our example is a hexagon with n=6, r=6, θ=60°, s=6, p=36, and A=95.53. We already knew that s=6 because, in the case of a hexagon, the triangles are equilateral.
Momentum Magnitude as a Function of Time
Log of the magnitude of the momentum of a 1 kg particle with a velocity of exp(t) I + 2 exp(t) over t=0 to 10 s.
Water Tower Measurement
You are given an assignment by a lawyer to measure the height of a water tower. However, due to the contentiousness between the parties with the dispute, you don't have access to the water tower directly. Therefore, you set your theodolite up and measure the angle to the top of the tower.
You are stuck with an ancient piece of technology because all the newer ones have been checked out.
This angle is 50°.
You then move the theodolite 100 m further away from the water tower and make another measurement.
This angle is 35°.
How tall is the water tower?
One Ton One km
Drop a one-ton weight into a 1 km pit. The weight starts at rest. One-ton cartoon curtesy of Carnildo. 2011. One-Ton Weight. Image/svg. Wikimedia Commons, the Free Media Repository. https://commons.wikimedia.org/wiki/File:One-ton_weight.svg.
Quadratic Function
The quadratic function has the form of x^2+2x-3. It is factorable to (x-1)(x+3), yielding roots of x1=1 and x2=-3.
Cubic Function
The cubic function has the form of x^3-x-2. It is irreducible. By inspection, there is a root around 1.8.
