In engineering, iso-elastic refers to a system of elastic and tensile parts (springs and pulleys) which are arranged in a configuration which isolates physical motion at one end in order to minimize or prevent similar motion from occurring at the other end. This type of device must be able to maintain angular direction and load-bearing over a large range of motion.
The most prominent use of an iso-elastic system is in the supporting armature of a Steadicam, used to isolate a film or video camera from the operator's movements. Steadicam arms all work in a fashion similar to a spring lamp since each arm has two sections (similar to and labelled like a human arm); both the upper and fore-arm sections consist of a parallelogram with a diagonal iso-elastic cable-pulley-spring system. The iso-elastic system is tensioned to counteract the weight of the camera and steadicam sled. This tensioning allows the camera and operator to move vertically and independently of each other. For example, as the operator runs, the bouncing of his body is absorbed by the springs, keeping the camera steady. The arm also has unsprung hinges at both ends of each arm allowing it to bend in the horizontal plane (just like your elbow, not like a spring lamp).
To understand how an iso-elastic system works, we must first understand how springs work. The tension (elastic force) in a spring is proportional to its extension according to Hooke's law. This means that if a weight is hung on a spring it will oscillate with simple harmonic motion about its balance point; when the weight is above the balance point the spring's tension is reduced so the weight falls due to gravity, and when the weight is below the balance point the spring's tension will pull it back upwards.
If a simple spring system were used in a steadicam, then as the operator moved vertically, the camera would be subject to simple harmonic motion, and bounce up and down. To counteract this tendency, an iso-elastic system is employed.
The springs used are large, stiff springs with a high modulus of elasticity, and they are highly tensioned. A compound pulley system is then used so that the large force exerted by the spring can be divided by a factor of five, for example, so the cable exiting the pulley system will have only moderate tension. Most importantly, however, when the cable is drawn in or out the extension of the spring changes by only a fifth of that distance, so that the tension force of the spring will not change much. The result is that the spring-pulley system can produce a fairly constant tension in the cable over a large range of movement.
The almost constant force exerted by an iso-elastic system is employed in the armature of a steadicam, to counteract the constant force of gravity on the camera's and mount's mass. The result is that the weight of the camera is almost exactly balanced by the tension force throughout the entire range of vertical movement, so even when the operator jumps vertically, the camera will retain its vertical position due to inertia, but remain balanced, just with the armature at a different angle.
As a result, the camera doesn't bounce up to the 'balanced' position after a move, for example when the operator steps up onto a curb from the road. This allows the camera to be more isolated and independent of the operator's moves. The operator can of course deliberately move the camera up or down, if desired. In reality however camera operators find it preferable for the arm to not be perfectly iso-elastic so that the camera will naturally rise to a comfortable operating height; the springs will be tensioned so this only happens very slowly and without bouncing so as to maintain the smoothness of the camera's motion."[1]
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Episode 16: Elasticity of Demand
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Elasticity and the Total Revenue Test- Micro 2.9
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Understanding Elasticity | Economics Help.org
Transcription
There are many types of elasticity; in particular I'll focus on the price elasticity of demand. Before I get into a specific discussion of elasticity, let me ask you question: if a business wants to generate more revenue, should it raise the price of its product, or lower the price of its product? I ask because I have a friend who runs a children's bookstore, and when she found out that I was economist, she asked me this question. Well actually, she asked if she should be giving an educator discount, but what this really meant was that she wanted to know if she should discount (or lower) her prices. So generally, what would you say? Should a business owner increase prices, or decrease prices in order to generate more revenue? The answer, as usual, is “it depends.” Think about it: when your local electric company wants to raise more revenue, it will enact a rate increase. Yet when an airline wants to quickly generate additional revenue, it will cut ticket prices. Which approach is correct? They both are. Here’s the issue: if I raise my prices, I know that quantity demanded, or the willingness to purchase on the part of my consumers, will drop. That's just the Law of Demand. But what the Law of Demand doesn't tell me is how much the quantity demanded will drop. When I raise my price, will my customers be very sensitive to the price increase, cutting back a lot on their purchases? This would be bad for me, because I would lose a lot of revenue. But if I raise my price, and my customers only by a little bit less, not reacting too much to the price increase, this is good; I'd see increased overall revenue. So the crucial issue here is to find out how sensitive my customers will be to a price change. Elasticity is a measure of sensitivity, or responsiveness, to price. In equation form, the elasticity of demand, or ed, is equal to the percentage change in quantity demanded over the percentage change in price. Because demand exhibits an inverse, or negative, relationship, elasticity of demand will be a negative number. I use percentage change to measure elasticity, rather than absolute change -- let me illustrate why. If I tell you that product price has gone up by one dollar, this would be the “absolute change.” Is this a big change, or a small change? It depends -- what's the product? More to the point, what was the original price? OK, look – say we’re talking about a pack of gum. Originally the price was one dollar; now it's two dollars. This represents an absolute change of one dollar, but is it a big change, or a small change? It's actually a pretty big change; price doubled, or increased by 100%. What if we're talking about textbook, rather than a pack of gum? Originally, the price was $100; now it's $101. This is still an absolute change of one dollar, but is it a big change, or a small change? In this case, it's a small change; prices increased by 1%. Bottom line is that we need to know not only the dollar amount of the price change, but also how this compares to where we started. Now technically, the formula for elasticity of demand is the percentage change in the quantity demanded over the percentage change in price, which can be found by taking the ratio of the difference between the new and the old quantities, over the average of the new the old quantities, all over the ratio of the difference between the new and the old price, over that the average of the new and the old prices... Frankly, I’ve found that if I use this version of the elasticity formula, students’ eyes glaze over. People get so hung up on the math that they lose sight of the intuition, and what elasticity means -- so I'll be sticking to the slightly easier form, and will frame my questions for you accordingly. How would you actually use this formula? Take a look at this article about the Clinton administration's proposed cigarette tax policy. If you look at the last paragraph, you'll find enough information to determine the elasticity of demand for youth smoking. Remember, elasticity of demand is the percentage change in quantity demanded, over the percentage change in price. The article states that for every 10% increase in price, there's a 7% decrease in youth smoking. This means that elasticity of demand, according to the formula, is -7% over +10%, or -.7. OK -- now what do I do? I know that elasticity of demand for youth smoking is -.7, but what does it mean? The critical component to look at when dealing with elasticity of demand is the magnitude -- how big is this number? The bigger the number, the more people respond to the price; the smaller the number, the less people respond to price. The fact that the number is negative only signifies that demand is a negative, or inverse, relationship between price and quantity demanded. Since I care about the size of the elasticity number, rather than the sign, let’s make things easier and just look at the absolute value, or the size only, of elasticity of demand. In this example, the absolute value of the elasticity of demand is .7. Again, what does this number really mean? What does it tell us? Ultimately, the key value, where elasticity is concerned, is 1. In the case of youth demand for cigarettes, the size of the elasticity figure is less than 1. Since elasticity of demand equals the percentage change in quantity demanded over the percentage change in price, this means that the absolute value of this ratio is less than 1; it follows then, in order for this ratio to be less than 1, it must be the case that the size of the price change is greater than the size of the quantity change. What this tells me is that it takes a relatively large price change to initiate a relatively small quantity demanded reaction -- in other words, if the elasticity of demand is less than 1, people don't react much to price changes. They’re insensitive to price changes, or their demand is inelastic. Question: Does this make sense -- that where cigarettes are concerned, people don't react much to price changes? Note that the article specifies data for youth smoking. Do you think that youth sensitivity to cigarette prices is any different from adult sensitivity? Which group would respond more to a price change, youth smokers or adult smokers? If you thought that youth smokers would respond more to a price change than adult smokers, you're right. Adults tend to have more disposable income, so a price increase affects them less. In addition, the nicotine addiction is likely to be stronger for someone who's been smoking longer. This means that the size of elasticity for adults will be even smaller than the magnitude elasticity of demand for youth smokers, indicating a smaller reaction to any price change. One last question for you regarding inelastic demand: if the absolute value of the elasticity of demand is less than one -- that is, people don't respond much to a price change -- would you raise your price, or lower your price to generate more revenue? Well, the demand for electricity is inelastic; when the price changes, people tend to purchase up the same amount of electricity. We don't like the rate increases, but other than trying to conserve a bit here or there, we continue to consume the electricity. This means that the electric company could raise prices quite a bit, and not see very much decrease in the quantity demanded. As a result, total revenue (price per unit, times the number of units sold) will increase overall. What if the absolute value of the elasticity had been greater than 1? That would mean that the absolute value of the percent change in quantity demanded over the percent change in price is greater than 1, which could only be true if the size of the quantity change is greater than the size of the price change. So having a value of the elasticity that's greater than one indicates a relatively large quantity demanded reaction to relatively small price change, or demand is elastic. Question: if it’s the case that demand is elastic, would you raise your price or lower your price in order to generate more revenue? Answer: well, demand for airline tickets is fairly elastic, meaning that customers react a lot to fairly small price changes, so by decreasing prices a little bit, the airlines will see a relatively large increase in quantity demanded, or ticket sales. Overall this would yield greater total revenue. Is it possible for elasticity of demand to be equal to 1? Technically it is; if so, the size of the quantity change is going to be equal to the size of the price change. The changes exactly offset one another. That is, a 10% increase in price results in a 10% decrease in quantity demanded, and there would be no change in total revenue. NEXT TIME: Characteristics that determine elasticity of demand TRANSCRIPT00(MICRO) EPISODE 16: ELASTICITY OF DEMAND
See also
References
- ^ Adustable, iso-elastic support apparatus US 5435515 A.
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