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Lubabalo Mgandela

Lubabalo M.

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Questions asked

INSTANT ANSWER

Consider the four-vector ( left(f^{0}, vec{f}right) ) defined by ( f^{mu}=F^{mu v} j_{v} ). Deduce, in a clear explicit calculation, that ( vec{f} ) is the Lorentz force density form.

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INSTANT ANSWER

13) 2 and 2 are space-time inertial coordinate frames such that at time ( 1=t=0 ), the origins coincide. The electromagnetic field tensor ( f^{30} ) has the following components in ( Sigma ) :(a) Write the covariant equation that link ( F^{2} ) to its sources.(b) Calculate and display the components of the electromagnetic field tensor.(c) Consider the lour-vector ( left(f^{t}, fright) ) defined by ( f^{*}=h^{2 i} f ). Deduce, in a clear explicit calculation, that if the Lorentz force density form.

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ANSWERED

Penny Riley verified

Numerade educator

10. A system of particles moves in a uniform gravitational field ( g ) in the direction. Show that ( g ) can be eliminated from the equations of motion by a transformation of coordinates given by[z=x, quad hat{y}=y, quad z=z-t g t^{2}](This is an example which forms the basis for the "principle of equivalence" in general relativity. The principle states that the gravitational field at any point in space and time can be eliminated by a suitable coordinate transformation)

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ANSWERED

Supratim Pal verified

Numerade educator

4. Show that for a satellite of mass ( m ) moving with velocity ( v ) in a circular orbit of radius ( r ) about an attracting center of mass ( M ),[v=sqrt{frac{G M}{r}}=frac{v_{e}}{sqrt{2}}, quad l=m sqrt{G M r}]where ( v_{0} ) is the escape velocity, and ( l ) is the orbital angular momentum.

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ANSWERED

Penny Riley verified

Numerade educator

1. A gun is mounted on a hill of height ( h ) above a level plain. Assuming that the path of the projectile is a parabola, find the angle of elevation ( alpha ) for greatest horizontal range and given muzzle speed ( V ).[operatorname{cosec}^{2} alpha=2left(1+frac{g h}{V^{2}}right)]What physical effects are neglected in the above approximation?2. With the same assumptions as in Exercise 1, show that if a projectile is thrown over a double inclined plane from one end of the horizontal base to the other and if it just graves the surmit in its flight, its angle of projection is[tan ^{-1}(tan theta+tan phi)]whero ( theta, phi ) are the slopes of the faces and the motion is in a vertiesl plane through the line of greaiest slope.

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INSTANT ANSWER

1. A gun is mounted on a hill of height ( h ) above a level plain. Assuming that the path of the projectile is a parabola, find the angle of elevation ( alpha ) for greatest horizontal range and given muszle speed ( V ).[operatorname{cosec}^{2} alpha=2left(1+frac{g lambda}{V^{2}}right)]What physical effects are neglected in the above approximstion?

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ANSWERED

Bcrypt_Sha256$$2B$12$We1Wwocamog01O5I.V2Tkouxdh4Ofnmgpwkor7Leaonfpu0Ubfpua Bcrypt_Sha256$$2B$12$We1Wwocamog01O5I.V2Tkokttmmj7Lscvwvlptp4Rlhbswcdg9.Wy verified

Numerade educator

7. Prove that[(a times b) cdot(c times d)=(a cdot c)(b cdot d)-(a cdot d)(b cdot c)]

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ANSWERED

Penny Riley verified

Numerade educator

2. A particle is constrained to move with constant speed on the ellipse $a_{ij} x_{i} x_{j}=1 quad(i, j=1,2)$. Find the cartesian and polar components of its acceleration.

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ANSWERED

Penny Riley verified

Numerade educator

1. A particle is constrained to move with constant speed in the circle ( r=a ). Find the cartesian and polar coordinates of its velocity and acceleration.

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INSTANT ANSWER

(c) ( boldsymbol{nabla} times nabla_{phi}^{phi}=0 )(d) ( nabla times(nabla times a)=nabla(nabla cdot a)-nabla^{2} a )

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