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14 Nov 2019

Can somene please show me the algebraic steps of how I get from z= 1/ ( √1-rs/r) -1z= gravitaional redshiftto make it look like r/rs= 1/ [1-(1/z+1)^2 ]I have no clue how to flip the rs/r into r/rsthanks so much

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Jarrod Robel
Jarrod RobelLv2
31 Aug 2019

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

A particle of mass m is constrained to move on the inside surfaceof a cone of half-angle a, under the influence of constantgravitational force. In the cylindrical coordinates (r, phi, z) theconstraint that the particle is moving on the surface of the coneis given by z=r cot a . [do not use lagrangian mothod)

a) Find the net force acting on the particle and derive theequation of motion for r and phi using Newton's 2nd law. Show thatthe angular momentum L is a constant of motion. (use a incylindrical coordinateshttp://mathworld.wolfram.com/CylindricalCoordinates.html
see eq 72)
b) Find the total energy in terms of r, r dot and L


My attempt:

a) I found all the forces acting on the particle and set them equalto the forces I get from using the acceleration in cylindricalcoordinates

so, F(in phi direction) = 0 = m (2(r dot)(phi dot) + r (phidoubledot))
F(r) = -N cos a = m( (r double dot - r* (phi dot)^2) [N = normalforce]
F(z) = -mg + N sin a = m (z double dot)

How should I proceed next ? I have to find the equations of motionfor r and phi.
And how should I show that L is a constant of motion?

b) I have no idea how to do this part!

Okay, I need to derive four different forms of variables for anRL Circuit. The four variables consist of: I, VR,VL, VT. Also, this is for a circuit which isclosed switch and current is still running through it.

So far, I have:

1.) I = I0(1-e-t/τ)

2.) VR = IR = I0(1-e-t/τ)R =ε(1-e-t/τ) R cancels out because I0 is equal to ε/R

3.) VL = ?

4.) VT = ?

Okay, this is what I have thus far. Could someone please lookover formulas one and two for accuracy and also help me deriveformulas three and four? Thanks. Will give a "lifesaver"rating.

calculate the angular momentum of the earth in its orbit around the sun?

 

 

m   5.97 10 kg 6 E R   6.38 10 m Orbital radius 11 r   1.50 10 m Period of rotation Prot = 24 h 86,400 s  Period of revolution Prev = 7 1 y 3.156 10 s   Identify: L I z z   Set Up: For a particle of mass m moving in a circular path at a distance r from the axis, 2 I mr  and v r   . For a uniform sphere of mass M and radius R and an axis through its center, 2 2 5 I MR  . The earth has mass 24 E m   5.97 10 kg , radius 6 E R   6.38 10 m and orbit radius 11 r   1.50 10 m . The earth completes one rotation on its axis in 24 h 86,400 s  and one orbit in 7 1 y 3.156 10 s   . Execute: (a) 2 24 11 2 40 2 7 2 rad (5.97 10 kg)(1.50 10 m) 2.67 10 kg m /s 3.156 10 s L I mr z z z                   . The radius of the earth is much less than its orbit radius, so it is very reasonable to model it as a particle for this calculation. (b)   2 2 2 24 6 2 33 2 5 5 2 rad (5.97 10 kg)(6.38 10 m) 7.07 10 kg m /s 86,400 s L I MR z z                  Evaluate: The angular momentum associated with each of these motions is very large. Note that the orbital angular momentum is over 7 orders of magnitude greater than its rotational angular momentum. In fact, most of the total angular momentum of the solar system comes from the sum of the orbital angular momenta of its planets.

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