SOLIDS

Geometry: Area and Volume of Solids - Math for Morons Like Us

18.1 CRYSTAL STRUCTURE

Carbon Structure Check out GIF or VRML images of graphite, diamond, and fullerenes -- three carbon structures with totally different geometries and properties. Visit NYU's MathMol Library for images of other molecular structures.

Diamond   Fullerene Graphite 

3-D VRML Crystal Gallery  There are some interesting structures to be found in this library of 3-D crystals provided by the Institute Laue Langevin in Grenoble, France.

Graphite layering 'intercalated' with another element

 

X-Ray Crystallography- How can X rays be used to study crystals? Find out in this crash course on X-ray crystallography from Indiana University

18.2 DENSITY

Density of Water and Ice Why does an ice cube float in water? Learn about the densities of ice and water in this activity page from the New York University Academic Computing Facility

Osmium Osmium, a hard, bluish-white, metallic element, is the densest substance on Earth. This page from WebElements shows a 3-D model of osmium's crystal structure. Check out the close spacing of osmium atoms that gives the crystal its great density.

18.3 Elasticity

 

Virtually all materials have some give to them. When pulled on, they stretch. For many materials this give is not apparent  to the naked eye but it is there. Some materials, natural rubbers and synthetic elastomers have a great deal of give. We use them every day. Rubber bands, tires, shoes, an wide assortment of plastic products and many metal products as well.

When objects are stretched (or compressed) and then return to their initial dimensions when the forces that produced the change are removed removed, the objects are said to be elastic  in behavior within that range of loading.

When the objects no longer return to their initial state, suffering permanent deformation, they have exceeded their elastic limit.

Materials that we typically do not consider elastic are usually very soft and malleable approaching to the point of approaching a fluid-like consistency. Examples include clay, some plastics, and very soft metals such as gold or lead. These materials begin have very low elastic limits and tend to stretch significantly before actually reaching the limits of their tensile strength and failing.

Other materials not generally thought of as elastic are very hard, usually brittle , often with highly oriented crystalline structures; glass, titanium, cast iron. These materials are the opposite of the previous one. They tend to have very high tensile strengths and are normally quite rigid. But unlike the clay they require very large loads to deform in any way. The problem with these materials is that when they reach their elastic limit they have also reached the limit of their tensile strength and immediately fail, often catastrophically.

This is most apparent in aircraft and race car design. Carbon fiber composites have extremely high strength to mass ratios and can be made into very light , very strong, and very rigid structures. They are often five times stronger, or five times lighter that the metal components they have replaced.

The drawback to these products is that when they fail, they fail in a catastrophic manner. Shattering or breaking rather than bending or stretching.

In this chapter there are example and problems using springs and modeling their behaviour based on Hooke's Law. F=kx. All of the examples assume that the springs are operatiog wll within their elastic limits and that they are not being exposed to excessive cycles or conditions. As springs are used they loose their elasticity with number of cycles they are put through. The also lose their linearity (if they were liner intially)  with use.

USE ONE OF THESE TO ANSWER YOUR SPRING PROBLEMS

The Physics of Springs and Spring-Like Systems Project - ELASTIC and SPRING SIMULATIONS http://www.glenbrook.k12.il.us/gbssci/phys/projects/yep/springs.html

NTNU JAVA - GOOD! http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=7

Spring Oscillator Applet http://lectureonline.cl.msu.edu/~mmp/kap13/cd361a.htm

SPRING SIM -Hooke's Law

Game and Simulation Programming http://cs.millersville.edu/~webster/cs406gamesimulation/cs406gamesimulation.html

Hooke's Law simulation http://www.mhhe.com/physsci/physical/jones/ol14-1.htm

The educational encyclopedia, physics: mechanics java applets
http://users.pandora.be/educypedia/education/physicsjavalabomechanics.htm

SPRING SIM -Hooke's Law

 

18.4 Compression and Tension

Build a Bridge read about four proposed bridge sites and four types of bridges. Then see if you can match the bridges to the correct sites. This activity page is part of Nova's SuperBridge site

18.5 SCALING

Scaling - Why Giants Don't Exist http://galileoandeinstein.physics.virginia.edu/lectures/scaling.html

Animal Scales http://hsb.iitm.ernet.in/~jm/ARCHIVES/May-Jun02/articles/scaling.htm

Walking with Giants Sasquatch - http://www.the-sisterhood.net/walkingwithgiants/

"How Strong Are Gorillas?"http://www.berggorilla.de/english/faq/dvers/fragen/stark.html

Hands and feet of a mountain gorilla and a human male for size comparison

What can we learn from scaling, Christian Schoenberger http://www.nccr-nano.org/nccr/study/printmaterial/archive/nano1_ws02/Scaling-laws.pdf-

Scaling in  Animals  Scaling in animals

 

Density of Water and Ice Why does an ice cube float in water? Learn about the densities of ice and water in this activity page from the New York University Academic Computing Facility.

Osmium Osmium, a hard, bluish-white, metallic element, is the densest substance on Earth. This page from WebElements shows a 3-D model of osmium's crystal structure. Check out the close spacing of osmium atoms that gives the crystal its great density

 

 


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Copyright 2005 -  S. B. EglI