Determine whether each of the following vector fields Fis path independent (conservative) or not. If it is path independent, enter a potential function for it, that is, a function f(x, y) so that V f = F. If it is path dependent, enter NONE.

Determine whether each of the following vector fields Fis path independent (conservative) or not. If it is path independent, enter a potential function for it, that is, a function f(x, y) so that V f = F. If it is path dependent, enter NONE.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

Determine whether each of the following vector fields Fis path independent (conservative) or not. If it is path independent, enter a potential function for it, that is, a function f(x, y) so that Vƒ = F. If it is
path dependent, enter NONE.

(f) If F(x, y) = 5y sin(xy)i + 5x sin(xy)j, then
f(x, y) =

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