I have spent a great deal of time trying to work this problem. I would like to see the full solution to this problem. I am not asking for you to do my homework but when I am stuck on a problem I do expect help with a full solution. I realize this is a tangent problem but when I work it I do not get the right answer. Please show me the solution. Thank you.

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Deanna HettingerLv2

22 Mar 2019

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Given the radius vector and the velocity vector of an orbiting bodyidentify the trajectory as either circular, elliptical, hyperbolicor parabolic.

r = J + 2K
v = .9I + .123K

Alright, so I guess my question is if I'm doing thiscorrectly?

I am trying to find the eccentricity of the orbital path which willtell me what type of trajectory it is on.
So I start by finding the angular momentum which is h. h = r crossv which gives me .123I + .18J - .9K

Then I use the equation for eccentricity, mag(e) = (v cross h)/mu -r/magnitude(r).
I need to find mu which is a gravitational constant and since itsgeneric units of DU (distance units) and TU (time units) the muconstant has units of DU^3/TU^2. To get these units I usemag(r)*mag(v)^2.
I do not know if this is the correct way of getting mu, thegravitational constant usually equals G*M (gravitational constant *mass of central body) but all I am given is the r and vvectors.

Anyway continuing on with the problem I get the magnitude of e =.02655 which is between 0 and 1 so the orbit is an ellipse.

Again, I just am wondering if I am doing this right.

Thanks.

I had previously worked this problem but after trying toformulate the Lagrange for r and phi, my work became a jumbled messthat took several lines of paper to write down. I thought this wasa problem so I checked Cramster to make sure I was following thecorrect path and found that the Cramster formula for Kinetic Energywas much different from mine. I found the correct answer forPotential Energy, but I do not understand how the Kinetic answerwas formed. The way I originally started the problem was by makinga drawing which was exactly like the one in the answer key andwriting out the conversions from Cartesian to sphericalcoordinates.

x = rsin(Î±)cos(Ï)

y = rsin(Î±)sin(Ï)

z = rcos(Î±)

The kinetic energy is then

T = (1/2)m[d/dt((rsin(Î±)cos(Ï))^2 + (rsin(Î±)sin(Ï))^2 +(rcos(Î±))^2)]

Applying the time derivative makes a mess of things and trigidentities are not simplifying things which has led me to theconclusion that something must be wrong in my initial setup. What Ido not understand is how the Cramster answer has a kinetic energyof

T = (1/2)m[rdot^2 + (rsinÎ±Ïdot)^2]

If an explanation of how this is achieved can be provided, Iwould be incredibly grateful.

Textbook: Physics 8e, Cutnell and Johnson
Chap 20 Problem 103

/solution/solution/714716

Question:
In a pacemaker, a pulse is delivered to the heart 81 times aminute.The capacitor that controls this pulsing ratedischarges through aresistance of 1.8*10^6 ohm. One pulse isdelivered everytime thefully charged capacitor loses 63.2% of itsoriginal charge. What isthe Capacitance of the Capacitor?

The equation that you suggest is q= q_o e^(-t/RC)

t =.7404
R=1.8*10^6

So to solve I take the (ln q/q_o) and I get 1.44

So the Capacitance should equal -t/(1.8*10^6)(1.44)

The corect answer in the back of the book is 4.1*10^-7 but whenIwork out the problem I keep getting 2.86*10^-7.

Could you please check the math on this problem and let me know ifIam making a mistake or if the answer given is incorrect?

Thank you so much for your time and help!

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