A good's price elasticity of demand is a measure of how sensitive the quantity demanded of it is to its price. When the price rises, quantity demanded falls for almost any good, but it falls more for some than for others. The price elasticity gives the percentage change in quantity demanded when there is a one percent increase in price, holding everything else constant. If the elasticity is -2, that means a one percent price rise leads to a two percent decline in quantity demanded. Other elasticities measure how the quantity demanded changes with other variables (e.g. the income elasticity of demand for consumer income changes).Price elasticities are negative except in special cases. If a good is said to have an elasticity of 2, it almost always means that the good has an elasticity of -2 according to the formal definition. The phrase "more elastic" means that a good's elasticity has greater magnitude, ignoring the sign. Only goods which do not conform to the law of demand, such as Veblen and Giffen goods, have a positive elasticity. Demand for a good is said to be inelastic when the elasticity is less than one in absolute value: that is, changes in price have a relatively small effect on the quantity demanded. Demand for a good is said to be elastic when the elasticity is greater than one. A good with an elasticity of -2 has elastic demand because quantity falls twice as much as the price increase; an elasticity of -0.5 indicates inelastic demand because the quantity response is half the price increase.Revenue is maximised when price is set so that the elasticity is exactly one. The good's elasticity can also be used to predict the incidence (or "burden") of a tax on that good. Various research methods are used to determine price elasticity, including test markets, analysis of historical sales data and conjoint analysis.
Price elasticity of demand further divided into:
Perfectly Elastic Demand (∞),
Perfectly Inelastic Demand ( 0 ),
Relatively Elastic Demand (> 1),
Relatively Inelastic Demand (< 1),
Unitary Elasticity Demand (= 1).
I'm trying to make a DIY 'ECG' machine, except that it'll only record heartbeats on a piece of paper. Basically the piece of paper will be wound round a cylinder like object, which will be being spun slowly by a motor. A pencil at the end of a stick or something will be writing to this piece of...
Hello, today we learned about elasticity, whose formula was the change of pressure over the volume change (∆p/∆v), which seemed very weird compared to the use of the adjective elastic daily, my question is can we say that a piece of wood is very elastic? because even applying a large pressure...
Hi,
Looking for the Elastic Constants for any rubber-like material such as Natural Rubber. It can be inorganic or organic. The constants I am looking for take the form of a fourth-rank tensor. I only need the first order elasticities, not the zeroth or higher (not Cij or Cijklmn.. just Cijkl)...
What I do not get is why should a stress much lower than yield point cause deformation in a material?
If temperature is high intermolecular attraction is reduced and thus even low stress can deform things.
But if it is low
Then a force lower than yield point should be less than intermolecular...
[Mentor Note -- Thread moved to the ME forum to get better views]
Let's consider an incompressible block of Neo-Hookean material. Let the initial reference geometry be described by ##B=[0,b] \times [0,b] \times [0,h]##. The professor gave me the following task:
Of course there can be many...
Hi everyone,
studying the bending of an incompressible elastic block of Neo-Hookean material, one finds out the first Piola-Kirchoff stress tensor as at page 182 (equation 5.93)
where $e_r = cos(\theta)e_1 + \sin(\theta)e_2$ and $e_{\theta} = -sin(\theta)e_1 + \cos(\theta)e_2$
How is the...
I am studying the finite bending of a rubber-like block, assuming Neo-Hookean response. In the following, ##l_0##,##h##, ##\bar{\theta}## are parameters, while the variables are ##r## and ##\theta##.
The Cauchy stress tensor is
##T= - \pi I + \mu(\frac{l_0^2}{4 \bar{\theta}^2 r^2} e_r \otimes...
I'm studying elasticity from classical Gurtin's book, and my professor gave us the following example, during lecture. Unfortunately, this is not present in our references, so I'm posting it here the beginning of the solution, and I will highlight at the end my questions. First I need to state...
In every book I checked, the energy (per unit mass) of elastic deformation is derived as follows:
## \int \sigma_1 d \epsilon_1 = \frac{\sigma_1 \epsilon_1}{2} ##
and then, authors (e.g. Timoshenko & Goodier) sum up such terms and substitute ##\epsilon ## from generalised Hooke's law i.e.
##...
If you take a rubber band and fix it in a stretched position for an extended period of time, would it eventually lose its elasticity? If yes, then how can you calculate how long it would take until its elasticity decreases by a certain amount, say, fifty percent? If no, why not? How does the...
Given, ##2A_P = A_Q## (cross-sections) ... (1)
and, ##Y_P = 2Y_Q## ... (2)
We have ##\frac {Y_P * x}{\Delta L} = \frac{Y_Q (L-x)}{\Delta L}##
Using (2) in the above expression we get ##x = L/3## whereas the correct answer is ##x = 2L/3##
I feel my initial idea is flawed, and that I am...
Homework Statement
The torsion balance shown in the figure consists of a 40 cm long bar with lead balls with a diameter of 2 cm on each end. The rod is hanging by a 100 cm long silver thread with a diameter of 0.5 mm. When two bigger lead balls (density = 11.4 g/cm3) with a diameter of 30 cm...
Consider a spring balance with no initial deflection. Let an object of mass 'm' be attached to it. We allow the spring to come into equlibrium, and 'd' is the deflection at this eqb position. We add another object of mass 'M', while m is also present, so that the final position is x, and hence...
I am 2nd year physics undergrad. Just want to study a bit about materials in my free time. I have no idea about engineering books. Please suggest some good books. Thanks.
In mechanical engineering we have various courses in strenght of materials, and I've noticed that graduate students learn the Theory of Elasticity. I've researched a little bit about it, and I know that the Theory of Elasticity is more general than strenght of materials. But I have some doubts...
Hi everyone,
I'm having some difficulty comprehending "normal" transmission of stress/strain through a solid body and "shock" transmission of stress/strain.
Imagine I have two bodies, one rigid - the other elastic.
If the rigid body is fixed in space, and the elastic body is flying at the...
I am new to elastic theory. I have a question about elasticity. We assume we have a body with no internal forces. Surface forces are applied on the border. Can we leave the elastic domain (reach the yield surface) in an interior point without leaving the elastic domain on the boundary?
If no...
Hi, I would like to do an experiment for my physics class about which balloon has the highest stretch ratio and found the following page on this forum:
https://www.physicsforums.com/threads/hookes-law-for-a-balloon.670566/
First of all, can you please explain this function? σ=σ(λ). I'm...
Hi PF,
As you may know, is the the elasticity/stiffness tensor for isotropic and homogeneous materials characterized by two independant material parameters (λ and μ) and is given by the bellow representation.
C_{ijkl} = \lambda\delta_{ij}\delta_{kl} + \mu(\delta_{ik}\delta_{jl} +...
Supose we have a ¨U-shaped" metal bar, stuck in the ground, and I aply a force on the top of the part on the right, trying to make it wider. If I were to avaliate the forces acting on a specific part of the bar that includes the point that I´m applying the force, let`s say the portion from that...
Homework Statement
Consider a spring of natural length L_0 with constant k which rests on a horizontal frictionless surface. The spring is attached at one end to a fixed post and at the other end to a mass m. Suppose the spring is rotating around the post in a circle with angular velocity w...
I am studying the following phenomenon for my project:
Thin horizontal elastic rod is fixed at both ends and small perpendicular force is applied at middle of the rod perpendicular to its length. I want to study this dynamics and extend it to cylindrical shell. Please suggest books/papers or...
I am a first year student and i am required to build one thing based on one physics law . if i build a rubber band powered airplane , what laws should i say it applies? and what about rubber band powered car??
Hi!
I know some constitutive models for elastic materials like Neo-Hooke or Mooney-Rivlin, which give a relation between elongation ##\lambda=y/y_o## (where ##y## and ##y_o## are the length of the elastic material in a uniaxial compression test in the direction of the compression at stress ##P##...
I have put together an equation whose purpose is:
With a desired 'magnitude of static friction' ( μ_s ), 'fundamental frequency' ( f ), and 'tension' ( T ),
initial conditions such as 'string breakover angle' ( Θ_0 ), 'nut-tuner distance' ( L_{h,0} ), and 'string diameter' ( d ),
and...
At one point I had been trying to construct an equation which would calculate the tension on a tuned string with a change in temperature (and therefore the fundamental frequency), but found my calculations were wrong. By extension, the purpose of the project was to be able to calculate what...
I am a part C Mechanical Engineering student and have been undertaking a project investigating the strain sensitivity of a particular glass filled composite.
From my quasi-static results, the stress-strain curves seem to be reasonable and match that of the mechanical material properties...
Homework Statement
A certain type of concrete has a tensile breaking stress of 3.1 MN/m^2, a compressive breaking stress of 37.7 MN/m^2 and a shear breaking stress of 9.4 MN/m^2. A circular pillar of this concrete has a radius of 0.6 m. What is the maximum load it can support assuming that it...
Hi all,
I'm a physicist, and I'm now trying to understand and model a problem with a multishafted cord, being pulled from one side in order to transfer force. The cord has its own elastic properties (elongation, bending etc.), it goes through several pulleys with friction, and most likely its...
Homework Statement
So I have to write a report based on an experiment that I have conducted. I know that my report is connected with Simple Harmonic motion and Elastic force, but I do not know how to describe it in a more efficient/scientific way. Essentially, I am dropping a weight (constant)...
Hi all,
I'm wondering if anyone knows of a way to obtain elasticity properties (Ex, Ey, Ez, Gxy, Gxz, Gyz, vxy, vxz, vyz) from the terms of a 6x6 anisotropic stiffness or compliance matrix. I'm looking for a closed form solution, preferably. I would think that there should be a closed form...
I am struggling with a question in my coursework, and would appreciate some guidance.
The question is:
The component shown in Fig 1 is made from a material with the following properties and is subjected to a compressive force of 5kN.
Material Properties :
Young’s Modulus of Elasticity – 200...