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The document describes the design of a bungee jumping system using rubber bands, including calculating the spring constant of individual rubber bands and determining that a chain of 1.2 rubber bands would be required based on conservation of energy calculations. It also analyzes the period of oscillation and time for the system to settle in water after being dropped, finding values that align with experimental results.
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The document discusses the effective mass approximation in quantum mechanics. It begins by defining the effective mass as inversely proportional to the curvature of energy bands. Having a effective mass allows electrons in crystals to be treated similarly to classical particles, with the crystal forces and quantum properties accounted for in the mass. The effective mass can be a tensor and depends on the crystal direction. It then discusses measuring the effective mass using cyclotron resonance and how it varies by crystallographic direction. In general, the effective mass incorporates the quantum mechanical behavior of electrons in crystals to allow a classical particle treatment.
8m_ATOMS__NUCLEI.pdf chapter best notes preparation
Rutherford's alpha scattering experiment showed that the atom consists of a small, dense nucleus surrounded by empty space. Most alpha particles passed through the gold foil, but a small percentage were deflected at large angles, indicating the positive charge and mass of the atom are concentrated in a tiny nucleus. The nucleus is composed of protons and neutrons, with the number of protons defining the atomic number. Nuclear forces hold the nucleus together despite the repulsive electromagnetic forces between protons. Nuclear fusion and fission can release or absorb large amounts of energy due to the strong binding energy within atomic nuclei.
NANO266 - Lecture 7 - QM Modeling of Periodic Structures
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
Norman John Brodeur Nuclear Physics.pdf
Norman John Brodeur worked at MIT’s instrumentation lab which later became Draper Labs. My responsibility was instrumentation and guidance systems for the Apollo command module and the lunar module. Previous to that I worked for Avco-Everett Research Lab in Everett. There we focused on testing materials for the vehicle’s heat shield. I was doing heat studies of various materials and what we eventually developed would just burn off and the heat with it.
Chenming-Hu-ch2-slides.ppt
1) Electrons and holes in semiconductors undergo thermal motion due to collisions with crystal imperfections, with an average time between collisions of 0.1 ps.
2) When an electric field is applied, electrons and holes also drift with mobilities dependent on material properties like doping concentration. Higher mobilities are found in materials like GaAs, desirable for high-speed devices.
3) Electron and hole concentrations can diffuse from higher to lower concentration regions due to gradients in electrochemical potential. Diffusion and drift currents, along with generation and recombination, determine the net carrier transport and distribution in semiconductors.
Chenming-Hu-ch2-slides.ppt
1) Electrons and holes in semiconductors undergo thermal motion due to collisions with crystal imperfections, with an average time between collisions of 0.1 ps.
2) When an electric field is applied, electrons and holes also drift with mobilities dependent on material properties like doping concentration. Higher mobilities are found in materials like GaAs, desirable for high-speed devices.
3) Electron and hole concentrations can diffuse from higher to lower concentration regions due to gradients in electrochemical potential. Diffusion and drift currents, along with generation and recombination, determine the net carrier transport and distribution in semiconductors.
Presentation.docx.ppt
1) Electrons and holes in semiconductors undergo thermal motion due to collisions with crystal imperfections, with an average time between collisions of 0.1 ps.
2) When an electric field is applied, electrons and holes also undergo drift motion with a drift velocity proportional to mobility. Mobility depends on temperature and doping concentration due to carrier scattering from phonons and dopant ions.
3) Electron and hole concentrations can differ from equilibrium values due to generation or recombination of carriers. Recombination occurs over carrier lifetimes ranging from 1 ns to 1 ms in silicon as carriers are captured by recombination centers.
WISWEC - A NEW CONCEPT FOR A WAVE ENERGY CONVERTER
The proposed wave energy converter consists of a floating tube filled with water and power units inside. As waves pass, the water level inside the tube fluctuates up and down, causing buoys attached to the power units to move. This motion is converted to electrical energy via gear systems and generators. The design aims for low cost production and maintenance to produce electricity at around €0.05/kWh. Key aspects are its modular structure, ability to withstand storms by sinking below waves, and potential organization into zig-zag farms for efficient energy capture and transmission. Experimental testing is needed to validate the power generation capabilities and viability of the concept.
Torsion test
This document describes a torsion test experiment to determine the modulus of rigidity of a steel wire. The experiment involves suspending a disc from the wire so that it acts as a torsional pendulum. Weights are added to the disc and the times for 20 oscillations are measured both with and without weights. Using the measured times, length of the wire, diameters and weights, the modulus of rigidity of the material can be calculated based on the formula provided. Key parameters like the diameter and mass moment of inertia of the disc and weights are measured and recorded in tables. The experiment is repeated with different weights to obtain an average modulus of rigidity value.
Thermal Neutrons & X-Ray Diffraction.pdf
Thermal neutrons produced in a reactor have a kinetic energy of approximately 0.0379 eV due to collisions that reduce their energy to approximately room temperature. Their de Broglie wavelength is approximately 0.4895 angstroms, which is on the same order as atomic lattice spacings. Neutron diffraction can therefore be used to study solid state structures, similarly to X-ray and electron diffraction.
Engineering science lesson 5
Here are the steps to solve this example:
1) Find the moment of inertia, I, of the composite section about the neutral axis:
I = I1 + I2 + A1*d1^2 + A2*d2^2
Where:
I1 = moment of inertia of rectangular section 1 = b1*h1^3/12 = 4*6^3/12 = 144 in^4
I2 = moment of inertia of rectangular section 2 = b2*h2^3/12 = 2*4^3/12 = 32 in^4
A1 = area of section 1 = b1*h1 = 4*6 = 24 in^2
A
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Weak Isotropic three-wave turbulence, Fondation des Treilles, July 16 2010
Weak Isotropic three-wave turbulence, Fondation des Treilles, July 16 2010
8m_ATOMS__NUCLEI.pdf chapter best notes preparation
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NANO266 - Lecture 7 - QM Modeling of Periodic Structures
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- 1. Group members Ademola Alimayu Reisha Flemming Ronnie Christian Floyd Bartlett
- 2. Introduction Bungee jumping involves jumping from a tall structure while connected to a large elastic cord The tall structure is usually a fixed object, such as a building, bridge or crane in some cases it can also be a mobile medium such as a hot air balloon or helicopter that has the ability to hover.
- 3. Design Specification Material used: 4’ length of 1.5mm electrical wire rubber bands a hook a 2” x 2” x 2” wooden block a plastic plate of 1” of water 5’ wooden stand
- 4. Spring constant This was obtained by measuring the original length of the rubber band and then adding the 2*2*2 cubic block and measuring its extension. (Xe- Xo)=X F=ma Hence the spring constant K = (ma)/x Using m= 0.060kg, a = g = 9.8, Xe- Xo=0.005m K=(.06x9.8)/.005 =117.6N/m
- 5. What is the stiffness of a chain of N rubber bands? W K1 KN Nd N The stiffness of a chain of Nd rubber bands is inversely proportional to the number of bands W
- 6. Where are we? We have the stiffness of an average rubber band K1 W K1 KN We have the length of Nd N an average rubber band L1 We have a way to predict the slack length and stiffness of a chain of N rubber bands LN NL1
- 7. Conservation of Energy gives drop distance as a function of the # N of RBs 1 K AV wh K N (h LN )2 where K N and LN NLAV 2 N 2 w w w h LN 2 LN KN KN KN 2 w w w N L1 2 L1 K1 K1 K1
- 8. Essentially: ½ kx2 = ½ mv2 + mgh, where m=mass of block, v= velocity of block during motion, h=height above datum level for the system Substituting values determined for k and x, we get: ½ (k/2n)(h-nL)2 = ½ mv2 + mgh So, ½ (117/2n)(0.0229-.072n)2 = ½ 0.06x(4.89)2 + (0.06x9.8x0.279) Solving gives n = 1.2 bands Note velocity, v determined from conservation of energy mgH= ½ mv2 + mgh
- 9. At equilibrum point, v = u + at However initial velocity =0, so using v=5.04s (from conservation of energy for first system) T = 5.04/9.8 = 0.5s For oscillation, T (period) = 2(pi)√m/k =0.15s So time to reach water = 0.5 + (.15/2) = 0.6s From experiment, time to settle (come to rest) = 4.7s Also Lifetime of system, bands fail after 3-4 attenpts.
- 10. Sources of Errors - Length not true due to looping and hooks - Also system is not fixed so energy dissipated (eg dampening effect of water.