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: ▼ × (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…

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

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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: 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…

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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…

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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 =…

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

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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: 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;…

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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)

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

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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: 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).

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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: 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…

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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: 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…

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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

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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→…