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

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: 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…

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

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

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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

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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: 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;…

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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)

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

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

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

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

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

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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…

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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→…