Question

Classical Mechanics problem: Show that F is conservative and find a scalar potential U such that...

Classical Mechanics problem:

Show that F is conservative and find a scalar potential U such that F = −∇U

F = y2z sinh(2xz)i + y cosh(2xz)j + y2x sinh(2xz)k

Homework Answers

Answer #1

Dear friend, if you have any doubts about this solution, make a comment please...

Thanks

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Classical Mechanics - Let us consider the following kinetic (T) and potential (U) energies of a...
Classical Mechanics - Let us consider the following kinetic (T) and potential (U) energies of a two-dimensional oscillator : ?(?,̇ ?̇)= ?/2 (?̇²+ ?̇²) ?(?,?)= ?/2 (?²+?² )+??? where x and y denote, respectively, the cartesian displacements of the oscillator; ?̇= ??/?? and ?̇= ??/?? the time derivatives of the displacements; m the mass of the oscillator; K the stiffness constant of the oscillator; A is the coupling constant. 1) Using the following coordinate transformations, ?= 1/√2 (?+?) ?= 1/√2...
For each of the following vector fields F , decide whether it is conservative or not...
For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, ∇f=F). If it is not conservative, type N. A. F(x,y)=(−4x+3y)i+(3x+16y)j f(x,y)= B. F(x,y)=−2yi−1xj f(x,y)= C. F(x,y,z)=−2xi−1yj+k f(x,y,z)= D. F(x,y)=(−2siny)i+(6y−2xcosy)j f(x,y)= E. F(x,y,z)=−2x2i+3y2j+8z2k
Find the Div of the vector field: F = 3e-xsin(y*x)i + 3e-xcos (y2z)j + 3excos (y2z2)k...
Find the Div of the vector field: F = 3e-xsin(y*x)i + 3e-xcos (y2z)j + 3excos (y2z2)k 3a) Graph the given vector field and the obtained scalar field 3b) Find the divergence point (2,5,4) and explain if it corresponds to a manager or a sink 3c) identify which are the main areas of sinks and springs (in the graph)
classical Mechanics problem: Find the ratio of the radius R to the height H of a...
classical Mechanics problem: Find the ratio of the radius R to the height H of a right-circular cylinder of fixed volume V that minimizes the surface area A.
Letu=2i−3j+k,v=i+4j−k,andw=j+k. (a) Find u × v and v × u, and show that each of those...
Letu=2i−3j+k,v=i+4j−k,andw=j+k. (a) Find u × v and v × u, and show that each of those vectors is orthogonal to both u and v. (b) Find the area of the parallelogram that has u and v as adjacent sides. (c) Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v, and w.
(1 point) For each of the following vector fields F , decide whether it is conservative...
(1 point) For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, ∇f=F). If it is not conservative, type N. A. F(x,y)=(10x+7y)i+(7x+10y)j f(x,y)= 10 B. F(x,y)=5yi+6xj f(x,y)= N C. F(x,y,z)=5xi+6yj+k f(x,y,z)= D. F(x,y)=(5siny)i+(14y+5xcosy)j f(x,y)= E. F(x,y,z)=5x2i+7y2j+5z2k
For F= ((1+2xy)ze^(2xy)+(1/x)+2x)i+(2x^2ze^(2xy)j+(xe^(2xy)+(1/z)k show that F is conservative and then find work on object moving from...
For F= ((1+2xy)ze^(2xy)+(1/x)+2x)i+(2x^2ze^(2xy)j+(xe^(2xy)+(1/z)k show that F is conservative and then find work on object moving from (1,0,1) to (2,0,5).
classical Mechanics problem: Suppose some particle of mass m is confined to move, without friction, in...
classical Mechanics problem: Suppose some particle of mass m is confined to move, without friction, in a vertical plane, with axes x horizontal and y vertically up. The plane is forced to rotate with angular velocity of magnitude Ω about the y axis. Find the equation of motion for x and y, solve them, and describe the possible motions. This is not meant to be a lagrangian problem.
For each of the following vector fields F , decide whether it is conservative or not...
For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, ∇f=F∇f=F ). If it is not conservative, type N. A. F(x,y)=(−10x+3y)i+(3x+10y)jF(x,y)=(−10x+3y)i+(3x+10y)j f(x,y)=f(x,y)= B. F(x,y)=−5yi−4xjF(x,y)=−5yi−4xj f(x,y)=f(x,y)= C. F(x,y,z)=−5xi−4yj+kF(x,y,z)=−5xi−4yj+k f(x,y,z)=f(x,y,z)= D. F(x,y)=(−5siny)i+(6y−5xcosy)jF(x,y)=(−5sin⁡y)i+(6y−5xcos⁡y)j f(x,y)=f(x,y)= E. F(x,y,z)=−5x2i+3y2j+5z2kF(x,y,z)=−5x2i+3y2j+5z2k f(x,y,z)=f(x,y,z)= Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"
1. a) Let F(x,y) = hcosy,−xsiny + 2yi. Show that F is conservative, and find a...
1. a) Let F(x,y) = hcosy,−xsiny + 2yi. Show that F is conservative, and find a function φ such that ∇φ(x,y) = F(x,y). b) Use the result from part a) to find R C F · Tds, where C is given by r(t) = ht,πti,0 ≤ t ≤ 1.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT
Active Questions
  • Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a...
    asked 7 minutes ago
  • Use the information from the following Income Statement to create and Projected Income Statement and solve...
    asked 20 minutes ago
  • An unequal tangent vertical curve has the following elements: g1=-3.25%, g2=75%, total length = 500.00’, length...
    asked 22 minutes ago
  • Please write clear definitions of the following legal terms. Commerce Clause Supremacy Clause Indictment Tort
    asked 27 minutes ago
  • Do you think Moralistic Therapeutic Deism is an accurate reflection of society today? What are relevant...
    asked 31 minutes ago
  • The mean operating cost of a 737 airplane is $2,071 per day. Suppose you take a...
    asked 40 minutes ago
  • Arguments can be made on both sides of this debate about the ethical implications of using...
    asked 46 minutes ago
  • In the Chapter, they mention the idea of strategizing around your cash flows. Why are cash...
    asked 51 minutes ago
  • Company A signed a fixed-price $6,500,000 contract to construct a building. At the end of Year...
    asked 52 minutes ago
  • An unequal tangent vertical curve has the following elements: g1=-3.25%, g2=1.75%, total length = 500.00’, length...
    asked 59 minutes ago
  • In a previous​ year, 61​% of females aged 15 and older lived alone. A sociologist tests...
    asked 1 hour ago
  • Topic: Construction - Subsurface Investigation (Note: Briefly discuss in your own words, 1 paragraph minimum.) Typically...
    asked 1 hour ago