Answered: prove this force are conserved…

Science

Physics

prove this force are conserved F(x,y)=2a(x-y)i-a(2x-y)j Where a is constant

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter1: Matrices, Vectors, And Vector Calculus

Section: Chapter Questions

Problem 1.26P

See similar textbooks

Related questions

Q: Find the length of vector u = <1,2,-3> using the dot product

A: The objective of the question is to find the length (or magnitude) of a given vector using the dot…

Q: ▼ × (a x b) = (V · b)a – (V · a)b + [b· V]a – [a · ▼]b - -

A: LHS : use f = a and g = b

Q: Prove that the Force : F = (x^2 y z) i - ( x y z^2) k Is Non Conservative Force

A: A force is said to be conservative if its curl is zero else it'll be a non conservative force.

Q: A spring has natural length 26 cm. Compare the work (in J) W₁ done in stretching the spring from 26…

Q: If W,, W, and W, represent the work done in moving a particle from A to B along three different…

Q: B = (3.72 , 0, 0) and C = (−3.72, 0, 0) and connected to the ceiling at point A = (−4.50 , 4.03 ,…

Q: The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z)…

A: F=kr→r3

Q: 2. (c) It changes with changes in the temperature. (d) It increases if the concentration of one of…

A: Disclaimer: “Since you have asked multiple question, we will solve the first question for you. If…

Q: A force with an x-component acts on a mass with a strength that varies only with the position x of…

A: According to question F(x) = -Ax2x>0F(x) = Ax2x<0 here A = 1575 N/m2 now formula of work…

Q: Two persons were practicing social distancing to aeviate the spread of COVID-19. Social distancing…

A: Given, Mass of two persons,m1=60 kg,m2=68 kg Initial distance,r1=3 feet=0.914 m Final distance,r2=12…

Q: Show that the irrotational condition V x F = 0 for a central force F = F(r)f to be conservative can…

Q: Find the dot product of the vectors F = -6.62 a₁ +8.68 ag + 1.90 ap and G = 1.50 a₁ + 7.08 ag + 8.27…

Q: Prove that the scalar product of a relative covariant vector of weight w and a relative…

A: Let Ai and Bi be respectively relative covarient tensor of weight w and relative contravarient…

Q: A particle moving in two dimensions is subject to the conservative force F = Fgi+Fyj. Fen that Fr =…

Q: The scalar product of vectors A and B is zero, therefore * O vectors A and B are equal vectors A and…

Q: 3) An obsect, acted on by various forces, moes along the parabolce y= 3x2 from the origin to the…

A: Work done is, W=∫CF→·dr→ Parametrizing the path, r=xi^+yj^=ki^+3k2j^…

Q: Find the angle between the vectors u = <1,2> and v =<4,-1> in degrees

Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 9i – 7j,V = 12i –…

A: Solution:-Given thatU→=9i^-7j^V→=12i^-2j^

Q: Consider the vector field F= Find the work done by F in moving a particle from (1,e,0) to (e,1,1),…

A: To determine: The work done by F in moving a particle from 1,e,0 to e,1,1 The field is…

Q: Find the work done by moving a particle in the vector field f along the curve c going counter…

A: The path is given in the figure below. It starts from A and ends at B.

Q: A NACA airfoil has a mean camber line given by z/c 0.600 [ 0.5 (x/c) - (x/c)² ] for 0< x /c< 0.25;…

Q: Two persons were practicing social distancing to alleviate the spread of COVID-19. Social distancing…

A: Given, m1=60kgm2=68 kgr1=3 feet = 0.9144mr2=12 inches =0.3048m

Q: Figure E1.24 В (15.0 m) Ď (10.0 m) 30.0° 53.0° 25.0° Č (12.0 m) A (8.00 m)

Q: A central force is defined to be a force that points radially,and whose magnitude and depends on…

Q: Problem 5: Two vectors in Cartesian coordinates have components A = (3, 1) and B = (2, y). a) If…

Q: emonstrate whether or not this force is conservative.

A: For a force to be conservative its curl must be zero. ∇×F→=0 i^j^k^∂∂x∂∂y∂∂zFxFyFz=0

Q: O False

A: work done by conservative force is zero in only close path

Q: Evaluate the work done by the force, F = 3xi+4yj, moving along the path y = x^2 from (0,0) to (3,9).

Q: Given the vectors →u=−9i−12j and →v=4i+9j, find the following: →u⋅→v=

Q: A spring has a natural length 10 in and requires a force of 5 lb to stretch the spring in. Find the…

A: GivenNatural length of spring, L=10 inForce , F=5 lbStretch length of spring, xo=2 in

Q: Q1/ The work done on an object is equal to the integral of the force on that object dotted with its…

A: Given: The force on the object is. Fx=3x2+x…

Q: The 3D vector field F = -r/(r|^3) represents the force of gravity exerted by a mass located at the…

Q: (c) Use both methods to calculate ā · b for each of the following cases: (i) if ā = (-4, –9) and b=…

A: Given data: (i) The coordinate of the vector is, a→=-4, -9b→=-1, 2 (ii) The magnitude of vectors and…

Q: o persons were practicing social distancing to alleviate the spread of COVID-19. Social distancing…

A: Given Mass m1 = 60 kg Mass m2 = 68 kg Initial distance r1 = 3 ft = 90 cm = 0.9 m Final distance r2 =…

Q: 2.1 Show that the force vectors F1=3(-i)+2j+k, F2=i+3(-j)+5k and F3= 2i+j+4k form a right triangle…

A: The force vectors F1 = 3(-i)+2(j)+k , F2 = I+3(-j)+5k, F3= 2i+j+4k forms a right triangle.

Q: Recall that the work WW done by a constant force F⃗ F→ at an angle θθ to the displacement Δr⃗ Δr→ is…

Q: Ex. 68 : Find the energy per unit of copper wire of uniform cross-section and the length 1.5 m, when…

A: To find-Energy stored per unit volume=?Given-L=1.5 ml=1.51-1.5=0.01 mStress=3×102…

Q: Using Gram-Schmidt algorithm, check for linear independence of the following vectors: v= (1, -2, 1,…

A: The solution is given below

Q: yA 60° А 3D 10.0 30° 30° 53° D = 20.0 37° 10 С %3D 12.0 F = 20.0 В 3 5.0

Q: A particle, of mass m, is moving in one dimension under the influence of a conservative force with…

A: Given data, Potential V(x) = x2 - x4

Q: Given the two vectors shown in the figure, calculate a) 2.00(B-C) b) -5.00 (B × C) There are no…

Q: Compute the work performed in moving a particle al ong the path r(t)=(r",te",2-t) for OSt54 by the…

A: Solution: The work by the force is given by, W=∫F→.dr→…

Question

prove this force are conserved F(x,y)=2a(x-y)i-a(2x-y)j Where a is constant

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Given the following information, find the unit vector of Force AForce A = 200 NΘ = 30o (on x-y plane)Φ = 50o (on x-z plane)
is the vector foeld conservative? prove it.
- Xercise V JA comstant force of monitude 4N has the same directton as the vector a =t+j+Te,!f the distance is measmed in meties, find the workkdone the y-onis from (Q2 0)'to (o, -1, 0). free PQ, vedn pi, w² Pp.pe u the line joinin the if the porint of applicetum moves aloy n o
Th unit vector from the origin {i.e. the point (0,0)} to the point B (3,4) is:
can you please ans g, h?
A central force is defined to be a force that points radially,and whose magnitude and depends on only r. That is F(r)=F(r)^r.show that a central force is a conservative force,by explicity showing that∆XF=0
Prove that the Force : F = (x^2 y z) i - ( x y z^2) k Is Non Conservative Force
Determine the scalar components Rb of the force R = 1,320 N along the nonrectangular axes a and b.
O Gilen the Vectors ů = 2 -j+ K ad 7 = 3i -3j + K fird the product ūy. Also Peo Gnd campre it with fiad üx ehat is 4-V? firsd The between u.V ongle e Wnte te pelor coordinste equation for Velecity and f define the 'terms.
(a) Find the curl of the following vector: A =r cos e f-( (sin & cos @ (spherical) (b) Find the divergence of the following vector A = f 2r sin o- @r cos o +2 4r (cylindrical) If u know both subparts then u try otherwise skip for other
Using Gram-Schmidt algorithm, check for linear independence of the following vectors: v= (1, -2, 1, -1), v2= (1, 1, 3, -1), and v3= (-3, 7, 1, 3).
Prove that the scalar product of a relative covariant vector of weight w and a relative contravariant vector of weight w' is a relative scalar of weight w+ w'.