PHYS1002 Physics 1 FUNDAMENTALS
Module 3 OSCILLATIONS & WAVES
Text: Physics by Hecht
Chapter 10 ELASTICITY & OSCILLATIONS
Section: 10.1 (exclude elastic materials)
Examples: 10.1 10.2
Even though we are usually not aware of it, we construct mental models to make sense of the physical world around us. Often, the mental models we construct do not agree with scientifically acceptable models used to explain the behaviour of physical phenomena. To help you development and improve the own unique mental models that will be more scientifically based, you should consider being more active in the learning process. Essential requirements in enhancing your scientific mental models include: familiarisation, visualisation, memorisation, simplification, assimilation, linking, associating, discrimination, representation / communication - verbal, written, mathematical (symbols, equations, graphs), visual (annotated diagrams).
CHECKLIST
· Hooke’s law (linearly elastic, Hookean objects), elastic & plastic materials
F = k s (10.1)
· Applied force F (N), spring constant or elastic constant k (N.m-1), F vs s graph (Fig. 10.2), elastic limit
· Elastic potential energy DPEe (J), area under force-distance curve equals the change in PE of the system
DPEe= ½ k s2 (10.2)
NOTES
Robert Hooke 1676 – Hooke’s Law
F = k s
Fe = - k s
Applied force (force applied to object to stretch or compress spring) F (N)
Elastic restoring force (force extended on object by spring which tends to restore the object back to its equilibrium position) Fe (N) Fe = - F
Extension or compression s (m)
Spring constant or elastic constant k (N.m-1)
Hooke’s Law is usually valid for small extensions or compression ( s is small).
Elastic materials – when an object is stretched or compressed by an applied force the change in length (or dimensions) is proportional to the size of the force. When the force is removed, the object quickly returns to its original size. For small applied forces, materials such as rubber, steel, glass, rock, bone, tenon, flesh are elastic. Hookean objects (linearly elastic) – steel bars and wires, springs, diving boards, rubber bands.
Plastic materials such as chewing gum, lead, moist clay and putty do not return to their original dimensions when an applied force is removed.
Elastic potential energy PEe – when a spring or any elastic entity interacts with another object the spring-object system stores energy via an electromagnetic interaction.
Consider an applied force F, acting on a block-spring system so that no work is done to increase the kinetic energy of the block. As the spring is stretch from its equilibrium position (s = 0) the work done on the system increases the elastic potential energy of the system.
The Northridge earthquake 4:31 am Monday morning 17 January 1994.
Adopted from the article by Fred Carrington, The Physics Teachers, April 1994
http://www.scecdc.scec.org/northreq.html
It was 4:31 Monday morning 17th January 1994, and I awoke with a jolt! The whole world seemed to be shaking down on my head. I said to my wife, "We've got a real earthquake this time." She said, "Hold me, I'm scared." I thought about getting up, put that thought out of my mind, and like a good (and scared) husband, I held her. After checking on our family and friends who live nearby, I started assessing all of the damage from the quake. Even though we had broken crystal that fell from our open shelves, stereo speakers that came off the wall, and numerous other minor breakage, we were lucky. There was no structural damage to our home and not one plate from our cupboards was broken. How could we be so lucky? After all, we were almost on top of the earthquake, the epicenter being about two kilometres east of our home.
…
Getting back to the sporadic nature of the quake, why should Santa Monica, some 24 km south of the epicenter, have taken so much damage over a fairly large area? The reason given by the experts is liquefaction. It means that the soil under Santa Monica, since it is very near the ocean, resembles jelly. The water level is high and the soil is sandy, making the composite a gelatin-like substance that amplifies the earthquake waves to levels found near the epicenter. On the other hand, just a few miles inland there was little damage, why?
Physics to the rescue again! Any good mechanics course deals with harmonic oscillators. Given that the two areas just mentioned are at about the same distance from the orthocenter, we can assume that they get about the same energy. If we imagine the "jelly area" near the ocean to be a lightweight spring with a small k, then it must have a big amplitude X. Inland where the ground is more compact, we can imagine a stiffer spring with a large K and a small amplitude x, giving us
½ K x2 = ½ k X2
Since large ground movement is one of the archenemies in earthquakes, we see a rationale for the level of destruction experienced at a great distance from a quake's source. Another area of great mystery was Sherman Oaks. Sherman Oaks, some 20 km from the epicenter, had as much structural damage as Northridge, and it was not near an ocean. This community is only a few miles from where I teach, and I really puzzled over this one. It finally dawned on me: the "mighty" Los Angeles River runs right through Sherman Oaks, or, I might say it once did. Nowadays the Los Angeles River is a cement flood-control channel, but in days gone by when storms opened the skies over Los Angeles, this area was a giant flood plain. Tons of silt and sand would wash off the mountains and settle here. The silt and sand, mixed with the ground water of this underground river, caused the same ground conditions as in Santa Monica. From this it is easy to see why many geophysicists now feel that liquefaction was also the culprit in Sherman Oaks.
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