The shape of a hanging chain between the points ((-a, b)) and ( (a, b)) is such

Question:

The shape of a hanging chain between the points $(-a, b)$ and \(

(a, b)\) is such that the gravitational potential energy

\[V[y]=ho g \int_{-a}^{a} y \sqrt{1+y^{\prime 2}} d x\]

is minimized subject to the length of the chain remaining constant,

\[L[y]=\int_{-a}^{a} \sqrt{1+y^{\prime 2}} d x\]

Find the shape, $y(x)$ of the hanging chain.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

A Course In Mathematical Methods For Physicists

ISBN: 9781138442085

1st Edition

Authors: Russell L Herman

See More Books

Question Posted: May 27, 2024 03:03 AM

See More Questions

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
Research Report Students name Professors name Institution Date Contents Title .. 3 Abstract 3 Acknowledgement .3 Introduction .4 Main body of Report/Methodology 5 Various kinds of isolation.6...
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
A stiff, straight, horizontal wire of length 25 cm and mass 20 g is supported by electrical contacts at its ends, but is otherwise free to move vertically upward. The wire is in a uniform, horizontal...
A method to measure soluble organic carbon in seawater includes oxidation of the organic materials to CO2 with K2S2O8, followed by gravimetric determination of the CO2 trapped by a column of...
Redline Publishers, Inc. produces various manuals ranging from computer software instructional booklets to manuals explaining the installation and use of large pieces of industrial equipment. At the...
If the assets are $2,000,000 and liabilities are $1,600,000, what is the owners equity? LO.1
The Holzmans signed an exclusive listing agreement with the Blum real estate brokerage firm. The contract provided that the Holzmans had an obligation to pay a commission if they enter into a written...
Crane uses the conventional retail method to determine its ending inventory at cost. Assume the beginning inventory at cost (retail) were $401000 ($605000), purchases during the current year at cost...
In Example 10. 34, the geodesic equations for geodesics in the plane in polar coordinates were found as \[\begin{align*} r\left(\frac{d \phi}{d s} ight)^{2}-\frac{d^{2} r}{d s^{2}} & =0 \\ \frac{d}{d...
Given the cylinder defined by $x^{2}+y^{2}=4$, find the path of shortest length connecting the given points. a. $(2,0,0)$ and $(0,2,5)$. b. $(2,0,0)$ and $(2,0,5)$.
When is a pie chart better than a bar chart for illustrating data?
Coronado Corporation accumulates the following data relative to jobs started and finished during the month of June 2025. Costs and Production Data Actual Standard Raw materials unit cost $2.20 $2.10...
Consider the following labor statistics for the adult population (age 16 and older) in Norway displayed in the table below (all numbers in millions). Employed 110 13 Not in Labor Force 75 Unemployed...
Blossom Variety Store uses the LIFO retail inventory method. Information relating to the computation of the inventory at December 31, 2026, follows: Cost Retail Inventory, January 1, 2026 $147,000...
Use polynomial division to show that the general expression for the factors of the difference of two cubes, x 3 - y 3 = ( x - y ) ( x 2 + xy + y 2 ) , is correct
A beam has a lenght of L = 9 m long and carrying the uniformly distributed load of w = 3 kN/m. w kN/m A RA a) Calculate the reaction at A. RA= KN L RB b) Calculate the maximum bending moment. Mmax=...
Enter each transaction into the accounting equation and identify its increase or decrease to assets, liabilities, shareholders equity, revenues, or expenses of Green Trees & Lawn Corp. 1. Green Trees...
What kind of financial pressures can an LBO cause?
C: The sor at the poopecin 0ieund to twe oxind places)
What information may an Appeals Officer not consider when reviewing a taxpayer's case? Select one: a. The cost involved for the IRS to hire an expert witness for litigation. b. Litigation hazards...
Carla Vista Cart Inc. has the following information for 2026 : The rate of return on assets Carla Vista Cart Inc. is 81.06%17.27%30.58%14.00%

The shape of a hanging chain between the points ((-a, b)) and ( (a, b)) is such

Question:

Step by Step Answer:

A Course In Mathematical Methods For Physicists

Students also viewed these Sciences questions